WO2010077380A2 - Global camera path optimization - Google Patents

Abstract

Global path optimization is employed to refine a camera path used to reconstruct a three-dimensional image. In hand-held dental scanning, spatial links can often be made between non-sequential frames of data, such as between separate camera path segments for buccal and lingual tooth surfaces, and these spatial links can be employed to minimize motion estimation parameters in a global optimization process.

Description

GLOBAL CAMERA PATH OPTIMIZATION

RELATED APPLICATIONS

[0001] This application claims priority to International Application No. PCT/US09/30068 filed on January 4, 2009, which claimed priority to U.S. Prov. App. No. 61/019,159 filed on January 4, 2008. Each of these applications is hereby incorporated by reference in its entirety.

FIELD OF INVENTION

[0002] This invention relates generally to three-dimensional imaging and more specifically to optimizing the calculation of a global camera path used in a three- dimensional reconstruction.

BACKGROUND

[0003] In one technique for three-dimensional image reconstruction, a number of images or image sets of an object are captured with a camera that travels in a path over the surface of the object. Information from this catalogue of information can then be used to reconstruct a three-dimensional model of the object based upon the camera path and individual three-dimensional measurements captured along the camera path. The path of a camera may be very long and complex involving motion estimation from image to image that accumulates significant errors along its length. These errors can result in a variety of reconstruction artifacts in a resulting three-dimensional model such as double surfaces where the camera path scans the same region twice with an error in camera position between the two scans.

[0004] While various techniques exist for minimizing errors along an entire camera path, there remains a need for improved global path optimization techniques suitable for use with data-intensive path optimizations typical of high-accuracy, three- dimensional dental reconstruction. SUMMARY

[0005] Global path optimization is employed to refine a camera path that is used to reconstruct a three-dimensional image of dental subject matter. In hand-held dental scanning, spatial links can often be made between non-sequential frames of data, such as between separate camera path segments for buccal and lingual tooth surfaces, and these spatial links can be employed to minimize motion estimation parameters in a global optimization process.

[0006] A method disclosed herein includes acquiring a data set from a surface of a dental object with a hand-held scanner from each one of a sequence of poses along a camera path, thereby providing a plurality of data sets; associating each one of the poses in the sequence of poses with a spatial link to a previous pose and a next pose, thereby providing a plurality of spatial links; identifying at least one non-sequential spatial link between two non-sequential ones of the poses; performing a global motion optimization to minimize an error among the plurality of spatial links and the at least one nonsequential spatial link, thereby providing optimized camera pose data; and reconstructing a three-dimensional model of the dental object using the optimized camera pose data and the plurality of data sets.

[0007] The hand-held scanner may be a structured light scanner. The handheld scanner may be a time -of- flight scanner. The hand-held scanner may be a video- based scanner.

[0008] The sequence of poses along the camera path may be determined using hardware-based positioning.

[0009] The global motion optimization may include creating consistency among motion parameters between the poses using an overdetermined system of motion equations.

[0010] The sequence of poses may include sequential pairs of key frames, wherein one or more additional data sets may be acquired from one or more additional poses between each sequential pair of key frames. Reconstrucing the three-dimensional model may include adding three-dimensional data based upon the one or more additional data sets and the one or more additional poses. The sequential pairs of key frames may be selected from a larger set of poses using a metric to evaluate a quality of a resulting three-dimensional reconstruction. The sequential pairs of key frames may be selected using a graph analysis.

[0011] The at least one non-sequential spatial link may associate two of the sequence of poses that may be separated by a substantially greater distance along the camera path than along the surface of the dental object.

[0012] The three-dimensional model of the dental object may include a full arch model.

[0013] The dental object may include an orthodontic component.

[0014] The three-dimensional model of the dental object may include one or more of gums and soft tissue.

[0015] Identifying at least one non-sequential spatial link may include identifying the at least one non-sequential spatial link based upon the data set for each of the two non-sequential ones of the poses. Identifying at least one non-sequential spatial link may include identifying the at least one non-sequential spatial link based upon an overlap in three-dimensional data reconstructed from the data set for each of the two nonsequential ones of the poses. Identifying at least one non-sequential spatial link may include displaying a region for one or more candidate links in a user interface and receiving a supplemental scan of the region.

[0016] The camera path may include a virtual camera path composed from two or more different physical camera paths.

[0017] The global motion optimization may optimize an alignment of reconstructed three-dimensional data from the data sets in a global coordinate system. The global motion optimization may improve consistency of the sequence of poses along the camera path in a global coordinate system. The global motion optimization may minimize errors in motion estimation parameters expressed as a function of one or more of rotation, translation, coupled rotation and translation, and decoupled rotation and translation.

[0018] A computer program product disclosed herein performs the steps of: acquiring a data set from a surface of a dental object with a hand-held scanner from each one of a sequence of poses along a camera path, thereby providing a plurality of data sets; associating each one of the poses in the sequence of poses with a spatial link to a previous pose and a next pose, thereby providing a plurality of spatial links; identifying at least one non-sequential spatial link between two non-sequential ones of the poses; performing a global motion optimization to minimize an error among the plurality of spatial links and the at least one non-sequential spatial link, thereby providing optimized camera pose data; and reconstructing a three-dimensional model of the dental object using the optimized camera pose data and the plurality of data sets.

[0019] The hand-held scanner may be a structured light scanner. The handheld scanner may be a time -of- flight scanner. The hand-held scanner may be a video- based scanner.

[0020] The global motion optimization may include creating consistency among motion parameters between the poses using an overdetermined system of motion equations.

[0021] The sequence of poses may include sequential pairs of key frames, wherein one or more additional data sets may be acquired from one or more additional poses between each sequential pair of key frames. Reconstrucing the three-dimensional model may include adding three-dimensional data based upon the one or more additional data sets and the one or more additional poses. The sequential pairs of key frames may be selected from a larger set of poses using a metric to evaluate a quality of a resulting three-dimensional reconstruction. The sequential pairs of key frames may be selected using a graph analysis.

[0022] The at least one non-sequential spatial link may associate two of the sequence of poses that may be separated by a substantially greater distance along the camera path than along the surface of the dental object.

BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The invention and the following detailed description of certain embodiments thereof may be understood by reference to the following figures.

[0024] Fig. 1 shows a three-dimensional scanning system.

[0025] Fig. 2 shows a schematic diagram of an optical system for a three- dimensional scanner. [0026] Fig. 3 shows a processing pipeline for obtaining three-dimensional data from a video scanner.

[0027] Fig. 4A and 4B illustrate camera paths for a three-dimensional scanner.

[0028] Fig. 5 shows a user interface image where additional data is requested by a software tool.

[0029] Fig. 6A and 6B illustrate accumulated error in camera paths.

[0030] Fig. 7 is a flow chart of a three-dimensional reconstruction process including global path optimization for improved accuracy.

[0031] Fig. 8 shows a dental object reconstruction process using numerical optimization.

DETAILED DESCRIPTION

[0032] In the following text, references to items in the singular should be understood to include items in the plural, and vice versa, unless explicitly stated otherwise or clear from the text. Grammatical conjunctions are intended to express any and all disjunctive and conjunctive combinations of conjoined clauses, sentences, words, and the like, unless otherwise stated or clear from the context.

[0033] In the systems and methods described herein, a number of techniques for global motion optimization are employed to improve accuracy of three-dimensional reconstructions based upon camera path.

[0034] The following description details specific scanning technologies and focuses on dental applications of three-dimensional imaging; however, it will be appreciated that variations, adaptations, and combinations of the methods and systems below will be apparent to one of ordinary skill in the art. For example, while an image- based system is described, non-image based scanning techniques such as infrared time- of-flight techniques or structured light techniques using patterned projections may similarly employ reconstruction based on camera path that may benefit from the improvements described herein. As another example, while digital dentistry is one useful application of the improved accuracy that results from the techniques described herein, global path optimization may also usefully be employed to refine three-dimensional animation models or three-dimensional scans for machine vision applications or for mapping applications. All such variations, adaptations, and combinations are intended to fall within the scope of this disclosure.

[0035] In the following description, the term "image" generally refers to a two-dimensional set of pixels forming a two-dimensional view of a subject within an image plane. The term "image set" generally refers to a set of related two-dimensional images that might be resolved into three-dimensional data. The term "point cloud" generally refers to a three-dimensional set of points forming a three-dimensional view of the subject reconstructed from a number of two-dimensional images. In a three- dimensional image capture system, a number of such point clouds may also be registered and combined into an aggregate point cloud constructed from images captured by a moving camera. Thus it will be understood that pixels generally refer to two-dimensional data and points generally refer to three-dimensional data, unless another meaning is specifically indicated or clear from the context.

[0036] The terms "three-dimensional model", "three-dimensional surface representation", "digital surface representation", "three-dimensional surface map", and the like, as used herein, are intended to refer to any three-dimensional surface map of an object, such as a point cloud of surface data, a set of two-dimensional polygons, or any other data representing all or some of the surface of an object, as might be obtained through the capture and/or processing of three-dimensional scan data, unless a different meaning is explicitly provided or otherwise clear from the context. A "three-dimensional representation" may include any of the three-dimensional surface representations described above, as well as volumetric and other representations, unless a different meaning is explicitly provided or otherwise clear from the context.

[0037] In general, the terms "render" or "rendering" refer to a two- dimensional visualization of a three-dimensional object, such as for display on a monitor. However, it will be understood that a variety of three-dimensional rendering technologies exist, and may be usefully employed with the systems and methods disclosed herein. For example, the system and methods described herein may usefully employ a holographic display, an autostereoscopic display, an anaglyph display, a head-mounted stereo display, or any other two-dimensional and/or three-dimensional display. As such, rendering as described herein should be interpreted broadly unless a narrower meaning is explicitly provided or otherwise clear from the context.

[0038] The term "dental object", as used herein, is intended to refer broadly to subject matter related to dentistry. This may include intraoral structures such as dentition, and more typically human dentition, such as individual teeth, quadrants, full arches, pairs of arches (which may be separate or in occlusion of various types), soft tissue, and the like, as well bones and any other supporting or surrounding structures. As used herein, the term "intraoral structures" refers to both natural structures within a mouth as described above and artificial structures such as any of the dental objects described below that might be present in the mouth. Dental objects may include "restorations", which may be generally understood to include components that restore the structure or function of existing dentition, such as crowns, bridges, veneers, inlays, onlays, amalgams, composites, and various substructures such as copings and the like, as well as temporary restorations for use while a permanent restoration is being fabricated. Dental objects may also include a "prosthesis" that replaces dentition with removable or permanent structures, such as dentures, partial dentures, implants, retained dentures, and the like. Dental objects may also include "appliances" used to correct, align, or otherwise temporarily or permanently adjust dentition, such as removable orthodontic appliances, surgical stents, bruxism appliances, snore guards, indirect bracket placement appliances, and the like. Dental objects may also include "hardware" affixed to dentition for an extended period, such as implant fixtures, implant abutments, orthodontic brackets, and other orthodontic components. Dental objects may also include "interim components" of dental manufacture such as dental models (full and/or partial), wax-ups, investment molds, and the like, as well as trays, bases, dies, and other components employed in the fabrication of restorations, prostheses, and the like. Dental objects may also be categorized as natural dental objects such as the teeth, bone, and other intraoral structures described above or as artificial dental objects such as the restorations, prostheses, appliances, hardware, and interim components of dental manufacture as described above.

[0039] Terms such as "digital dental model", "digital dental impression" and the like, are intended to refer to three-dimensional representations of dental objects that may be used in various aspects of acquisition, analysis, prescription, and manufacture, unless a different meaning is otherwise provided or clear from the context. Terms such as "dental model" or "dental impression" are intended to refer to a physical model, such as a cast, printed, or otherwise fabricated physical instance of a dental object. Unless specified, the term "model", when used alone, may refer to either or both of a physical model and a digital model.

[0040] It will further be understood that terms such as "tool" or "control", when used to describe aspects of a user interface, are intended to refer generally to a variety of techniques that may be employed within a graphical user interface or other user interface to receive user input that stimulates or controls processing including without limitation drop-down lists, radio buttons, cursor and/or mouse actions (selections by point, selections by area, drag-and-drop operations, and so forth), check boxes, command lines, text input fields, messages and alerts, progress bars, and so forth. A tool or control may also include any physical hardware relating to the user input, such as a mouse, keyboard, display, keypad, track ball, and/or any other device that receives physical input from a user and converts the physical input into an input for use in a computerized system. Thus in the following description the terms "tool", "control" and the like should be broadly construed unless a more specific meaning is otherwise provided or clear from the context.

[0041] Fig. 1 depicts a three-dimensional scanning system that may be used with the systems and methods described herein. In general, the system 100 may include a scanner 102 that captures images from a surface 106 of an object 104, such as a dental patient, and forwards the images to a computer 108, which may include a display 110 and one or more user-input devices 112, 114 such as a mouse 112 or a keyboard 114. The scanner 102 may also include an integrated input or output device 116 such as a control input (e.g., button, touchpad, thumbwheel, etc.) or a display (e.g., LCD or LED display) to provide status information.

[0042] The scanner 102 may include any camera or camera system suitable for capturing images from which a three-dimensional point cloud or other three-dimensional data may be recovered. For example, the scanner 102 may employ a multi-aperture system as disclosed in U.S. Pat. No. 7,372,642 to Rohaly et al., the entire content of which is incorporated herein by reference. While Rohaly discloses one multi-aperture system, it will be appreciated that any multi-aperture system suitable for reconstructing a three-dimensional point cloud from a number of two-dimensional images may similarly be employed. In one multi-aperture embodiment, the scanner 102 may include a plurality of apertures including a center aperture positioned along a center optical axis of a lens that provides a center channel for the scanner 102, along with any associated imaging hardware. In such embodiments, the center channel may provide a conventional video image of the scanned subject matter, while a number of axially offset channels yield image sets containing disparity information that can be employed in three-dimensional reconstruction of a surface. In other embodiments, a separate video camera and/or channel may be provided to achieve the same result, i.e., a video of an object corresponding temporally to a three-dimensional scan of the object, preferably from the same perspective, or from a perspective having a fixed, known relationship to the perspective of the scanner 102. The scanner 102 may also, or instead, include a stereoscopic, triscopic or other multi-camera or other configuration in which a number of cameras or optical paths are maintained in fixed relation to one another to obtain two- dimensional images of an object from a number of different perspectives. The scanner 102 may include suitable processing for deriving a three-dimensional point cloud from an image set or a number of image sets, or each two-dimensional image set may be transmitted to an external processor such as contained in the computer 108 described below. In other embodiments, the scanner 102 may employ structured light, laser scanning, direct ranging, or any other technology suitable for acquiring three-dimensional data, or two-dimensional data that can be resolved into three-dimensional data. While the techniques described below can usefully employ video data acquired by a video-based three-dimensional scanning system, it will be understood that any other three- dimensional scanning system may be supplemented with a video acquisition system that captures suitable video data contemporaneously with, or otherwise synchronized with, the acquisition of three-dimensional data.

[0043] In one embodiment, the scanner 102 is a handheld, freely-positionable probe having at least one user-input device 116, such as a button, lever, dial, thumb wheel, switch, or the like, for user control of the image capture system 100 such as starting and stopping scans. In an embodiment, the scanner 102 may be shaped and sized for dental scanning. More particularly, the scanner may be shaped and sized for intraoral scanning and data capture, such as by insertion into a mouth of an imaging subject and passing over an intraoral surface 106 at a suitable distance to acquire surface data from teeth, gums, and so forth. The scanner 102 may, through such a continuous data acquisition process, capture a point cloud of surface data having sufficient spatial resolution and accuracy to prepare dental objects such as prosthetics, hardware, appliances, and the like therefrom, either directly or through a variety of intermediate processing steps. In other embodiments, surface data may be acquired from a dental model such as a dental prosthetic, to ensure proper fitting using a previous scan of corresponding dentition, such as a tooth surface prepared for the prosthetic.

[0044] Although not shown in Fig. 1, it will be appreciated that a number of supplemental lighting systems may be usefully employed during image capture. For example, environmental illumination may be enhanced with one or more spotlights illuminating the object 104 to speed image acquisition and improve depth of field (or spatial resolution depth). The scanner 102 may also, or instead, include a strobe, flash, or other light source to supplement illumination of the object 104 during image acquisition.

[0045] The object 104 may be any object, collection of objects, portion of an object, or other subject matter. More particularly with respect to the dental techniques discussed herein, the object 104 may include human dentition captured intraorally from a dental patient's mouth. A scan may capture a three-dimensional representation of some or all of the dentition according to particular purpose of the scan. Thus the scan may capture a digital model of a tooth, a quadrant of teeth, or a full collection of teeth including two opposing arches, as well as soft tissue or any other relevant intraoral structures. The scan may capture multiple representations, such as a tooth surface before and after preparation for a restoration. As will be noted below, this data may be employed for subsequent modeling such as designing a restoration or determining a margin line for same. During the scan, a center channel of the scanner 102 or a separate video system may capture video of the dentition from the point of view of the scanner 102. In other embodiments where, for example, a completed fabrication is being virtually test fitted to a surface preparation, the scan may include a dental prosthesis such as an inlay, a crown, or any other dental prosthesis, dental hardware, dental appliance, or the like. The object 104 may also, or instead, include a dental model, such as a plaster cast, wax-up, impression, or negative impression of a tooth, teeth, soft tissue, or some combination of these.

[0046] The computer 108 may include, for example, a personal computer or other processing device. In one embodiment, the computer 108 includes a personal computer with a dual 2.8GHz Opteron central processing unit, 2 gigabytes of random access memory, a TYAN Thunder K8WE motherboard, and a 250 gigabyte, 10,000 rpm hard drive. In one current embodiment, the system can be operated to capture more than five thousand points per image set in real time using the techniques described herein, and store an aggregated point cloud of several million points. Of course, this point cloud may further processed to accommodate subsequent data handling, such as by decimating the point cloud data or generating a corresponding mesh of surface data. As used herein, the term "real time" means generally with no observable latency between processing and display. In a video-based scanning system, real time more specifically refers to processing within the time between frames of video data, which may vary according to specific video technologies between about fifteen frames per second and about thirty frames per second. More generally, processing capabilities of the computer 108 may vary according to the size of the object 104, the speed of image acquisition, and the desired spatial resolution of three-dimensional points. The computer 108 may also include peripheral devices such as a keyboard 114, display 110, and mouse 112 for user interaction with the camera system 100. The display 110 may be a touch screen display capable of receiving user input through direct, physical interaction with the display 110. In another aspect, the display may include an autostereoscopic display capable of displaying stereo images.

[0047] Communications between the computer 108 and the scanner 102 may use any suitable communications link including, for example, a wired connection or a wireless connection based upon, for example, IEEE 802.11 (also known as wireless Ethernet), BlueTooth, or any other suitable wireless standard using, e.g., a radio frequency, infrared, or other wireless communication medium. In medical imaging or other sensitive applications, wireless image transmission from the scanner 102 to the computer 108 may be secured. The computer 108 may generate control signals to the scanner 102 which, in addition to image acquisition commands, may include conventional camera controls such as focus or zoom.

[0048] In an example of general operation of a three-dimensional image capture system 100, the scanner 102 may acquire two-dimensional image sets at a video rate while the scanner 102 is passed over a surface of the subject. The two-dimensional image sets may be forwarded to the computer 108 for derivation of three-dimensional point clouds. The three-dimensional data for each newly acquired two-dimensional image set may be derived and fitted or "stitched" to existing three-dimensional data using a number of different techniques. Such a system employs camera motion estimation to avoid the need for independent tracking of the position of the scanner 102. One useful example of such a technique is described in commonly-owned U.S. App. No. 11/270,135, filed on November 9, 2005, the entire content of which is incorporated herein by reference. However, it will be appreciated that this example is not limiting, and that the principles described herein may be applied to a wide range of three-dimensional image capture systems.

[0049] The display 110 may include any display suitable for video or other rate rendering at a level of detail corresponding to the acquired data. Suitable displays include cathode ray tube displays, liquid crystal displays, light emitting diode displays and the like. In general, the display 110 may be operative Iy coupled to, and capable of receiving display signals from, the computer 108. This display may include a CRT or flat panel monitor, a three-dimensional display (such as an anaglyph display), an autostereoscopic three-dimensional display or any other suitable two-dimensional or three-dimensional rendering hardware. In some embodiments, the display may include a touch screen interface using, for example capacitive, resistive, or surface acoustic wave (also referred to as dispersive signal) touch screen technologies, or any other suitable technology for sensing physical interaction with the display 110.

[0050] The system 100 may include a computer-usable or computer-readable medium. The computer-usable medium 118 may include one or more memory chips (or other chips, such as a processor, that include memory), optical disks, magnetic disks or other magnetic media, and so forth. The computer-usable medium 118 may in various embodiments include removable memory (such as a USB device, tape drive, external hard drive, and so forth), remote storage (such as network attached storage), volatile or non- volatile computer memory, and so forth. The computer-usable medium 118 may contain computer-readable instructions for execution by the computer 108 to perform the processes described herein such as the process described in detail with reference to Fig. 3. The computer-usable medium 118 may also, or instead, store data received from the scanner 102, store a three-dimensional model of the object 104, store computer code for rendering and display, and so forth.

[0051] Fig. 2 depicts an optical system 200 for a three-dimensional scanner that may be used with the systems and methods described herein, such as for the scanner 102 described above with reference to Fig. 1.

[0052] The optical system 200 may include a primary optical facility 202, which may be employed in any kind of image processing system. In general, a primary optical facility refers herein to an optical system having one optical channel. Typically, this optical channel shares at least one lens, and has a shared image plane within the optical system, although in the following description, variations to this may be explicitly described or otherwise clear from the context. The optical system 200 may include a single primary lens, a group of lenses, an object lens, mirror systems (including traditional mirrors, digital mirror systems, digital light processors, or the like), confocal mirrors, and any other optical facilities suitable for use with the systems described herein. The optical system 200 may be used, for example in a stereoscopic or other multiple image camera system. Other optical facilities may include holographic optical elements or the like. In various configurations, the primary optical facility 202 may include one or more lenses, such as an object lens (or group of lenses) 202b, a field lens 202d, a relay lens 202f, and so forth. The object lens 202b may be located at or near an entrance pupil 202a of the optical system 200. The field lens 202d may be located at or near a first image plane 202c of the optical system 200. The relay lens 202f may relay bundles of light rays within the optical system 200. The optical system 200 may further include components such as aperture elements 208 with one or more apertures 212, a refocusing facility 210 with one or more refocusing elements 204, one or more sampling facilities 218, and/or a number of sensors 214a, 214b, 214c. [0053] The optical system 200 may be designed for active wavefront sampling, which should be understood to encompass any technique used to sample a series or collection of optical data from an object 220 or objects, including optical data used to help detect two- or three-dimensional characteristics of the object 220, using optical data to detect motion, using optical data for velocimetry or object tracking, or the like. Further details of an optical system that may be employed as the optical system 200 of Fig. 2 are provided in U.S. Pat. No. 7,372,642, the entire content of which is incorporated herein by reference. More generally, it will be understood that, while Fig. 2 depicts one embodiment of an optical system 200, numerous variations are possible. On salient feature of the optical system related to the discussion below is the use of a center optical channel that captures conventional video or still images at one of the sensors 214b concurrent with various offset data (at, e.g., 214a and 214c) used to capture three- dimensional measurements. This center channel image may be presented in a user interface to permit inspection, marking, and other manipulation by a user during a user session as describe below.

[0054] Fig. 3 shows a three-dimensional reconstruction system 300 employing a high-speed pipeline and a high-accuracy pipeline. In general, the high-speed processing pipeline 330 aims to provide three-dimensional data in real time, such as at a video frame rate used by an associated display, while the high-accuracy processing pipeline 350 aims to provide the highest accuracy possible from scanner measurements, subject to any external computation or time constraints imposed by system hardware or an intended use of the results. A data source 310 such as the scanner 102 described above provides image data or the like to the system 300. The data source 310 may for example include hardware such as LED ring lights, wand sensors, a frame grabber, a computer, an operating system and any other suitable hardware and/or software for obtaining data used in a three-dimensional reconstruction. Images from the data source 310, such as center channel images containing conventional video images and side channels containing disparity data used to recover depth information may be passed to the real-time processing controller 316. The real-time processing controller 316 may also provide camera control information or other feedback to the data source 310 to be used in subsequent data acquisition or for specifying data already obtained in the data source 310 that is needed by the real-time processing controller 316. Full resolution images and related image data may be retained in a full resolution image store 322. The stored images may, for example, be provided to the high-accuracy processing controller 324 during processing, or be retained for image review by a human user during subsequent processing steps.

[0055] The real-time processing controller 316 may provide images or frames to the high-speed (video rate) processing pipeline 330 for reconstruction of three- dimensional surfaces from the two-dimensional source data in real time. In an exemplary embodiment, two-dimensional images from an image set such as side channel images, may be registered by a two-dimensional image registration module 332. Based on the results of the two-dimensional image registration, a three-dimensional point cloud generation module 334 may create a three-dimensional point cloud or other three- dimensional representation. The three-dimensional point clouds from individual image sets may be combined by a three-dimensional stitching module 336. Finally, the stitched measurements may be combined into an integrated three-dimensional model by a three- dimensional model creation module 338. The resulting model may be stored as a highspeed three-dimensional model 340.

[0056] The high-accuracy processing controller 324 may provide images or frames to the high-accuracy processing pipeline 350. Separate image sets may have two- dimensional image registration performed by a two-dimensional image registration module 352. Based on the results of the two-dimensional image registration a three- dimensional point cloud or other three-dimensional representation may be generated by a three-dimensional point cloud generation module 354. The three-dimensional point clouds from individual image sets may be connected using a three-dimensional stitching module 356. Global motion optimization, also referred to herein as global path optimization or global camera path optimization, may be performed by a global motion optimization module 357 in order to reduce errors in the resulting three-dimensional model 358. In general, the path of the camera as it obtains the image frames may be calculated as a part of the three-dimensional reconstruction process. In a post-processing refinement procedure, the calculation of camera path may be optimized - that is, the accumulation of errors along the length of the camera path may be minimized by supplemental frame -to-frame motion estimation with some or all of the global path information. Based on global information such as individual frames of data in the image store 322, the high-speed three-dimensional model 340, and intermediate results in the high-accuracy processing pipeline 350, the high-accuracy model 370 may be processed to reduce errors in the camera path and resulting artifacts in the reconstructed model. As a further refinement, a mesh may be projected onto the high-speed model by a mesh projection module 360. The resulting images may be warped or deformed by a warping module 362. Warped images may be utilized to ease alignment and stitching between images, such as by reducing the initial error in a motion estimation. The warped images may be provided to the two-dimensional image registration module 352. The feedback of the high-accuracy three-dimensional model 370 into the pipeline may be repeated until some metric is obtained, such as a stitching accuracy or a minimum error threshold.

[0057] Various aspects of the system 300 of Fig. 3 are described in greater detail below. It should be understood that various processing modules, or the steps implied by the modules, shown in this figure are exemplary in nature and that the order of processing, or the steps of the processing sequence, may be modified, omitted, repeated, re-ordered, or supplemented, without departing from the scope of this disclosure.

[0058] Fig. 4A shows an object 410 for imaging, along with a path 415 that a camera may follow while obtaining a three-dimensional scan of a surface of the object 410. The direction of the path 415 is indicated generally by an arrow 416. The object 410 may be an upper dental impression (as shown) or any other object from which three- dimensional surface data is sought. Starting the camera at a starting point 420, the camera may follow an arc 430 to a second point 422. The camera may then follow a segment 432 to a third point 424. The camera may then follow a second arc 434 to a fourth point 426. The camera may then follow a second segment 436 to return approximately to the starting point 420. It should be noted that the path 415 followed by the camera may be irregular rather than smooth, and that while a particular path 415 is depicted, more generally any path may be taken by the camera including paths that double back upon themselves, cross over identical regions two or more times, and/or entirely skip various surfaces of the object 410. It should also be noted that the camera path 415 may usefully return to the starting point 420, but this is not strictly required for three-dimensional reconstruction as described herein. The camera may take hundreds or thousands of images or more as the camera traverses the path around such a dental object 410.

[0059] Fig. 4B shows locations where additional scan data might usefully be acquired to improve the accuracy of a three-dimensional reconstruction. For example, arcs 440, 442, 444, and 446 may be scanned (e.g., traversed by the camera path) to provide cross linking between various lengths of the camera path. Data might usefully be acquired, for example, from any area that can improve computational accuracy of a three- dimensional reconstruction such as regions where the length of a camera path between two measurements of the surface (e.g., image sets or image data) is significantly greater than the distance between the two corresponding surface locations in the world coordinate system for the camera path. It will be appreciated that this may be a Euclidean distance or any suitable proxy for distance. For example, the length of the camera path may be measured in terms of the number of camera path segments, or the number of camera path segments from key frame to key frame, between two camera poses in Euclidean space. As another example, this may include regions where separate three- dimensional measurements for a general region of the reconstructed three-dimensional model fail to register to one another, or other indicia of accumulated error in the global camera path might be present.

[0060] Fig. 5 shows a user interface depicting a graphical request for additional scan data. After the camera follows the path 415 illustrated above, a software tool may be utilized to identify various locations where additional data might usefully be acquired to reduce accumulated error in a global camera path, such as two frames of image data that represent a candidate for an accumulated error in camera path relative to one another using, for example, any of the techniques described above. A monitor 510 may display an image 520 such as a three-dimensional reconstruction of scanned subject matter, and an arrow 530 may be displayed on the monitor 510 indicating where additional scanning is recommended. The user may then proceed to use a scanner, such as the scanner 102 from Fig. 1, to scan the area indicated by the arrow 530. More generally, areas for additional scanning may be identified to a user in a graphical user interface that displays a reconstructed three-dimensional model from the camera path, along with arrows or other identifiers or graphical annotations that illustrate a recommended scan path. After a user augments a camera path with additional scans, the resulting data can be employed to resolve differences (i.e., errors) in the global camera path, as described generally throughout this disclosure.

[0061] Fig. 6A illustrates a simple camera path in a world coordinate system. The camera starts at a starting point 610 and follows a path 620 in a counterclockwise direction as indicated by an arrow 625, returning to an ending point coincident with the starting point 610 in a fixed coordinate system, such as an arbitrarily selected world coordinate system.

[0062] Fig. 6B shows a simple camera path in a camera coordinate system. When a camera traverses the path 620 in the world coordinate system, errors may accumulate in a calculated camera path 635 so that a measured ending point 640 appears to be located away from the measured starting point 630 in the camera coordinate system, even though these points are identical in the world coordinate system. In one aspect, one or more cross links such as those described above with reference to Fig. 4 may be employed to mitigate accumulated errors in the calculated camera path 635.

[0063] Fig. 7 is a flow chart of a three-dimensional reconstruction process including global path optimization for improved accuracy.

[0064] The process 700 may begin with preprocessing as shown in step 710. It will be understood that preprocessing as described herein presupposes the availability of a number of frames of image data from which a camera path and three-dimensional model can be reconstructed. The information for the three-dimensional reconstruction may be generated in numerous ways including coming from structured light projection, shading based three-dimensional reconstruction, or disparity data. Disparity data may be generated by a conventional image plus one or more other channels or side channels. The preprocessing may include determining the number of available frames, the time duration over which all the frames were taken, the amount of overlap between neighboring frames, identification and elimination of frames with blurred or badly distorted images, and any other suitable preprocessing steps. An estimate of the number of desired key frames may be initially determined during the preprocessing step.

[0065] As shown in step 712, key frames may be selected from among all of the frames of data acquired from a scanner along a camera path. In general, computational costs can be reduced by storing certain data and performing certain calculations and processing steps exclusively with reference to key frames. In principle, these key frames should be related to one another in a manner that permits characterization of a camera path, typically through the registration of overlapping three-dimensional data in respective key frames. Various methods are known in the art for selecting a subset of frames of data as key frames, including techniques based on image overlap, camera path distance, the number of intervening non-key frames and so forth. For example, key frames may be selected based on time duration from an immediately preceding key frame. Key frames may also or instead be selected based upon an amount of image overlap from the preceding key frame and/or a candidate for a following key frame (if available). Too little overlap makes frame-to-frame registration difficult. Too much overlap drives larger numbers of key frames and therefore larger amounts of data to analyze. Key frames may be selected based on spatial displacement, meaning that an upper limit may be placed on the amount of overlap from one key frame to the next. Key frames may also be selected based on sequential displacement. This type of sequential displacement could mean that every tenth frame is determined to be a key frame, for example. In one aspect, key frames may be selected as data is acquired based on any number of suitable criteria. In another aspect, key frame pairs may be determined post hoc by examining all possible candidate key frames. All possible key frame pairs may be examined and candidates may be removed, for example, where there is insufficient overlap to form a stitch. Still more generally, any technique suitable for selecting a subset of frames in a data set may be usefully employed to select key frames for processing in order to reduce computational complexity.

[0066] Once key frames have been selected, additional processing may be performed. For example, full image data (e.g., full resolution center and side channel images) may be stored for each key frame, along with image signature data, point cloud centroid calculations, and any other measured or calculated data to support use of the key frames in a three-dimensional reconstruction process as described herein.

[0067] As shown in step 714, candidate stitches may be identified. In general, a stitch is a relationship between two separate three-dimensional measurements from two different camera positions. Once a stitch is established, a rotation and a translation may be determined for the path of a camera between the two different camera positions. In a complementary fashion, the three-dimensional measurements from the two different camera positions may be combined into a portion of a three-dimensional model. Candidate stitches may be analyzed around each key frame, such as from the key frame to some or all of the frames of data between the key frame and neighboring key frames. Stitches may be based on the originally imaged frames. It may also be useful to deform or warp two-dimensional images during registration and other steps in a stitching process in order to improve accuracy and/or speed each stitch calculation. Stitches may also or instead be based on other observed epipolar relationships in source data.

[0068] As shown in step 716, stitches may be selected for the complete camera path from the universe of candidate stitches. The selection of stitches may be made based upon, e.g., the lowest calculated error in resulting portions of the three-dimensional model.

[0069] As shown in step 718, a graph analysis may be performed using the key frames and the associated stitching to calculate a global path for the camera used to obtain a three-dimensional model. The graph analysis may consider each key frame as a node or vertex and each stitch as an edge between a pair of nodes. A key frame is selected as a starting point. A breadth- or depth- first search may be performed through the graph to identify stitches which may connect the current key frame to another key frame. Each key frame is marked as the graph is proceeded through. A check may be performed to see if all key frames have been reached within the graph. If all key frames have not been reached through traversing stitches in the graph analysis, the largest subgraph is identified. This sub-graph may be examined to see if the entire three-dimensional image may be modeled.

[0070] It may be that certain sub-graphs are not required to complete the three- dimensional imaging. If the camera lingered over a particular region of a surface of an object, or if the camera looped on a region multiple times, the associated sub-graph(s) may not be needed. If a separate sub-graph is identified, which is needed to complete the three-dimensional imaging, an optional branch back to step 712 may be performed. For example, a set of key frames may have been selected which did not have sufficient stitching from one key frame to the next key frame. By choosing a different set of key frames, sufficient stitching may be obtained in order to obtain a complete graph of all needed aspects of the three-dimensional imaging. A key frame which is too sparse, meaning it has insufficient stitches to aid in building a graph, may indicate that a different set of key frames should be selected. Based on the graph analysis, a global path may be selected, and the graph may then be analyzed to optimize the path calculation.

[0071] As shown in step 720, a numerical optimization may be performed to reduce errors in the calculated camera path based upon available data for the complete camera path such as, for example, cross links that interrelate temporally distant measurements. In general, the objective of numerical optimization is to minimize a calculated error based upon an error function for the camera path and/or reconstructed three-dimensional model. A useful formulation of the error minimization problem for a global camera path is presented below.

[0072] There may be a set of candidate camera positions and orientations referenced to a world coordinate system. A camera position and orientation collectively may be referred to as a camera pose. There may be a set of measured frame-to-frame camera motions. A camera translation and rotation collectively may be referred to as a camera motion. A measured camera motion may be referenced in the coordinate system of one camera pose. An example set of three key frames may be obtained from three camera positions, A, B, and C, each of which may be referenced to an origin, O, of a world coordinate system in three-dimensional space. In addition to the position of these points, a camera at each of these points may have a different orientation. A combination of the position and orientation is generally referred to as a camera pose. Between each of these points are motion parameters including a translation (a change in position) and a rotation (a change in orientation). The relationship between a point, X, expressed in the world coordinate system as Xo and the same point expressed in the A coordinate system, X_A may be given by equation (1):

(1) X_A = R_0AX₀ + T_0A

R_OA is the rotation, taking points from the world to the A coordinate system. T_OA is the translation of the world coordinate system as represented in the A coordinate system. It should be understood that symbols X and T may represent a vector, rather than a scalar, e.g. where X includes x, y, and z coordinate values. Further, it should be understood that symbol R may represent a matrix. Equations (2) and (3) may similarly represent a transform transformation between the world and the B and C coordinate systems respectively:

(2) X₃ = R₀₃X₀ + T₀₃

(3) X_c = R_0CX₀ + T_oc

[0073] By rearranging, equation (1) and equation (2) may be represented as shown in equation (4):

(4) X₀ = ^ROA \^XA ^{~ T}OA ) = ^ROB \^XB ^{~ T}OB )

[0074] The representation of a point in one camera's coordinate system may be related to the same point in another coordinate system. For example, as in equations 1-3, coordinates of a point, X, may be transformed from the A coordinate system to the B coordinate system as follows:

(5) X₃ = R_A3X_A + T_A3

[0075] The rotation R_AB rotates points from the A to the B coordinate system and T_AB is the position translation of the origin of the A coordinate system in the B coordinate system.

[0076] In an optimization, the pose of every camera may be optimized based on measured transforms between camera poses. That is, a number of camera-to-world or world-to-camera rotations and translations, e.g., Ro_n and To_n may be performed. It will be appreciated that the world coordinate system is arbitrary, and one of these transforms may conveniently be an identity rotation with zero translation, or a constant motion transfer can be applied to all camera poses without altering the underlying optimization.

[0077] The rotations and translations may be measured for many pairs of cameras. For the zth such measured frame-to-frame motion, let one of the cameras of the pair be camera A and the other be camera B. This may also be considered the zth stitch that relates the camera poses for A and B. Let R_Λ'₃ be the measured rotation taking points in the A system to the B system and T_A3 be the coordinates of the A position expressed in the B system, as in equation (5).

[0078] The rotations and translations for all cameras, Ro_n and To_n may be optimized. It will be appreciated that, while these expressions and the following discussion are cast in terms of rotations and translations from the individual camera coordinate systems to a single world coordinate system, this characterization is not intended to limit the generality of this disclosure. A similar or complementary analysis may be performed using the reverse of these transforms, or any other transform or collection of transforms (typically, although not necessarily rigid transforms) capable of describing a camera path across multiple poses. The constraints on camera motion from one pose, A, to another pose, B, for an f¹ stitch or relationship may be expressed relative to a world coordinate system as rotations, R_c' _0A and R_c' _0B, and translations, T_c ^l _0A and

T_c ^l _0B . This relationship is further constrained by the camera path from A to B, which may be expressed as a rotation and a translation as follows: (⁶) ^RC,ΛB = ^RC,OB (^RC,OA Y¹

K ¹ J ^l C,AB ^{~ l} C,OB ^ΛC,AB ¹ C,OA

[0079] Note that with sufficient stitches, these relationships may form an overdetermined system of motion constraint equations. Using these equations as a starting point, numerical optimization may be performed on the rotational and translational components of each camera pose based on the measured stitches.

[0080] In a decoupled optimization, the rotational and translational components may be independently optimized. This approach may generally be used where there are constraints on one component (e.g., rotation) that do not depend on the other component. Given a candidate set of camera rotations, R_c' , the corresponding candidate camera-to-camera rotations, R_c' _M , may be computed that correspond to each of the measured camera-to-camera rotations, R_ΛB . The corresponding residual rotations, which should be identity in an error free camera path, are given by K_eSιduai_,AB ^{= R} _C' _,AB (^R _A'_B ) ^~l • ^ scalar-valued rotational cost function, e_r, may be computed that depends on the candidate camera rotations:

#stιtches

(8) e_r (Rco_n ) = ∑ K ^rU where r; = hg_S0(3) R_r'_{esidual AB} ι=l [0081] In equation (8),

returns an axis-angle vector, v, that corresponds to the rotation R. In other words,

returns the vector, v, that has a cross-product matrix, [v]_x , that is the matrix logarithm of R.

[0082] Next, a similar scalar- valued cost function may be computed for translation that depends on the candidate rotations and translations.

(9) e_t (R_Cfin , T_Cfin ) = ∑ rfr] , where r/ = T^ - T_M ι=l

[0083] In one conventional, decoupled approach to solving these simultaneous systems of equations, the rotational error function may be converted into a quaternion expression in order to translate the numerical problem into a linear system of equations for solution, as described for example in Combining two-view constraints for motion estimation, Govindu V., Proc. of the Int. Conf on Computer Vision and Pattern Recognition, vol. 2, pp. 218-225 (July 2001). While this approach may be numerically convenient, it does not enforce the unit norm constraint for the quaternion solution, which may result in inaccuracy. Thus in one aspect, a path optimization technique may be improved by minimizing equation (8) for rotation as a nonlinear optimization and minimizing equation (9) for translation as a linear optimization. In another aspect, the more computationally efficient linear system of equations may be used to generate an initial estimate for an iterative optimization that uses non-linear optimization.

[0084] More generally, the decoupled approach described above may fail to provided a truly optimal result, in a maximum-likelihood sense, where it cannot use information from the translation portion of the stitches in determining rotation. Nonetheless, a substantial amount of work in this field aims to overcome the disadvantages of decoupled optimization, as described for example in A solution for the registration of multiple 3D point sets using unit quaternions, Benjemaa R. and F. Shmitt, Proc. ECCV '98, pp. 34-50 (June 1998); Global registration of multiple 3D point sets via optimization-on-a-manifold, Krishnan S., Lee P.Y., Moore J.B., Venkatasubramanian S., Eurographics Symp. Geometry Processing (2005); and Simultaneous registration of multiple corresponding point sets, Williams J., Bennamoun M., Computer Vision and Image Understanding, vol. 81, no. 1, pp. 117-142 (2001). [0085] In one aspect disclosed herein, a coupled approach to optimization may instead be used to minimize overall error in a camera path. In order to achieve a coupled optimization a weighting may be used to balance the contributions of rotational and translational components to a combined cost function: es

Multiple approaches may be used to weight the relative contribution of translations and rotations. In one embodiment the weights may be expressed as matrices, with different stitches receiving different weightings based upon any of a number of factors. For example, the weights may be based on the number of points in a stitch (e.g., the shared content), the quality of a particular three-dimensional measurement, and/or any other factors impacting the known reliability of a stitch. In one approach, the weight matrices may also account for anisotropic error in the individual points collected, such as due to acquisition of depth information from disparity measurements, which results in measurement precision that varies with distance from the camera.

[0086] In some cases, equation (10) may be reformulated so that the rotation and translation weights are decoupled for each stitch (i.e., W_c' is a block diagonal). In particular, this may occur in the case that the motion stitches are recovered from three- dimensional point correspondences with isotropic point error. In that case, for a given stitch i, between poses A and B, the optimal solution may bring the point cloud as seen from pose A into correspondence with that seen from pose B. If X_A' and X_B' are the positions of the center of the point cloud in the A and B systems respectively, then if r_t' is replaced in equation (10) with the residual displacement between the point-cloud centers based on the candidate camera pose. This latter residual displacement may be expressed as:

( \ \ \ ^r''^{ctr =} B ^~ \^C,AB^ A ⁺ * C,AB )

Equation (10) may then be reformulated as:

# stitches

(12) e_c{Rc,o_n Jc,on) = ∑ \rU Kr_t',_ctr + r; W_r'r_r' ι=\ [0087] In general, by minimizing equation (10), both rotational errors and translational errors may be minimized simultaneously. The weight matrices can be chosen for example according to "First Order Error Propagation of the Procrustes Method for 3D Attitude Estimation" by Leo Dorst, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 27, No. 2, pp. 221-9 (Feb. 2005) which is incorporated in its entirety by reference. Once a more consistent set of motion parameters has been generated the three-dimensional model may be updated.

[0088] When total error or some portion of error has been minimized, the resulting value may be evaluated. The calibration state of the scanner and associated equipment may be evaluated based on the minimized error values. If a minimized error falls beyond a certain threshold then calibration for the scanner and associated hardware may be recommended. The threshold value may be empirically determined based on the specific scanner hardware equipment or it may be learned experientially over time for a given system. When a system is new or has been freshly aligned, expected minimized error values may be obtained. When minimized error values deviate from these expected values, a calibration state evaluation flag may be set indicating that the tool should be calibrated. Thus in one aspect, a coupled (or uncoupled) error function may be employed to validate calibration and determine when re-calibration of a device is appropriate.

[0089] As shown in step 722, upsampling may be performed to augment a three-dimensional model with data from non-key frames. In general, upsampling may include any technique for addition of data to a result. For example, while the global optimization described above generally refers to optimization among key frames in a contiguous camera path, the resulting optimized three-dimensional model may be supplemented by registering non-key frames to one or more nearby key frames in a manner that creates small, local reconstruction patches that include additional three- dimensional detail available from non-key frames. Or upsampling may be performed by correcting the corresponding camera path for non-key frames according to a globally optimized path for the key frames. Thus in one aspect, upsampling may more generally be understood as any use of optimized data to incorporate related, non-optimized data into a camera path or three-dimensional model. [0090] Fig. 8 shows a reconstruction process 800 using numerical optimization as described above. In one aspect, this optimization technique may be usefully applied to minimize errors in a camera path where spatial links between non-sequential camera poses (or corresponding data sets used to recover three-dimensional surface data) can be identified. For example, where a scan path covers a buccal surface followed by an occlusal or lingual surface, many spatial links might be identified between non- continguous camera path segments associated with each surface. Under these conditions, a global optimization may significantly improve the accuracy of a three-dimensional reconstruction by reducing errors in the motion estimation parameters for the camera path. It will be understood that the disclosed method may also or instead be embodied in a computer program, a computer program product, or an apparatus embodying any of the foregoing.

[0091] As shown in step 802, the process may begin with acquiring data sets such as a data set from a surface of a dental object with a hand-held scanner from each one of a sequence of poses along a camera path, thereby providing a plurality of data sets. The hand-held scanner may, for example, be the video-based scanner described above. The hand-held scanner may instead include any other type of hand-held scanner suitable for intraoral dental scanning, such as a time-of- flight scanner, a structured light scanner, and so forth. The data sets may be any corresponding data acquired for each camera pose that is used to recover three-dimensional data.

[0092] It should be understood that in this context, the camera path may correspond to a physical camera path that describes the path actually taken by a scanner during a scan, or the camera path may also or instead include a virtual camera path formed from a plurality of different physical camera paths or other virtual camera paths that intersect with one another. Such a virtual camera path may be created wherever poses from two or more physical paths can be interrelated in a global coordinate system, as established for example by three-dimensionally registering two different scans of the same physical subject matter. The use of virtual camera paths may be particularly useful, for example, where a large scan such as a full arch scan is created from data acquired during two or more discontinuous scanning sessions. Under these conditions, global optimization of a virtual camera path can be used to improve consistency of the combined data in a global coordinate system.

[0093] As shown in step 804 each one of the poses in the sequence of poses may be associated with a previous pose and a next pose by a spatial link such as motion estimation parameters or other camera path information. It should also be understood that while a system may infer camera path from the resulting three-dimensional measurements at each camera position and orientation, the camera path may also, or instead be obtained using a hardware-based positioning system based upon, e.g., accelerometers, a geopositioning system, external position sensors, transducers in an articulating arm or any other combination of sensors and techniques suitable for detecting camera position and/or orientation with sufficient accuracy for the intended three- dimensional reconstruction.

[0094] This spatial link data reflects the physical camera path in the order in which data was acquired, thus providing a plurality of spatial links that characterize the camera path during a data acquisition process. The sequence of poses may, for example, be made up of key frames (or sequential pairs of key frames) as generally described above, where additional data sets are acquired from one or more additional poses between each sequential pair of key frames. Key frames may be usefully employed, e.g., to reduce the computational complexity of path optimization while retaining a contiguous camera path of sequential poses. After path optimization is complete, additional three- dimensional data may be added based upon the one or more additional data sets and the one or more additional poses from between key frames. As described above, key frames may be selected from a larger set of poses using a metric to evaluate a quality of a resulting three-dimensional reconstruction, a quality of the estimated motion parameters between poses, a degree of overlap in scanned subject matter, a graph analysis or any other useful technique or metric.

[0095] As shown in step 806, at least one non-sequential spatial link may be identified between two non-sequential ones of the poses based upon the data set for each of the two non-sequential ones of the poses. Thus for example two data sets from a buccal and lingual scan segment may be related to one another based upon camera position, the three-dimensional data recovered from the respective data sets, or any other data acquired during a scanning process. In one aspect, a metric may be employed to identify candidates for non-sequential spatial links, such as a ratio of spatial distance between two data sets to the length of an intervening camera path. Thus the nonsequential spatial link(s) may associate two of the sequence of poses that are separated by a substantially greater distance along the camera path than along the surface of the dental object. This may be based on the data set for each of the two non-sequential ones of the poses, such as by using camera pose data to determine a surface position or by identifying an overlap in the reconstructed three-dimensional data obtained using the data set for two non-sequential poses. This may also inlcude displaying a region for one or more candidate links in a user interface and receiving a supplemental scan of the region, as described above for example with reference to Fig. 5.

[0096] As shown in step 808, a global motion optimization may be performed on the camera path to minimize an error among the plurality of spatial links and the at least one non-sequential spatial link, thereby providing an optimized camera path. This may employ, for example, any of the optimization techniques described above. More generally, this may include any technique for minimizing errors in motion estimation parameters expressed as a function of one or more of rotation, translation, coupled rotation and translation, and decoupled rotation and translation, and/or any technique for aligning the three-dimensional data reconstructed from the data sets in a global coordinate system or improving a consistency of the sequence of poses along the camera path in the global coordinate system.

[0097] As shown in step 810, a three-dimensional model of the dental object may be reconstructed using known techniques based upon the optimized camera path and the plurality of data sets.

[0098] Thus by observing the actual camera paths typical of intra-oral dental scanning, the applicants have devised improved techniques for error minimization when camera path is used for three-dimensional reconstruction. More specifically, by observing that intra-oral scanning often employs a number of adjacent, relatively straight global paths such as for lingual, occlusal, and buccal surfaces (as dictated in part by the relatively restricted oral access to the relatively large surfaces of dentition) , and by observing that intra-oral scanning regularly returns to earlier scan positions, the applicants have devised an optimization technique that takes advantage of the spatial relationship between certain non-sequential frames of data. The approach described above solves the problem of conflicting data for local measurements by using an error minimization technique that globally addresses the camera path, including the interrelationship of non-sequential frames of data. This may be particularly useful, for example for scans covering gums, soft tissue, full arches, orthodontic components and the like where scanning a large area typically entails multiple passes over various regions of the scanned surface.

[0099] It will be understood that numerous variations, modifications, rearrangements, omissions, and additions to the method described above are possible without departing from the scope of this disclosure. For example, while Fig. 8 illustrates a process in which spatial links are determined after the camera path is composed, this may vary significantly where, for example, the pose-to-pose links are inferred from the three-dimensional data acquired at each pose. All such variations as would be apparent to one of ordinary skill in the art are intended to fall within the scope of this disclosure.

[00100] It will be appreciated that any of the above system and/or methods may be realized in hardware, software, or any combination of these suitable for the data acquisition and modeling technologies described herein. This includes realization in one or more microprocessors, microcontrollers, embedded microcontrollers, programmable digital signal processors or other programmable devices, along with internal and/or external memory. The may also, or instead, include one or more application specific integrated circuits, programmable gate arrays, programmable array logic components, or any other device or devices that may be configured to process electronic signals. It will further be appreciated that a realization may include computer executable code created using a structured programming language such as C, an object oriented programming language such as C++, or any other high-level or low-level programming language (including assembly languages, hardware description languages, and database programming languages and technologies) that may be stored, compiled or interpreted to run on one of the above devices, as well as heterogeneous combinations of processors, processor architectures, or combinations of different hardware and software. Thus in one aspect there is disclosed herein a computer program product comprising computer executable code that, when executing on one or more computing devices, performs any and/or all of the steps described above. At the same time, processing may be distributed across devices such as a camera and/or computer and/or fabrication facility and/or dental laboratory and/or server in a number of ways or all of the functionality may be integrated into a dedicated, standalone device. All such permutations and combinations are intended to fall within the scope of the present disclosure.

Claims

CLAIMSWhat is claimed is:

1. A method of three-dimensional reconstruction comprising: acquiring a data set from a surface of a dental object with a hand-held scanner from each one of a sequence of poses along a camera path, thereby providing a plurality of data sets; associating each one of the poses in the sequence of poses with a spatial link to a previous pose and a next pose, thereby providing a plurality of spatial links; identifying at least one non-sequential spatial link between two non-sequential ones of the poses; performing a global motion optimization to minimize an error among the plurality of spatial links and the at least one non-sequential spatial link, thereby providing optimized camera pose data; and reconstructing a three-dimensional model of the dental object using the optimized camera pose data and the plurality of data sets.

2. The method of claim 1 wherein the hand-held scanner is a structured light scanner.

3. The method of claim 1 wherein the hand-held scanner is a time -of- flight scanner.

4. The method of claim 1 wherein the hand-held scanner is a video-based scanner.

5. The method of claim 1 wherein the sequence of poses along the camera path are determined using hardware -based positioning.

6. The method of claim 1 wherein the global motion optimization includes creating consistency among motion parameters between the poses using an overdetermined system of motion equations.

7. The method of claim 1 wherein the sequence of poses comprises sequential pairs of key frames, wherein one or more additional data sets are acquired from one or more additional poses between each sequential pair of key frames.

8. The method of claim 7 wherein reconstrucing the three-dimensional model includes adding three-dimensional data based upon the one or more additional data sets and the one or more additional poses.

9. The method of claim 7 wherein the sequential pairs of key frames are selected from a larger set of poses using a metric to evaluate a quality of a resulting three- dimensional reconstruction.

10. The method of claim 7 wherein the sequential pairs of key frames are selected using a graph analysis.

11. The method of claim 1 wherein the at least one non-sequential spatial link associates two of the sequence of poses that are separated by a substantially greater distance along the camera path than along the surface of the dental object.

12. The method of claim 1 wherein the three-dimensional model of the dental object includes a full arch model.

13. The method of claim 1 wherein the dental object includes an orthodontic component.

14. The method of claim 1 wherein the three-dimensional model of the dental object includes one or more of gums and soft tissue.

15. The method of claim 1 wherein identifying at least one non-sequential spatial link includes identifying the at least one non-sequential spatial link based upon the data set for each of the two non-sequential ones of the poses.

16. The method of claim 1 wherein identifying at least one non-sequential spatial link includes identifying the at least one non-sequential spatial link based upon an overlap in three-dimensional data reconstructed from the data set for each of the two non-sequential ones of the poses.

17. The method of claim 1 wherein identifying at least one non-sequential spatial link includes displaying a region for one or more candidate links in a user interface and receiving a supplemental scan of the region.

18. The method of claim 1 wherein the camera path includes a virtual camera path composed from two or more different physical camera paths.

19. The method of claim 1 wherein the global motion optimization optimizes an alignment of reconstructed three-dimensional data from the data sets in a global coordinate system.

20. The method of claim 1 wherein the global motion optimization improves consistency of the sequence of poses along the camera path in a global coordinate system.

21. The method of claim 1 wherein the global motion optimization minimizes errors in motion estimation parameters expressed as a function of one or more of rotation, translation, coupled rotation and translation, and decoupled rotation and translation.

22. A computer program product comprising computer executable code embodied in a computer readable medium that, when executing on one or more computing devices, performs the steps of: acquiring a data set from a surface of a dental object with a hand-held scanner from each one of a sequence of poses along a camera path, thereby providing a plurality of data sets; associating each one of the poses in the sequence of poses with a spatial link to a previous pose and a next pose, thereby providing a plurality of spatial links; identifying at least one non-sequential spatial link between two non-sequential ones of the poses; performing a global motion optimization to minimize an error among the plurality of spatial links and the at least one non-sequential spatial link, thereby providing optimized camera pose data; and reconstructing a three-dimensional model of the dental object using the optimized camera pose data and the plurality of data sets.

23. The computer program product of claim 22 wherein the hand-held scanner is a structured light scanner.

24. The computer program product of claim 22 wherein the hand-held scanner is a time-of-flight scanner.

25. The computer program product of claim 22 wherein the hand-held scanner is a video-based scanner.

26. The computer program product of claim 22 wherein the global motion optimization includes creating consistency among motion parameters between the poses using an overdetermined system of motion equations.

27. The computer program product of claim 22 wherein the sequence of poses comprises sequential pairs of key frames, wherein one or more additional data sets are acquired from one or more additional poses between each sequential pair of key frames.

28. The computer program product of claim 27 wherein reconstrucing the three- dimensional model includes adding three-dimensional data based upon the one or more additional data sets and the one or more additional poses.

29. The computer program product of claim 27 wherein the sequential pairs of key frames are selected from a larger set of poses using a metric to evaluate a quality of a resulting three-dimensional reconstruction.

30. The computer program product of claim 27 wherein the sequential pairs of key frames are selected using a graph analysis.

31. The computer program product of claim 22 wherein the at least one nonsequential spatial link associates two of the sequence of poses that are separated by a substantially greater distance along the camera path than along the surface of the dental object.