CN102509301A - Novel sub-pixel registration method - Google Patents

Abstract

The invention relates to a novel sub-pixel registration method, which is used for simply performing high-precision registration on sub pixels. The sub-pixel registration method comprises the following steps of: 1, calculating an optimal position on a corresponding axis Y when delta x is equal to (-1, 0, 1); 2, taking acquired optimal registration positions as three points on a quadratic function to acquire a theoretical error, and solving a minimum value (delta xv, delta yv) on a tangent plane; 3, calculating an optimal position on a corresponding axis X when delta y is equal to (-1, 0, 1); 4, taking acquired optimal registration positions as three points on a quadratic function to acquire a theoretical error, and solving a minimum value (delta xh, delta yh) on a tangent plane; and 5, forming two lines close to two positions (delta xv, delta yv) and the (delta xh, delta yh) by means of the acquired two positions (delta xv, delta yv) and (delta xh, delta yh), wherein the intersection of the two lines is the optimal sub-pixel registration point.

Description

A kind of novel inferior pixel method for registering

Technical field

The present invention relates to image processing method, relate in particular to a kind of novel inferior pixel method for registering of mathematical model algorithm.

Background technology

Image registration (Image registration) is at computer vision (computer vision), computer vision (machine vision), and a plurality of fields such as image understanding (Image Understanding) and image/video compression are all as a core technology.Image registration then just begins in the application of three-dimensional movie post-production.In three-dimensional movie post-production field; Image registration mainly is with at different sensors (range sensor and imageing sensor), and the image that different camera angle (two video cameras at diverse location) are obtained matees and superposes to obtain the needed series of parameters of three-dimensional post-production.

Computer vision, all there is very high accuracy requirement aspects such as video compress for image registration (Image registration).Except the degree of accuracy that will reach integer pixel, image registration must reach the precision of time pixel (subpixel) under a lot of situation.The accompanying drawing 1 of this instructions has shown locations of pixels 1/2 time, and wherein stain is an integer pixel, and white point is 1/2 location of pixels in the middle of integer pixel.

Registration in inferior pixel region can be divided into two kinds.A kind of method that is based on search.This method is the more method of using at present.This method uses the way of interpolation (Interpolation) that former figure is amplified to the size that time pixel needs earlier; After the amplification; Use the SSD scheduling algorithm identical that inferior pixel is carried out comparison one by one, find out optimal match point (match point) with the integer pixel registration.The formula of SSD does

E(Δx，Δy)＝∑[s(x，y)-c(x ₀+Δx，y ₀+Δy)]

Formula 1

(x wherein ₀, y ₀) be best integer position, (x y) is the target square, c (x to s ₀+ Δ x, y ₀+ Δ y) is the retrieval square ,-1＜Δ x, Δ y＜1.

The core of searching algorithm is to find out one can make E (Δ x, Δ y) (improper value match error) drop to minimum offset value (Δ x, Δ y).The benefit of this algorithm is that accuracy is high, and the position of finding is actual optimum position.Harm is a calculation of complex; The own calculated amount of interpolation algorithm relatively more commonly used now is also bigger; Computer memory is required high through the image after the interpolation amplification; Add and need compare pixel one by one, especially when the macro block of search usefulness itself is bigger, just become very big of calculated amount.In practical operation, the limitation of system makes the limitation of this algorithm than higher, and general this algorithm generally uses in field of video compression.

Because searching algorithm is for the restriction of precision and macroblock size; Higher and the larger-size field of search macro block for accuracy requirement; Computer vision etc. for example; Generally can adopt another kind of method: utilize to combine integer pixel misdata (match error) that obtains and the wrong face (error surface) that the algorithm of mathematical model goes to simulate time pixel, utilize model to calculate the optimal registration point then.The advantage of this algorithm is that speed is fast, and is low to request memory, more suitable for the large area region registration.And this in theory algorithm can satisfy the inferior pixel accuracy of any needs.But present mathematical model is pair too simple with the simulation of wrong face, and reasonable effect can only be arranged specific image; The error rate of some image is too high in the practical application.The accompanying drawing 2 of this instructions has shown the more typical wrong face that existing mathematical model algorithm obtains in actual tests.Because this uncertainty, the usable range limitation of this algorithm is bigger.

Relative compression of three-dimensional making and industrial robot are different; High for the requirement of degree of accuracy on the one hand; On the other hand owing to be the relation of film, TV; Also can't effectively control for image-context, therefore these two kinds of algorithms all can not solve desired pixel registration of three-dimensional production of film and TV well now.

Summary of the invention

In order to overcome the defective of prior art, the present invention has adopted a kind of novel inferior pixel method for registering, can under the situation that reduces computation complexity, carry out high registration accuracy to inferior pixel.

Technical scheme of the present invention may further comprise the steps:

1) at first the first step at Δ x=(1; 0,1) calculates the optimum position

on the corresponding Y axle on

2) second step is with acquired optimal registration position

Regard three points on the quadratic function as, obtain theoretical amount of error, and bring best theoretical position and theoretical amount of error into a new quadratic function, solve minimum value (the Δ x on the tangent plane _v, Δ y _v);

3) the 3rd step is at Δ y=(1; 0,1) calculates the optimum position

on the corresponding X axle on

4) the 4th step will obtain the optimal registration position

Be seen as three points on the quadratic function, obtain theoretical amount of error, and bring best theoretical position and theoretical amount of error into a new quadratic function, solve minimum value (the Δ x on tangent plane _h, Δ y _h);

5) the 5th step was utilized two position (Δ x that obtained _v, Δ y _v), (Δ x _h, Δ y _h), near these two positions, to select 2 positions and form two lines, the point of crossing of these two lines is best time pixel registration point.

The formula that step 1 relates to has:

e(-1，Δy)＝A _-1Δy ²+B _-1Δy+C _-1

e(0，Δy)＝A ₀Δy ²+B ₀Δy+C ₀

E (1, Δ y)=A ₁Δ y ²+ B ₁Δ y+C ₁Formula 2

E (1, Δ y) wherein, e (0, Δ y), e (1, Δ y) are Δ x=(1,0,1) time, the improper value in the integer pixel zone of obtaining on the Y axle, A _-1, B _-1, C _-1, A ₀, B ₀, C ₀, A ₁, B ₁, C ₁Parameter for quadratic function on diverse location (Quadratic Function);

${\mathrm{\Δy}}_{-1}^{*}=\frac{1}{2}\frac{e(-\mathrm{1,1})-e(-1,-1)}{e(-\mathrm{1,1})+e(-1,-1)-2e(-\mathrm{1,0})}$

${\mathrm{\&Delta;<figure-callout\; id="0"\; label="y"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_0^{*}=\frac{1}{2}\frac{e\left(\mathrm{0,1}\right)-e(0,-1)}{e\left(\mathrm{0,1}\right)+e(0,-1)-2e\left(\mathrm{0,0}\right)}$

${\mathrm{\&Delta;\; y}}_1^{*}=\frac{1}{2}\frac{e\left(\mathrm{1,1}\right)-e(1,-1)}{e\left(\mathrm{1,1}\right)+e(1,-1)-2e\left(\mathrm{1,0}\right)}$ Formula 3.

The formula that step 2 relates to has:

$e\left({\mathrm{\&Delta;y}}_{-1}^{*}\right)=A_{-1}{\left({\mathrm{\&Delta;y}}_{-1}^{*}\right)}^2+B_{-1}{\mathrm{\&Delta;y}}_{-1}^{*}+C_{-1}$

$e\left({\mathrm{\&Delta;y}}_0^{*}\right)=A_0{\left({\mathrm{\&Delta;y}}_0^{*}\right)}^2+B_0{\mathrm{\&Delta;y}}_0^{*}+C_0$

$e\left({\mathrm{\&Delta;\; y}}_1^{*}\right)-A_1{\left({\mathrm{\&Delta;\; y}}_1^{*}\right)}^2+B_1{\mathrm{\&Delta;\; y}}_1^{*}+C_1$ Formula 4

e _f(t)=A _ft ²+ B _fT+C _fFormula 5.

The formula that step 3 relates to has:

e(Δx，-1)＝D _-1Δx ²+E _-1Δx+F _-1

e(Δx，0)＝D ₀Δx ²+E ₀Δx+F ₀

E (Δ x, 1)=D ₁Δ x ²+ E ₁Δ x+F ₁Formula 6

E (Δ x ,-1) wherein, e (Δ x, 0), e (Δ x, 1) is at y=1,0, the improper value in the integer pixel zone of obtaining on the x axle in the time of-1, D _-1, E _-1, F _-1, D ₀, E ₀, E ₀, D ₁, E ₁, F ₁Parameter for quadratic function on diverse location (Quadratic Function).

${\mathrm{\&Delta;x}}_{-1}^{*}=\frac{1}{2}\frac{e\left(\mathrm{1,1}\right)-e(1,-1)}{e(-1,-1)+e(1,-1)-2e(0,-1)}$

${\mathrm{\&Delta;x}}_0^{*}=\frac{1}{2}\frac{e\left(\mathrm{1,0}\right)-e(-\mathrm{1,0})}{e(-\mathrm{1,0})+e\left(\mathrm{1,0}\right)-2e\left(\mathrm{0,0}\right)}$

${\mathrm{\&Delta;\; x}}_1^{*}=\frac{1}{2}\frac{e\left(\mathrm{1,1}\right)-e(-\mathrm{1,1})}{e(-\mathrm{1,1})+e\left(\mathrm{1,1}\right)-2e\left(\mathrm{0,1}\right)}$ Formula 7.

The formula that step 4 relates to has:

$e\left({\mathrm{\&Delta;x}}_{-1}^{*}\right)=D_{-1}{\left({\mathrm{\&Delta;x}}_{-1}^{*}\right)}^2+E_{-1}{\mathrm{\&Delta;x}}_{-1}^{*}+F_{-1}$

$e\left({\mathrm{\&Delta;x}}_0^{*}\right)=D_0{\left({\mathrm{\&Delta;x}}_0^{*}\right)}^2+{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">E</figure-callout>}}_0{\mathrm{\&Delta;x}}_0^{*}+F_0$

$e\left({\mathrm{\&Delta;\; x}}_1^{*}\right)=D_1{\left({\mathrm{\&Delta;\; x}}_1^{*}\right)}^2+E_1{\mathrm{\&Delta;\; x}}_1^{*}+F_1$ Formula 8

e _f(t)=D _ft ²+ E _fT+F _fFormula 9.

The invention has the beneficial effects as follows: visual degree of accuracy is high, and computation complexity is low.

Description of drawings

Fig. 1 is 1/2 locations of pixels figure;

Fig. 2 is existing mathematical model algorithm more typical wrong face figure in actual tests;

Fig. 3 is the optimum position figure that calculates on the Δ x=(1,0,1) on the corresponding Y axle;

Fig. 4 is with optimal registration position

the function vertical view as three points on the quadratic function;

Fig. 5 is the optimum position that calculates on the Δ y=(1,0,1) on the corresponding X axle;

Fig. 6 is with optimal registration position the function vertical view as three points on the quadratic function;

Fig. 7 is the best time pixel registration point location drawing.

Embodiment

The first step: at first in the optimum position that calculates on the Δ x=(1,0,1) on the corresponding Y axle, three positions that promptly on Fig. 3, mark with x.Computing formula is following

e(-1，Δy)＝A _-1Δy ²+B _-1Δy+C _-1

e(0，Δy)＝A ₀Δy ²+B ₀Δy+C ₀

E (1, Δ y)=A ₁Δ y ²+ B ₁Δ y+C ₁Formula 2

E (1, Δ y) wherein, e (0, Δ y), e (1, Δ y) are Δ x=(1,0,1) time, the improper value in the integer pixel zone of obtaining on the Y axle, A _-1, B _-1, C _-1, A ₀, B ₀, C ₀, A ₁, B ₁, C ₁Be the parameter of quadratic function on diverse location (Quadratic Function),

Utilize above formula, the optimum position that can calculate on the pairing Y axle of Δ x=(1,0,1) does

${\mathrm{\&Delta;y}}_{-1}^{*}=\frac{1}{2}\frac{e(-\mathrm{1,1})-e(-1,-1)}{e(-\mathrm{1,1})+e(-1,-1)-2e(-\mathrm{1,0})}$

${\mathrm{\&Delta;<figure-callout\; id="0"\; label="y"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_0^{*}=\frac{1}{2}\frac{e\left(\mathrm{0,1}\right)-e(0,-1)}{e\left(\mathrm{0,1}\right)+e(0,-1)-2e\left(\mathrm{0,0}\right)}$

${\mathrm{\&Delta;\; <figure-callout\; id="1"\; label="y"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1^{*}=\frac{1}{2}\frac{e\left(\mathrm{1,1}\right)-e(1,-1)}{e\left(\mathrm{1,1}\right)+e(1,-1)-2e\left(\mathrm{1,0}\right)}$ Formula 3

The x position of these three positions for being marked on Fig. 3.Calculate A simultaneously _-1, B _-1, C _-1, A ₀, B ₀, C ₀, A ₁, B ₁, C ₁Parameter

Second step:

Obtain optimal registration position

and be seen as three points on the quadratic function.Fig. 4 is the vertical view of this function, and wherein to have marked

dotted line be the equation that runs through three points to 3 x.

Will And A _-1, B _-1, C _-1, A ₀, B ₀, C ₀, A ₁, B ₁, C ₁Parameter substitution formula two just can obtain theoretical amount of error

β=-1 wherein, 0,1

$e\left({\mathrm{\&Delta;y}}_{-1}^{*}\right)=A_{-1}{\left({\mathrm{\&Delta;y}}_{-1}^{*}\right)}^2+B_{-1}{\mathrm{\&Delta;y}}_{-1}^{*}+C_{-1}$

$e\left({\mathrm{\&Delta;<figure-callout\; id="0"\; label="y"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_0^{*}\right)=A_0{\left({\mathrm{\&Delta;<figure-callout\; id="0"\; label="y"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_0^{*}\right)}^2+{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">B</figure-callout>}}_0{\mathrm{\&Delta;<figure-callout\; id="0"\; label="y"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_0^{*}+{\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">C</figure-callout>}}_0$

$e\left({\mathrm{\&Delta;\; <figure-callout\; id="1"\; label="y"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1^{*}\right)-A_1{\left({\mathrm{\&Delta;\; <figure-callout\; id="1"\; label="y"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1^{*}\right)}^2+{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">B</figure-callout>}}_1{\mathrm{\&Delta;\; <figure-callout\; id="1"\; label="y"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1^{*}+{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">C</figure-callout>}}_1$ Formula 4

These best theoretical position

and the theoretical amount of error

into a new quadratic function

e _f(t)=A _ft ²+ B _fT+C _fFormula 5

Just can solve minimum value (the Δ x on tangent plane _h, Δ y _h), be the rhombus position that marks on Fig. 4

The 3rd step

At first in the optimum position that calculates on the Δ y=(1,0,1) on the corresponding X axle, three positions that promptly on Fig. 5, mark with x.Computing formula is following

e(Δx，-1)＝D _-1Δx ²+E _-1Δx+F _-1

e(Δx，0)＝D ₀Δx ²+E ₀Δx+F ₀

E (Δ x, 1)=D ₁Δ x ²+ E ₁Δ x+F ₁Formula 6

E (Δ x ,-1) wherein, e (Δ x, 0), e (Δ x, 1) is at y=1,0, the improper value in the integer pixel zone of obtaining on the x axle in the time of-1, D _-1, E _-1, F _-1, D ₀, E ₀, E ₀, D ₁, E ₁, F ₁Parameter for quadratic function on diverse location (Quadratic Function).

Utilize above formula, the optimum position that can calculate on the pairing X axle of Δ y=(1,0,1) does

${\mathrm{\&Delta;x}}_{-1}^{*}=\frac{1}{2}\frac{e\left(\mathrm{1,1}\right)-e(1,-1)}{e(-1,-1)+e(1,-1)-2e(0,-1)}$

${\mathrm{\&Delta;x}}_0^{*}=\frac{1}{2}\frac{e\left(\mathrm{1,0}\right)-e(-\mathrm{1,0})}{e(-\mathrm{1,0})+e\left(\mathrm{1,0}\right)-2e\left(\mathrm{0,0}\right)}$

${\mathrm{\&Delta;\; x}}_1^{*}=\frac{1}{2}\frac{e\left(\mathrm{1,1}\right)-e(-\mathrm{1,1})}{e(-\mathrm{1,1})+e\left(\mathrm{1,1}\right)-2e\left(\mathrm{0,1}\right)}$ Formula 7

The 4th step:

Obtain optimal registration position

and be seen as three points on the quadratic function.Fig. 4 is the vertical view of this function, and wherein to have marked

dotted line be the equation that runs through three points to 3 o.

Will

And D _-1, E _-1, F _-1, D ₀, E ₀, F ₀, D ₁, E ₁, F ₁Parameter substitution formula two just can obtain theoretical amount of error,

β=-1 wherein, 0,1

$e\left({\mathrm{\&Delta;x}}_{-1}^{*}\right)=D_{-1}{\left({\mathrm{\&Delta;x}}_{-1}^{*}\right)}^2+E_{-1}{\mathrm{\&Delta;x}}_{-1}^{*}+F_{-1}$

$e\left({\mathrm{\&Delta;x}}_0^{*}\right)=D_0{\left({\mathrm{\&Delta;x}}_0^{*}\right)}^2+{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">E</figure-callout>}}_0{\mathrm{\&Delta;x}}_0^{*}+{\mathrm{<figure-callout\; id="0"\; label="F"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">F</figure-callout>}}_0$

$e\left({\mathrm{\&Delta;\; x}}_1^{*}\right)=D_1{\left({\mathrm{\&Delta;\; x}}_1^{*}\right)}^2+{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">E</figure-callout>}}_1{\mathrm{\&Delta;\; x}}_1^{*}+{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="HDA0000109734570000011.png,HDA0000109734570000021.png"\; state="\{\{state\}\}">F</figure-callout>}}_1$ Formula 8

With these best theoretical positions

and new quadratic function of theoretical amount of error

substitution

e _f(t)=D _ft ²+ E _fT+F _fFormula 9

Just can solve minimum value (the Δ x on tangent plane _v, Δ y _v), be the rhombus position that marks on Fig. 4.

The 5th step

Utilize two position (Δ x that got _v, Δ y _v), (Δ x _h, Δ y _h), near these two positions, select 2 positions and form two lines,

v＝mΔx+n

h＝pΔy+q

The point of crossing of these two lines is best time pixel registration point Δ x _Opt, Δ y _Opt

Claims (5)

1. novel inferior pixel method for registering is characterized in that may further comprise the steps:

1) at Δ x=(1; 0,1) calculates the optimum position

on the corresponding Y axle on

2) with acquired optimal registration position

Regard three points on the quadratic function as, obtain theoretical amount of error, and bring best theoretical position and theoretical amount of error into a new quadratic function, solve minimum value (the Δ x on the tangent plane _v, Δ y _v);

3) at Δ y=(1; 0,1) calculates the optimum position

on the corresponding X axle on

4) will obtain the optimal registration position

Be seen as three points on the quadratic function, obtain theoretical amount of error, and bring best theoretical position and theoretical amount of error into a new quadratic function, solve minimum value (the Δ x on tangent plane _h, Δ y _h);

5) utilize two position (Δ x that obtained _v, Δ y _v), (Δ x _h, Δ y _h), near these two positions, to select 2 positions and form two lines, the point of crossing of these two lines is best time pixel registration point.

2. a kind of novel inferior pixel method for registering as claimed in claim 1, it is characterized in that: the formula that described step 1) relates to has:

e(-1，Δy)＝A _-1Δy ²+B _-1Δy+C _-1

e(0，Δy)＝A ₀Δy ²+B ₀Δy+C ₀

E (1, Δ y)=A ₁Δ y ²+ B ₁Δ y+C ₁Formula 2

E (1, Δ y) wherein, e (0, Δ y), e (1, Δ y) they are Δ x=(1,0,1) time, the improper value in the integer pixel zone of obtaining on the Y axle,

A _-1, B _-1, C _-1, A ₀, B ₀, C ₀, A ₁, B ₁, C ₁Parameter for quadratic function on diverse location (Quadratic Function);

${\mathrm{\&Delta;y}}_{-1}^{*}=\frac{1}{2}\frac{e(-\mathrm{1,1})-e(-1,-1)}{e(-\mathrm{1,1})+e(-1,-1)-2e(-\mathrm{1,0})}$

${\mathrm{\&Delta;y}}_0^{*}=\frac{1}{2}\frac{e\left(\mathrm{0,1}\right)-e(0,-1)}{e\left(\mathrm{0,1}\right)+e(0,-1)-2e\left(\mathrm{0,0}\right)}$

${\mathrm{\&Delta;\; y}}_1^{*}=\frac{1}{2}\frac{e\left(\mathrm{1,1}\right)-e(1,-1)}{e\left(\mathrm{1,1}\right)+e(1,-1)-2e\left(\mathrm{1,0}\right)}$ Formula 3.

3. a kind of novel inferior pixel method for registering as claimed in claim 1, it is characterized in that: the formula that described step 2) relates to has:

$e\left({\mathrm{\&Delta;y}}_{-1}^{*}\right)=A_{-1}{\left({\mathrm{\&Delta;y}}_{-1}^{*}\right)}^2+B_{-1}{\mathrm{\&Delta;y}}_{-1}^{*}+C_{-1}$

$e\left({\mathrm{\&Delta;y}}_0^{*}\right)=A_0{\left({\mathrm{\&Delta;y}}_0^{*}\right)}^2+B_0{\mathrm{\&Delta;y}}_0^{*}+C_0$

$e\left({\mathrm{\&Delta;\; y}}_1^{*}\right)-A_1{\left({\mathrm{\&Delta;\; y}}_1^{*}\right)}^2+B_1{\mathrm{\&Delta;\; y}}_1^{*}+C_1$ Formula 4

e _f(t)=A _ft ²+ B _fT+C _fFormula 5.

4. a kind of novel inferior pixel method for registering as claimed in claim 1, it is characterized in that: the formula that described step 3) relates to has:

e(Δx，-1)＝D _-1Δx ²+E _-1Δx+F _-1

e(Δx，0)＝D ₀Δx ²+E ₀Δx+F ₀

E (Δ x, 1)=D ₁Δ x ²+ E ₁Δ x+F ₁Formula 6

E (Δ x ,-1) wherein, e (Δ x, 0), e (Δ x, 1) is at y=1,0, the improper value in the integer pixel zone of obtaining on the x axle in the time of-1, D _-1, E _-1, F _-1, D ₀, E ₀, E ₀, D ₁, E ₁, F ₁Parameter for quadratic function on diverse location (Quadratic Function).

${\mathrm{\&Delta;x}}_{-1}^{*}=\frac{1}{2}\frac{e\left(\mathrm{1,1}\right)-e(1,-1)}{e(-1,-1)+e(1,-1)-2e(0,-1)}$

${\mathrm{\&Delta;x}}_0^{*}=\frac{1}{2}\frac{e\left(\mathrm{1,0}\right)-e(-\mathrm{1,0})}{e(-\mathrm{1,0})+e\left(\mathrm{1,0}\right)-2e\left(\mathrm{0,0}\right)}$

${\mathrm{\&Delta;\; x}}_1^{*}=\frac{1}{2}\frac{e\left(\mathrm{1,1}\right)-e(-\mathrm{1,1})}{e(-\mathrm{1,1})+e\left(\mathrm{1,1}\right)-2e\left(\mathrm{0,1}\right)}$ Formula 7.

5. a kind of novel inferior pixel method for registering as claimed in claim 1, it is characterized in that: the formula that described step 4) relates to has:

$e\left({\mathrm{\&Delta;x}}_{-1}^{*}\right)=D_{-1}{\left({\mathrm{\&Delta;x}}_{-1}^{*}\right)}^2+E_{-1}{\mathrm{\&Delta;x}}_{-1}^{*}+F_{-1}$

$e\left({\mathrm{\&Delta;x}}_0^{*}\right)=D_0{\left({\mathrm{\&Delta;x}}_0^{*}\right)}^2+E_0{\mathrm{\&Delta;x}}_0^{*}+F_0$

$e\left({\mathrm{\&Delta;\; x}}_1^{*}\right)=D_1{\left({\mathrm{\&Delta;\; x}}_1^{*}\right)}^2+E_1{\mathrm{\&Delta;\; x}}_1^{*}+F_1$ Formula 8

e _f(t)=D _ft ²+ E _fT+F _fFormula 9.

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