WO1990002465A2 - Hierarchically range adaptive coding method for signals, especially suitable for picture analysis and codings - Google Patents

Abstract

Signal quantities form a relief. The smaller the segments or blocks IK(n) of this INFORMATION SOLID IK are, the less become their (dynamic) ranges between their minimum and maximum. This forms range adaptively reduced code lengths CL for a range reduced PCM (RRPCM). Using hierarchically more and more narrow nestings of the space given by addresses and functional values, especially TRUE/FALSE-codes for CL-reduction/division, minimal CL(n) are obtained for a blockwise RRPCM. Depending on cumulations, composed RPCM-codes of variable lengths will result by exclusion. All IK(n) coded by RPCM, make IK reconstructable without informations about extremes (!), utilizing overlappings or differences at the border, especially along CORRELATION LINES. Overhead reduction: 81 % ! The possible punctual exactness allows range reduced application of other methods. Activity dependent, exactness becomes reducible within components step by step, enabling (non-) linear interpolations. In static areas the temporal mean value is codable.

Description

H I E R A R C H I C A L L Y R A N G E A D A P T I V E C O D I N G

M E T H O D F O R S I G N A L S , E S P E C I A L L Y S U I T A B L E F O R P I C T U R E A N A L Y S I S A N D C O D I WG S .

A B S T R A C T

State of art

Samples of a signal transmitted by PULSE CODE MODULATION (PCPl) are usually coded within a whole absolute scale, e.g. as one of 256 values represented by one byte. The caused tremendous data stream may be reduced by preceding the extremes MIN, MAX of a block by two 8bit-codes. Each pel within the black is codable exactly between such precoded ("pre-dicted") ranges by a RANGE REDUCED PCM (RRPCM).

The basic problem:

Coming down to average block sizes of less than 6x6 the overhead for precodes still prevents to achieve steady bit rate reductions by steady range reductions (CONVERGENCE): The increasing (divergent) pel-specific overhead is no more compensated by statistically decreasing (convergent) ranges R between MIN and MAX.

The basic idea:

Convergence is achieved by diminishing the overhead of those PRECODES to a NEAR ZERO VALUE: Like the well ordered elements of a segmented (broken) ceramic are reconstructable without any precodes, using the SURFACE INFORMATION only, it must be possible to reconstruct a comparable INFORMATION SOLID by its surface information, at least with few overhead only, being able to utilize CONVERGENTLY DIMINISHED RANGES, being often distributable upon multiple dimensions.

Summary of the solution

In first, still unoptimized tests, the method has reached the state of art or was even better. Optimized versions, utilizing 3D-spaces should reach an average bit rate of less than 1 bit/pel and very small faults, still remaining below the signal noise ratio of video recorder systems (meaning to be quite exact). To enable convergence, the block overhead has been reduced from 16 to 2.9 bit! The automatic system specific RELEVANCE AND IRRELEVANCE SELECTION is very useful for COMPUTER VISION and every kind of advantageous SIGNAL PREPROCESSING, being predestined for HIGH SPEED PARALLEL PROCESSING, reducing data rates until a size of 1 pel (activity of 2 pels) only! I I ) I n t r o d u c t i o n

In Octocer 88, a first experimental digital 8mm-consurmer Video was presented, by SONY Corp., Tokyo, compressing a 215-Mbps signal to a bandwith of 25Mbps "without visible degradation" , called ADAPTIVE DYNAMIC RANGE CODING /5/. ADRC utilizes a PRECODING of the minimum and the maximum to obtain reduced block ranges, allowing an exact, but RANGE REDUCED PCM. A range acaptively fins or coarse quantization diminishes that reduced bit rate again,while coding the picture and changed areas to a subsequent picture. Still,the extremes MIN,MAX are precoded by two 8bit words, limiting the rentable block size of a plane to6x6pel.

A HIERARCHICALLY RANGE ADAPTIVE CODING METHOD will be described here, overcoming those size limits, given by the tremendous overhead of 16bit/block. By reducing the overhead step by step, a furthermore significantly reduced bit rate is reached. Sincs the codes become distributable within multidimensional spaces, a bit rats below 1bit/pel will be achievable coding more exact.

ADVICE: Ths main procedure will be detailled in chapter III,3!

III) DES C R I P T I O N O F T H E M ETH O D

1. Basic rulss

The new method is based upon some fundamental rules, partly of statistical nature, reproduced hers briefly:

R1 : Any limited area contains its extremes, the minimum (MIN) and the maximum (MAX), a common principle indicated by WEIERSTRASS (FIG. 1).

R2: The smaller an area is, the smaller the range of a seals becomes between its 2 extremes. This was already indicated by CAUCHY for exactly continuous areas but may always be utilized as a statistical fact.

R3: Ths smaller the scales, the less the average bit rate to code the areas separately by RANGE REDUCED PCM (RRPCM).

(=) FIG. 1 PA : Segments, coded by RRPCM ars reconstructable like segments of a broken solid, especially utilizing ths SURFACE INFORMATION by offset minimization or even the knowledge based block specific offset code of the area. 2. Detaining those rules

R1 to R3 must be detailed to be suitable for optimized SIGNAL SEGMENTATION.

Ths range of an area is definable alternatively by the following parameter sets :

1. MAX; MIN

2. MIN; MAX - MIN = MIN; RANGE R = MIN; MAXIMAL OFFSET OFM

3. MIN; CODE LENGTH CL of R = MIN; CL(OFM)

Of coarse, MIN and R may be replaced by MAX and -R (inverted scale directionl). Knowing only one of these parameter sets, a RANGE REDUCED SCALE is defined to achieve an exact but RANGE REDUCED PCM (RRPCM-) coding of each signal area.

This is already mentioned in ref. /7 a/, page 9 (4.1.2).

(=) FIG. 2 a) According to version 1., ths most simple realization of defining a RANGE is the prseoding and transmission of both extremes MIN and MAX of a defined area (e.g. fixed block). Patent applications of SONY Corp. as mentioned in ref. /5/, are based upon this principle. The RANGE REDUCED or RANGE ADAPTIVE coding of ref./5a,b/ is called there ADAPTIVE "DYNAMIC" RANGE CODING (ADRC). But, since stored quantities of signal points are known "STATIC" SIGNAL QUANTITIES, this slight correction will help to utilize some aspects of STATIC FIELDS /1/ for the new method, to enable furthermore considerably reduced bit rates. b) According to version 2., the maximal offset, OFM = MAX-MIN = R, defines the RANGE of scale necessary to cods every point of an area and any partial sector of ths area as an offset to MIN (equivalent: deviation +/-D from a mean value, or a negative offset to MAX). This range R defines the absolute code length, necessary for a RANGE REDUCED PCM scale to code the value v(j) of each point P(j) of the area, with j=1,2,3... - At first sight R seems to nesd 8 bit and the precoded set (MIN, R) would have no advantage compared with (MIN, MAX): c) The RRPCM (range reducible PCM) code length CL(i) for each range R(i) of blocks, e.g. of 32x32, 16x16, 8x8, 4x4, 2x2 (and even rectangulars as 2x1) pel, is continuously diminishing according to rule R2. Knowing R(i), this is usable to code the blocks B(i) independently by values v(i,j) within CL(i) by RRPCM. d) Using only R instead of MIN and MAX, an important information is lost:

Without knowing MIN explicitely, RRPCM remains a relative coding for each block. Thereby coded blocks are similar to well ordered puzzle segments where a pointwise RRPCM coding of the blocks B(i) within R(i), i=1,2,3..., produces ths puzzle segments. Their SYNCHRONIZATION PROBLEM is solvable according to R4. 2.1. Basic reflections about the reduction of the overhead a) According to 2c) the (dynamic) range of a secarately coded block decreases continuously. Utilizing only their preceded range R(i), all blocks 5(i) are codable secarately point by pont. Since they seemed to be irreconstructable witnout MIN, ths overhead for precoding two parameters by 15 bit/block still prevented to exploit ths CONVERGENCE PRINCIPLE (R2) for significant bit rate reductions. Therefore, according to ref. /5b/+/6/ the "rentable" block size BS in planes of single pictures was statistically determined to lie near 5x5 pel: In smalisr blocks, the constant block overhead DV=16bit, distributed upon all picture elements(pels) in bit/pel, is no more compensatable by the convergence according to R2. The object of the new method is to minimize that overhead to a rate as near as possible to ZERO. - An analogy will be helpful: b) Like a segmented real (physical) solid, the RRPCM-coded segments should be reconstructabls to the complete signal without MIN: The signal relief will now be considered as the surface of an INFORMATION SOLID SI. The blocks (or any kind of signal areas) are considered as SEGMENTS SI(i) of ths complete S1. c) Information sets equivalent to (MIN, R) would also reduce the code lengths. Any kind of direct or indirect RANGE PRECODING, even ths confirmation (or negation and additional correction) of a RANGE PREDICTION within EXTREME MARGINS EM(i) by one bit, enables detailed reconstruction of all elements by

- punctual RRPCM codes within predefined areas (segments, blocks), especially

- within nested PARTIAL RANGES, placed within the primarily given reduced scale. d) According to R2, a successive proceeding may be used in every PARTIAL AREA, e.g. 32x32, (32x16,) 16x16, (16x8, )...2x2 pel, with successively reduced scales. Thus in the hierarchical stage h+1 of a NESTING h = 1, 2, 3..., the values of MIN(h+1), MAX(h+1) and R(h+1) are codable within the (normally already reduced) scale R(h) = MAX(h) - MIN(h) = EM(i,h) of the stage h, as shown in FIG. 2. s) Constant areas are coded comoletely by the single information "MIN", meaning, that R = 0 and MIN = MAXI - Normally this is prevented by signal noise. Nevertheless, areas with small ranges demand only small scales and code lengths for all contained points, as shown in FIG. 2. f) As in pel by pel codings, also decreasing exacthess of RANGE PRECODING is subjectively alloued, if R only contains MIN and MAX. On the other sids, any overhead O V becomes better distributable within polydimensional spaces . 2.2. Approaching the aim

Object of the method is to utilize a CONVERGENCE of the whols resulting bit rate b consisting of their components, utilizing hierarchical nestings. a) Using (MIN, R), the bit rate b (in bit/pel) consists of

b = bmin + br + bp, with

bmin = BMIN/n pel for the MIN, br = BR/n pel for the RANGE and bp for the pointwise RRPCM code (BMIN.BR: bits/block of n pels for the informations MlN,R). b) Reducing the MINIMAL BLOCK SIZE from 9x9 to 5x5 and 3x3, the RRPCM component bo was measured by the FTZ,Darmstadt,W.Germany/B/(p.46), extrapolated (approx.)hers for 2x2, 2x1, showing the following statistical characteristics:

m e a s u r e d (FTZ) ! esti mated

BS: 9x9 = 81pel 5x5 = 25pel 3x3 = 9pel ! (2x2 = 4pel) 2pel....1pel bp: 6.4 5.B 5.0 ! (4 bit ?) (2.7 ?)...0 (I) dbp (=difference): -0.6 -0.3 (-1.0?) (-1.3?) c) According to 2.1d) each value MIN(h+k), k=0,1,2..., is already codable within CL(h) of a block of any higher hierarchy (h) instead of 8 bits!

Thus ths value bmin = BMIN / n pel reaches the following components:

BS: 8x3(9x9) 4x4(5x5) 2x2(3x3) bp = CL (= BMINI): 6.4 5,8 5,0 bmin computed by BMIN/BS: 0.10 0.35 1.25 bmin as measured by the FTZ: 0.099 0.35 1.2

Unfortunately, the institute (FTZ) measured R within the next higher size (in brackets), when testing the method according to /7c/, pp.19. This overlapping border of 1pel thickness is highly redundant, resulting in wrong conclusions! An overlapping of 1pel absolute according to /7c/ is quite sufficient to get far better results! Nevertheless, the table shous clearly the exacthess of the basic idea, already reducing the overhead for MIN to 62.5% (5.0 / 8.0). d) Even R must not be coded by 8 bit: The code length CL=8 is codable with the bit number BN of CL, meaning a maximum of 3bit for the lengths 1...3 of CL. By this way, the second overhead BR=BR1 is reduced from CL=8 to BN(CL)=3bit/block, meaning to 38%! Utilizing the later mentioned hierarchical algorithm, a further reduction is possible, its result, as msasured by the FTZ, already shown here:

B5: 8x8 4x4 2x2

br1 = BR1/BS computed in bit/block: 0.047 0.153 0.75 (absolute values) br2 by hierarchical method as measured: 0.032 0.13 0.55 (mean value)

Thus, the complete overhead MIN,R has already been halvened by the methods c.d! 2.3. Primary hierarchical relevance selection

According to 2.1 d and 2.2d as much stages h as useful should be reached, sines any halving of scales results in one bit oain for every PCM-coefficient of any coding method of any signal component. Any lower number of bit (BN) for ths cods length CL, precodsd by method 2.2d,means a further halvening of the scale. Preliminary considerations are helpful to understand the hierarchical rules: a) Rule R2 is locally valid, wherever no great local alternations occur.

Inverting the principle, hierarchically unreducible scales may indicate EDGES, in planes represented by CONTOURS. Especially near contours, the mentioned convergence is locally disturbed, since contours discriminate 2 NATURAL AREAS. Their ranges R are treatable like those of the mentioned (fixed) blocks! b) Regarding only one coordinate (x-axis) of the luminance function, a CONTOUR becomes a linear EDGE, as shown in FIG.2,3: Using hierarchical linear division, smaller and largsr (EXPECTIVE) QUANTITIES of points are selected within scales R as defined urithin EXTREME MARGINS EM(i), i = 1,2,3... According to 2.1d they ars nestable. Vertically they indicate ranges R(i) for LIMITED QUANTITIES OF SIGNAL VALUES v(i,j) of horizontally accumulated LIMITED QUANTITIES OF POINTS S(j). c) Using the inverss orinciole, any fixed (preselectsd) scale R defines a run length t, addressing the points t(i), i = 1,2,3..., where the predefined range is TRUE/FALSE, (FIG. 3): Each value t(i) may also define one side of a square! - Any measurable time constant T shows ths delay fault as caused by the system, uhen transmitting an ideal edge (small FIG.3): The ideal edge is characterized by sharp CUMULATION POINTS HP1 , HP2. Transmitted or unideal edges degenerate to functional distributions within EM21 , EM22 along ths ordinate f(t). Such CUMULATION FUNCTIONS(DISTRIBUTIONS) characterize more or less each area(FIG.3). Their deneities and widths are measurable like T and HP along all coordinates. Especially they may be utilized for variable lenghts codings (HUFMANN CODES).

(*) FIG. 3 d) Using such a SCALE or a fixed code length CL instead, a cumulated quantity of points is searched,where CL is valid for. In a plane, asking in every valid point x for the valid range y as well (e.g. valid for CL=4), two run length codes (x,y) are selectable to define rectangular areas or simple squares.

(*) FIG. 4 e) A predicted or arbitrary fixed scale (code length CL=4) is chosen to select RELEVANT and IRRELEVANT blocks (R/I) by subsequent nesting. That single method as shown in FIG.4 is used now for a PICTURE ANALYSIS in correspondancs with FIG.3 selectin now 2D-blocks (of different sizes) as defined by a certain CL. f) If ths statistical probability for a certain range is high, 1bit may code, if an estimated R or set of EM(i,h) is TRUE/FALSE. If FALSE, the STATISTICAL RANGE PREDICTION is correctable by direct RANGE PRECODING, as defined by MIN and MAX of a given area. The word PRE-DICTION is used by ths inventor in that extensive sense, meaning every kind of implicite (statistical) and explicits PRE-CODING!

2.4. How to achieve block synchronization (nearly) without MIN-information a) More than 60% of the range precode R_ (to MAX) became redundant by precoding CL with 3 bit only. If CL=1 is sufficient, a further bit may tell, if CL=0 is TRUE (meaning that the whols area is already coded by a transmission of MIN)! Ths last step already contains ths the basic idea for HIERARCHICAL CL-REDUCTION. Any precoding of CL(h) will enable exact codings of all relative offset (OFR) by reduced PCM-codes RRPCM(h,j) within the scals given and precoded by CL(h)! b) In the next step the overhead of MIN will be reduced furthermore:

In the first step the problem was reduced to pure RRPCM coding of separated blocks! Well ordered, those blocks, coded by RRPCM, represent the segments SI(i) of a solid SI. Like the reconstruction of reliefs of segmented physical solids doss not need MIN-information, using ths SURFACE INFORMATION only, to reconstruct an 51 by a minimization of ths block to block offset until zero!

This method, as described now, is suitable to synchronize big and medium sized blocks (small blocks are advantageously synchronized by method 3.3): c) A possible minimization of the block to block αffset is achieved by well known mathematic algorithms, utilized for the method, especially using:

- 1. CORRELATION LINES, indicating ths place of a local difference dp at the

border of each SI(i) even using WELL DIRECTED CORRELATONS (vectors) and/or:

- 2. A PREDICTION of each BLOCK DIFFERENCE D8 along a border for each point, by

- utilizing the mean value dpm of (at least) two bidirectionally neighbouring right and left differences dpr, dpl, with: dp1 = 1/2 * (dpr1 + dpl1)

- each estimated difference dp(j) weightened reciprocal to its amount to obtain a mean value dpm of all differences: dpm = a * dp1 + b * dp2 + c * dp3...

- to result in the REPRESENTATIVE ESTIMATION dpm = DB of the difference between the blocks B(i) and B(i+1), - or another kind of:

- 3. Other MINIMIZATICN ALGORITHMS (OF THE SECOND DIFFERENTIAL) near the border,

- 4. Even combined with an exact HUFFMAN-CODE CF THE FAULT for BLOCK SYNCHRONIZATION. 3. The best solution; A simple and highly efficient hierarchical method /7c/

3.1. Block range precoding witn automatic relevance selection

In 2.2., a hierarchical nesting was described, resulting in reduced scales P. for MIN (and MAX) and a recucsd CL-coding as shown in the tables of 2.3.

FIG. 5 shows a hierarchical plane division (QUAD TREE) as ussd by BRIT. TELECOM for its method RECURSIVE BINARY NESTING (RBN) /2/. The basic principle will be combined with R2 to result in a successive hierarchical division of the area, resulting now in sucessive code length reductions (for planes and 3D-spaces):

(*) FIG. 5 a) One transmitted bit informs the receiver if a block, e.g. of 64x64 pel (or even a whole frame!), dhly needs a PCM-scale codable by less than 8 bits.

b) The binary value TRUE is followed by (an)other bit(s), informing whether a certain block needs a scale given by less than CL=7, (then: 6, 5,...1) bits. c) Any binary value FALSE causes a programmed geometric division of the

initial block, e.g. in square subblocks of BS = 32x32, 16x16...2x2 pel.

d) The proceedings b) and c) will continue, until CL or BS (the blocksize) reaches a predefined value CLO or BSD (e.g. 2x2) or a stop sign, e.g.:

e) Befors(after) step c(d) an INTERRUPT CODE (1bit) informs the receiver of the result of an ANALYSIS, made by the transmitter, if the optimum is reached.

- This results in a BLOCK AND RANGE ADAPTIVE SUITCHING OFF of the procedure. Far all steps of the inverted BS-hisrarchy of 4x4, 8x8, 15x15... a minimal size of BS=2x2 will be reached then with a bit rate of only

bc = 1/(4*4) + 1/(8*8) + 1/(16*16)...

= 1/16 + 1/64 + 1/256... = 0.0834 bit/pel

- As the transmitter knows the optimum of each region by the defined analysis, this SWITCHING OFF still gives, region adaptively, far better results.

f) Of course the (quasi-)binary trees defined by the procedures are codable in quite arbitrary (programmed) sequences and steps remaining reconstructable! g) Variants, using 2bit steps of CL or x-, y-, or z-division will be described without leaving the basic principle, even when utilizing exact DELTA CODES: h) Instead of absolute values, smaller (point-to-point) differences may be used, i) If high CL-reductions are estimated, a 2 or 3-bit reduction code may replace b. k) If high activity is estimated, (additionally) a lower initial BS may be chosen.

3.2. Preliminary result: The hierarchical CL reduction a) The preliminary result is an unsynchronized HIERARCHICAL CODE LENGTH REDUCTION (HCLR) enabling to code each block in its reduced scale by RRPCM as an offset value OFR(j), building up on the mentioned still unknown Minimum MIN(i)! b) A needed BLCCK SYNCHRONIZATION will be enabled by method 2.4 or method 3.3. HCLR causes an automatic SELECTION OF RELEVANCE CHAINS along contours, suitable for ARTIFICIAL VIEWING, since many remaining small blocks will need mere bits than their environment (FIG. 4). - That CONTOUR SELECTION, may be accomplished by a CONTOUR (better new: CORRELATION LINE-) PREDICTION, as given by ZSCHUNKE /4/, for BLOCK SYNCHRONIZATION according to 2.4c. Since such relevance chainsmay also be selected in the next picture of a sequence, the RANGE CORRELATION OF CL is advantageously measurable: Effects like flickering water or fade cuts, preventing movement detections, still have correlations in the luminance RANGE ! c) Including the temporal dimension of the mentioned plane blocks a further dimension may still be divided in common (or separately along the z-axis) by such (1bit-)codes, depending on ths degree of (z-)changament within a 3D-block, containing several pictures. Since a sum of all elementary differences caused by noise is ZERO, the mean value along z may be coded to obtain static plane blocks, noiseless codes being distributable upon all blockwiss static pictures.

3.3. Block synchronization by including one overlapping point (one difference!) a) For great blocks the methods 2.4. are suitable, enabling a NEAR ZERO FAULT along the borders, correctable by a,now RANGE LIMlTED AND CUMULATION DEPENDENT HUFFMAN CODE. That kind of DIFFERENCE MINIMIZATION along block borders is comparable to the reconstruction of a ceramic, segmented by falling down. The smaller the blocks, the greater the average faults (differences to be coded). b) For small blocks a simple efficient way is given by an overlapping algorithm: Only one Minimum MIN1 of a (first) block 31 must be precoded now by one PCM¬word of 8 bit. CL is already preceded for each block according to 3.1 ! Then, the first block is codable with its RRPCM-codes OFR within CL1. The other blocks are computed subsequently by a CONTINUATION, as described now: c) It can be supposed that a (left) neighbouring block B1 is already coded! A second adjacent (right) block 32 will be chosen. Method 3.1. has already reduced their scales, e.g. down to CL1=3 and CL2=2 bits, see FIG. 5 (+FIG. 4). One common point P12 (e.g. the right upper corner of the precoded block 31) is chosen at the border of those neighbouring blocks. The distance P12 - MIN2 defines a REFERENCE WORD RW(12). Previously, the (PCM value RW of the) point P12 must be included in both scales (dynamic ranges) defined by CL1=3 and CL2=2. d) Tne value RW of the common point P12 was ceded by a 3 bit RRPCM-word C1 for its offset to MINI to compute its exact 3 bit-PCM value RW, using CL1=3 within the block B1. Thus RW is known new! According to the (even vectorial) equation

RW(P12) = MINI + Cl - MlN2 + C2

the value RW may be coded as well using a positive 2-bit-word C2 within CL2 from the still unknown MIN2. - Thus C2 is known and MIN2 may be calculated as an exact PCM value within 62 (the address of MIN2 in 82 should also be coded! ) . All other points P2(j) of S2 are codable new as a pure positive offset to , MIN2. Since each point Pl(j) of B1 is chcosable as RW, it may even be MINI itself! e) MIN2 is computed as its PCM- word and all points of B2 as an offset, to MIN2. The same msthod may oe used to obtain MIN3, MIN4, MIN5, MIN6.., using points P included within CL of ths blocks 82 and 83, S3 and 84..., as shown in F1G. 5. f) BLOCK SYNCHRONIZATION of the single segments SI(i) of SI is also possible prior to the RRPCM codes since that methematic problem is solvable separately! Each FUNCTION PLANE, as clockwise DIFFERENTIAL CHAINS of point to point offsets inregrable to the ORIGINAL FUNCTION, or the DIFFERENCE FUNCTION to a PREDICTOR FUNCTION, is codable quite exactly by such a HIERARCHICAL RRPCM (HRRPCM).

3.4. Preliminary 20-test: Comparing bit rates using quits exact codings a) Whiis ceding the INTRAFRAiΕ LII-11MANCE FUNCTION of standardized sequences quite exact, ths FTZ measured the following results by combining the methods 3.1 a,b,c (using unoptimized fixed limits of BS and CL) and 3.3c, but still coding MIN = ZERO twice per block Instead of its (vectorial) address, /6/,p,55:

bits/pel ENTROPY SONY/***/ HRRPCM-1 HRRPCM-2 ! Gain

ORIGINAL FUNCTION: 5.73 5.B3 5.53 5.21 ! 12...23%

PREDICTOR FUNCTION: 4.61 5.34 5.00 4.61 ! 0...14%

Versicn 1 (HRRPCM-1 ) is a direct coding, version 2 uses HUFFMAN CODES. Still, the tested version only reaches a 50%-OVERHEAD REDUCTION as mentioned in 2.2d. b) Those first results demonstrate, that already a very unoptimizsd HRRPCM is at least equivalent or even significantly better than other methods:

Unfortunately, the less active point-to-point differences were net measured! Furthermore, the lowest possible code length was fixed to CL=3bit, according to prior tests with highly redundant overlapping borders, as mentioned in 2.2c. Supposing a correct test report /6/, unefficient minimal block sizes BS = 8x8 were used to segment the PREDICTION PLANE, while the ORIGINAL was segmented in minimal blocks of 4x4, statistically determined as an optimum (SONY: 5x5!) under those, still uncopimized conditions. At least, the method should not be used to code changing signs (+/-). Positive codes from MIN are always possible. 3.5. A further reduction of the MIN-overhead a) In the cass of smaller blocks, CL is often high, dus to the above mentioned RELEVANCE SELECTION. In this case LOCALIZATIONS CF THE BLOCK MlNIMUM are very suitable since each MIN(i) is a relative BLOCK-ZERO! If CL is greater than the acdress cede given by the block size, WIN should be localized by the short address cods of a small block! More generally, MIN (and MAX) are representing a VECTOR , localizing apoint in the 30-space given by its plane block addresses and its functional value(s) accomplished by a (logical) SIGN, according to

V12 = RW - MIN2 = Vx; Vy; (Vz); F(x,y,(z)); SIGN(F).

Net) VECTOR RULES are applicable, constructing BRIDGES betueen RW(i) and MIN(i), especially between (small!) adjacent blocks. - see FIG. 5. b) The possible gain may be shown by an example of very high entropy, where a top-down coding until a minimal size BS=1x1 pel (83.6%!!) produces excessive relative overhead. This overhead is never compensatable by such sincle pels! Furthermore the (highly redundant) range of a border of 1pel thickness was included in the measures, meaning the range R(4pel) of a 2x2 block measured for each 1x1 -pel-block instead of the correct difference between 2 pels only:

Primary field BSC=255x255 pei: 8MIN as FUNCTION/6/, as VECTOR, saving SIGN GAIN BP (amount of RRPCM-codes ) 327 283 same same

8MIN (additional MIN-codes) 158 668 42513 10 408 93.4 % BR (hierarchical precodes ) 80 705 sams same o υ e r h e a d : 91 113 bp 4.95 same same bmin 2.42 0.65 0.159 br 1.23 same same

TOTAL (Blocks = 31000) 8.60 6.83 6.34 26.3%

Nevertheless about 6.34 bit/pel instead of 8.6 are reached as detailled in section 3.6 to 3.9. Because of redundant overlappings, about 5 bit/pel should be reached according to 2.2b even in that extreme situation, a further gain by ANALYTICALLY SUITCHING OFF (3.1e) for optimized reduction not included! c) Thus the second aim is rsached by reducing the overhead for MIN to a near zero rate. - According to first tests, the rentable minimal block size is even reducible now to less than 4 pel (e.g.2x2 pel). A steady convergence down to a 2x1 size (2pel-block, including 1 precoded pel within R) seems to be possible. The block specific overhead has been reduced from 16 to 2.9 bit (91113/31000). 3.6. Detailling the important excessive test 3.5 (/6/, annex) using 1pel-blocks

Since the bit rate seemed to be excessively high, the importance of the abovementioned test (3.5b) was not seen clearly by /6/. But it should be considered as a very important CONVERGENCE TEST for each variant of the method! Thereforethe results of the computations are reproduced here, still containing all the above mentioned imperfections. A field of the TEST SEQUENCE "DOLLA" was taken: a) Tabls of the amount of blocks of a certain CL and BS (according to 3.5b). CL !BS(psl): 1 4 16 64 256 1024 ! total blocks

3 0 0 0 0 0 ! 3

1 13 0 0 0 0 0 ! 13 2 146 9 1 0 0 0 ! 156

858 99 13 1 0 0 ! 971

4 3960 815 104 25 0 0 ! 4 905 5 10726 3411 523 73 10 3 ! 14 746

6 9368 0 0 0 0 0 ! 9368

834 0 0 0 0 0 ! 834

6 ! 4 0 0 0 0 0 ! 4 total:! 25912 4 334 641 100 10 3 I 31 000

b) Table of the amount of pel coded now within blocks of a certain CL and BS.

CL !BS(pel): 1 4 16 64 256 1024 ! total pels

0 ! 3 0 0 0 0 0 ! 3 1 ! 13 0 0 0 0 0 ! 13

2 ! 146 36 16 0 0 0 ! 198

3 ! 858 396 208 54 0 0 ! 1 526

4 ! 3960 3 260 1 664 1 664 0 0 ! 10548

5 ! 10726 13 644 8368 4 672 2 560 3 072 ! 43042

6 ! 9 368 0 0 0 0 0 ! 9368

7 ! 834 0 0 0 0 0 ! 834

8 ! 4 0 0 0 0 0 ! 4 total:! 25912 17 336 10256 6 400 2 560 3 072 ! 65536 c) Table of the amount of bit when coding all pels within each block by RRPCM. CL ! BS ( pel ) : 1 4 16 64 256 1024 ! total bits

0 ! 0 0 0 0 0 0 ! 0

1 ! 13 0 0 0 0 0 ! 13

2 ! 292 72 32 0 0 0 ! 396

3 ! 2 574 1 188 624 192 0 0 ! 4 578

4 ! 15 840 13 040 6 656 6 656 0 0 ! 42 192 5 ! 53 630 68 220 41 840 23 360 12 800 15 360 ! 215 210 6 ! 55 208 0 0 0 0 0 ! 56 208 7 ! 5 838 0 0 0 0 0 ! 5 838 8 ! 32 0 0 0 0 0 ! 32 total:! 134 427 82 520 49 182 30208 12 800 15 360 ! 324 467

The result of the line(s) CL=5 shows clearly the excessive importance of small blocks (edges) for the resulting bit rates, here and in all other tables!

d) Table of the amount of bit when coding 1pel of each block only (e.g. BMIN!) CL !BS(pel): 1 4 16 64 256 1024 ! total bits

0 ! 0 0 0 0 0 0 ! 0

1 ! 13 0 0 0 0 0 ! 13

2 ! 292 18 2 0 0 0 ! 312

3 ! 2574 297 39 3 0 0 ! 2913

4 ! 15 840 3 280 416 104 0 0 ! 19 620

5 ! 53 630 17 055 2 615 365 50 15 ! 73730

6 ! 56 208 0 0 0 0 0 ! 56208

7 ! 5 838 0 0 0 0 0 ! 5 838

8 ! 32 0 0 0 0 0 ! 32 total: 134 427 20 630 3 072 472 50 15 158 666

This is the overhead produced by the fact, that each MIN was coded once as the BLOCK SPECIFIC ZERO and a second time as a DELTA CODE to RW, a (coded) point of the previous block. 3.7. Avoiding the sign especialiy using alternatively MAX and MIN

Since the former adjacent block B1 may be supposed as coded, there is only one difference D12=RW1 -P2 to code within the mentioned 1pel-blocks, to accomplish the coding of whole block B2. Since there is one address only, one directed difference, counted from RW, is sufficient. Normally that difference must have a SIGN, acccmplished by an amount, limited by a (hierarchically) precoded CL2 of the block 82. Within 1 pel-blocks a 1bit-SIGN is a very significant overhead for the pel specific bit rate. But the sign may be avoided: a) Since a correctly measursd CL of RW12 and P2 indicates, that a halfscals as given by CLH=(CL-1 ) is not sufficient to code the point P2 and RW12 from MI N2-C (P2 cr RW12l), the amount of the difference D12 must exceed CL-1. Therefore it is sufficient to cods only that part of the amount, which exceeds the halfscale! The DECISION-BIT (SIGN-BIT) is saved within each 1pel-block by measuring tns range correctly without redundant overlappings. b) Within blocks of more pels, the sign fait (decision bit) is also avoidable by several methods (different seaming, according to the decisions to be made, giving the same result), e.g. using the following DECISION-BIT, if RW12 lies nearer to MIN2 or MAX2, compensated again by a halfseals CLH=CL-1 (case 1 or 2):

- case 1: If RW12 lies nearer to MIN2, a positive halfscale is sufficient to code the distance D12 = RW12-MIN2, else:

- case 2: If RW12 lies nearer to MAX2, a negative halfseals is sufficient to code the distance D12 = MAX2-RW12 with the effect, that MAX2 instead of MIN2 is determined as the ZERO-REFERENCE for the coding of the offsets of all other points of 82. - Or: The offset to-MIN is coded in the 2.halfscale!.

Equivalent methods may use possible contradictions of an arbitrary sign and its real ranges R(h), R(h-1)..., to invert it, or even a statistical method.

3.8. The extremes MIN, MAX as a vector

According to 3.7, the VALUE of one extreme (normallyMIN, aternatively MAX) was precoded as a quasi sign-free difference from RW. Its VALUE would be coded redundantly twice as a RELATIVE ZERO, while the address is unknown. If the length CLA, used for the addressing of the selected extreme MIN or MAX is less than CL2, the extreme should advantageously be addressed, the complete code containing now the address and the difference D12. a) Tabls of the amount of bit according to 3.6., but coding now one address in each block for one EXTREME (MIN2, MΑX2) instead of one MIN-code (relative block-zero!). Where the cods CLA for the address exceeds CL2, CL2 is taken (*).

CL2 !CLA for BS(pel): 1(1) 2(4) 4(16) 6(64) 8(256) 10(1024) 0 ! 0 0 * 0 * 0 * 0 * 0 *

1 ! 1 1 * 1 * 1 * 1 * 1 *

2 ! 1 2 2 * 2 * 2 * 2 *

3 ! 1 2 3 * 3 * 3 * 3 *

4 ! 1 2 4 4 * 4 * 4 *

5 ! 1 2 4 5 * 5 * 5 *

6 ! 1 2 4 6 6 * 6 *

7 ! 1 2 4 6 7 * 7 *

8 ! 1 2 4 6 8 * 8 *

b) Resulting tabls of the amount of bit coding all MIN-addresses instead of the MIN-values (relative block-zero!) with additional SIGN for all blocks. - At places (*), CL (double coding of MIN, see e) remains the better method.

CL !BS(pel): 1 4 16 64 256 1024 ! total blocks

0 ! 0 0 0 0 0 0 ! 0

1 ! 0 0 0 0 0 0 ! 0

2 ! 0 12 2 0 0 0 ! 14

3 ! 0 198 26 3 0 0 ! 227

4 ! 0 1 630 208 104 0 0 ! 1 942

5 ! 0 6 822 1 046 292 50 15 ! 8 225

6 ! 0 0 0 0 0 0 ! 0

7 ! 0 0 0 0 0 0 ! 0

8 ! 0 0 0 0 0 0 ! 0 total: ! 0 8 652 1 282 399 50 15 ! 10408 computed by table 3. 6a and table 3.8a, instead of (see table 3.6d): 158 666 g) Computed per pel of the field 256x256, the above mentioned (3.5b) bit rates are obtained, the range still measured within the highly redundant border. Considering the total part of the MIN-codes only, it was reduced from 158666 to 10408 bit, its localpart of the bit rate from 2.42 to 0.16 (reduction;93%), reducing the resultingtotalbit rate by more than 26%! 3.9. Results on box level and pel level a) As a result, ths block level must be optimized before making anything on pel level! In the bad example 3.5. the remaining one pel of 1x1-blocks was coded twice, nor only as a FUNCTION DIFFERENCE RW(i)-MIN(i), but also as a redundant ZERO 3.5b! If pel codings are done before the optimization of all logical correlations on block level, an awful increasing of the bit rate occurs. In /6/, that important test 3.5b, left side, intended to demonstrate the limits of the method. - Instead, it shows clearly defects and mistakes of test variants and should become ths standard test for the new method! b) Optimizations are achieved by

- using LOCAL ADAPTIVE CONTROL CODES (well defined stop bits) according to 3.1e,

- measuring R of the REAL BLOCK SIZE only, including one pel of an adjacent block, for BS = nxn + 1 this means: ths range of nxn point-to-point differences( ! ), enabling to chose a well defined (suitable x-,y-) chain of DELTA OFFSETS instead.

- regarding the extreme(s) es a VECTOR (address and value), even cass dependent,

- AVOIDING ITS SIGN, if the amount (of the luminance) is only uniquely (+/-)

interpretabls within the precoded CL (or range R),

- BS dependent selections between method 2.4c and 3.3 + 3.5, sometimes even 2.2d,

- multi-dimensional codings utilizing correlations, wherever possible,

- all codes should refer to a MIN(i) of the function to be coded. Codes from

a mean value make increass the bit rate because of further additional SIGNS! c) According to 2.4c, completely separate coded blocks (with a CL(i) excluding the overlapping point) may also be synchronized by an exact BLOCK DELTA CODE. If the difference is well predictable, this saves bits within greater blocks. d) The complets block overhead is reduced to a NEAR ZERO VALUE by the method.

Then, known and unknown methods of optimized codings on pel level may be involved to obtain further reductions! Range reduced HUFFMAN CODES may serve to diminish the bit rate furthermore, but even any other (nonexact) method. 4. Including other methods

4.1. Pure boxes with the parameter sat MIN,R (no point initially coded by RRPCM) a) The BOXES, defined by method 3.1 and by constructing BLOCK SYNCHRONISATIONS, with BRIDGES only according to 3.3, even if using one point per block only with RW=MIN(i), MIN(i) coded as a reference RW for MIN(i+1), then MIN(i+1) coded as a refarence for MIN(i+2) , etc., result in PURE BOXES, by defining now DEFINITE RANGES for any suitable coding method applied within the reduced boxes defined by a complete information set MIN(i), R(i) according to section 2!

(*) FIG. 6 b) An additional knowledge of MAX as a regional (box-)vector, with block address and functional value, uill result in an additional address overhead, but offers advantages while the boxes are not too small, since CORRELATIONS are easily to be found in subsequent pictures, also using CUMULATIONS.

4.2. Shared ranges a) The RANGE NUMBER is precodable by 0 or 1 (continuing with additional 0 or 1): One bit may precode, if the value is part of the first or the second (the residual) quantity, one excluding the other. The quantities are sharable again, if suitabls. Utilizing such EXCLUSION PRINCIPLES, the average bitrate per block may be reduced, e.g. coding 0..1 with 1bit and 2..9 with 3 bit (one added for the range number) instead of coding 0...9 constantly with 4bit. b) Any kind of (indirect) additional precode for MAX allows to utilize SHARED RANGES: Vmax(i) = MAX(i) - MIN(i) is nearly always advantageously divisible into two RHPCM codes, one of them being codable with two (or more) bits less.

- The range Dmax = 0...11 is devided in two ranges of 0...7 (CL=3) and 8...11 (CL=2). with a precode 0/1; OR: in 3 precodes 0/10/11 for 3 ranges of 0...3 (CL=2).

- 0...9 is devisible in two codes of 0...7 (CL=3) and 8...9 (CL=1).

- 0...18 = 0..15 + 16..18 being more advantageously sharable in 4bit + 8bit

(instead of 4+1 and 2+1) by the codes 0000...1110 and 1111.00...1111.11 c) Knowing the extreme margins MIN(i) andMAX(i) , redundant EMPTY RESIDUAL RANGES RE may be excluded. Thus, if ths REAL RANGE R lies between 0 and 8, the range 9...15 is completely redundant within a measured code length of CL=4. d) Such SHARED RANGES are also obtained by other methods, e.g. employing the above mentioned CUMULATIONS and their local densities (probabilities)! DENSITY and CUMULATION DEPENDING RANGE REDUCED (HUFFMAN) CODES may be used then. 4.3. Example: A table of usual sharεd ranges

R. A ( R ) I C O D E L E N G T H ! TRUE/!

!CL/invers: S-CL! 8N(CL) ! FALSE! d e c i m al ! b i n a r y I decimal, binary ! dec. bin.! e.g. ! dec. normal or e.g. ! minimal maximal ! ! ! CL=4:!No. / col.: 1 ! 2 ! 3 ! 4 ! 5 ! 6 !0.! 0 0....0 ! ! 0 0 ! ! ! ! 1.! 2 0....1 ! 1....2 ! 0 1 ! 1 / 8 0/111 ! 1 01 ! 1 !

2.! 4 0....3 ! 3....6 ! 00 11 ! 2 / 7 1/110 ! 1 ! ! 3. ! 8 0. ...7 ! 7...14 ! 000 111 ! 3 / 6 10/110 ! 2 10 ! ! 4.! 16 0. ..15 ! 15...30 ! 0000 1111 ! 4 / 5 11 /100 ! 2 ! ! 5.! 32 0. ..31 ! 31...62 ! 0000011111 ! 5 / 4100/ 11 ! 3 11 ! 0 ! 6.! 64 0. ..63 ! 62..126 ! 000000111111 ! 6 / 3101/ 10 ! 3 ! ! 7.! 128 0. .127 !127..254 ! 00000001111111 ! 7 / 2110/ 1 ! 3 ! ! 8.! 256 C. .255 ! ( 1..254)(0000000011111111) ! 8 / 1 111/ 0 ! 3 ! ! a) According to 4.3, a scale R may consist of R2 + R3 even of R3 + R6 only, if no value lies within another RANGE NUMBER, which are all defining EMPTY RANGES! In the normal scals(col.1), each ZERO is counted from a local MIN=0 of a block or now: as a ZERO of a SHARED RANGE COMPONENT, the functional coordinate being regarded as an (also separately) 0/1-sharable coordinate interval in x,y,z,..F. b) Each value within 1 to 254 of col.2 lies within one of seven ranges codable with CL=7 instead of CL=8 bit, meaning an advantageous (method adaptively reduded) PCM scals of 254 values only using SUCCESSIVE EXCLUSIONS (monotonies) as each kind of not rising or not falling function (subsequent address points)! c) The value CL=0 (MIN = MAX) may be substituted by a (now virtual) stage CL=1 , meaning now, that each possible witdh of a range is codable by BN(CL) = 3bit or 7 subsequent bits instead of 8, according to 3.1b. d) Generally 3 ranges are giving the full scale, normally 8bit: (MIN - ZERO; MAX - MIN; HIGH VALUE - MAX), each third range being a complement to the others:

- If one of those CL(k), k=1,2,3, needs 8bit, the others need only 7 bit scales!

- If MIN is determined to be 225 and CL(R=31..64) = 6bit, MAX is codable by 4bit, counted down from HIGH VALUE,e.g. 255, but valid for each limited R(i)I

- Thus, an exact DELTA CODE never needs 9bit, as commonly supposed: In a continuously circular scale, HIGH and LOW-VALUE (e.g. BLACK and WHITE) are neighbouring values (G, 255), each offset being codable with 7bit + SIGN!

- The same rule ma be used now advanta eously for each smaller range (scale)! 5. Using constant block sizes and/or steps of more than one bit.

Of course the methods 2.2d, 3.1 a,b and 3.3 are applicable within constant block sizes, diminishing significantly the MIN-overhead bmin of formula 2.2a. The R-overhead br, reduced to (less than) 3 bit, may hardly be diminished.

5.1. Reducing CL in 2 bit steps instead of 1 bit steps

An initial size of 15x15 may be chosen and initial 2bit will code directly its rangs reduction BN(CL), a modified method 3.1, as the following example shows: a) Initially the range (-reduction) of a block with BS=16x16 will be coded by 2bit for the numbers CL=8,7,6,5. The total overhead becomes:

BSpel BS 2bit/npel br ! ! addr.MIN bmin TOTAL BS256 = 15x15: br255 = 2/25S = 0.C0791 !! 8bit/256 = 0.0325 0.04 OR:BS64 = 8x8: br64 = 2/64 = 0.03125 !! 6bit/64 = 0.125 0.156 b) this may be used sucessivsly.e.g.: If CL reaches 6bit, the ranges (or their reduction) of each block of a set of subblocks (e.g. of BS=4x4 instead of 8x8) is precoded directly with further 2 bits, reaching until CL=3 with:

BSpel B5 br !! addr.MIN bmin TOTAL

BS16 = 4x4: br15 = 2/16 = 0.125 !! 4bit/16 = 0.25 0.375 CR:BS4 = 2x2: br4 = 2/4 = 0.5 !! 2bit/4: 0.5 1.0

Version a) or b) may be accomplished by a 1bit-stepping according to 3.1 (or even a further 2bit diminishing at BS=4x4), causing the additional rate:

BSpel BS br addr.MIN bmin2 TOTAL

BS2 = 2x1: br2 = 1/2 = 0.5 !! 1 bit/2: 0.5 1.0

TOTAL of br2 + br4 + br64 = 1.03 + bmin2 1.53 TOTAL of br2 + br16 + br256 = 0.63 + bmin2 1.13

5.2. Reducing a fixed 2x2-pattern in 3bit steps

Even taking a fixed block size BS=2x2, each CL(i) or the reduction is codable by 8N(CL(i)) = 3bit, resulting in 0.75bit/pel. - Accomplished by bmin4 = 0.5bit/pel an overhead rate of 1.25 bit/pel is reached. At BS=2x1 : (3+1 )bit/2pel = 2bit/pel. 5.3. The break even point, proving for the best method a) A BREAK EVEN POINT is reached now near BS=2x1, whers the overhead

bo = bmin + br

increases by C.75 bit/pel from BS = 2x2 to 2x1, according to 5.2 and the component bp decreases by approximately the same value, according to table 2.2b. Thus, the method reaches a nearly STEADY CONVERGENCE until BS=2x1. b) Using a constant block size BS, a_ small constant plane must be codable with

b2 (2x1) b4 (2x2) b1S (4x4)

5.1: 1.53 (meth. 3.1 about 1.3) 1.0 0.37

5.2: 2.0 ^' 1.25 0.44 c) Compared with known OPTIMAL CODING METHODS, is to be seen, that the method becomes superior to any other method, at least until a BREAK EVEN POINT!

- Since any non-constant function F appears as an OFFSET FUNCTION F1 to a CONSTANT FO, codable by the same exact method here as there, the formula

F = FO + F1

shows, that this stated advantage of the new method must remein, at least until a measurable break even point, where an AUTOMATIC SWITCHING is possible. d) Coming down to a code length for BS1=1x1 (+1pel), the overhead br is no more distributable on a plurality of points, resulting in reincreasing rates! Measuring the local differences instead of the absolute values, the ACTIVITY of 2 subsequent pels (meaning one relative difference between 2 points) is far less than the absolute values of 2 points (2 differences to MIN). Within a 4x4-block, 3 DELTA-CODES (e.g. forming a way like an U or C) are accomplished by a 4th cods to a pel (e.g. the last right upper corner) of a former adjacent block. This results in a similar HIERARCHICALLY RANGE REDUCED DELTA MODULATION. e) Of course the mentioned planar way (U) may continue in the z-axis within a 30-block, advantageously along spatial CORRELATION LINES as describsd later: The way of SIGNIFICANT POINTS (their new address) is advantagsously determined within 3 special coordinates x,y,z like the mentioned "addresses" of fuctional values in 3 coordinates x,y,F(x,y). For each planar block, a most significant point (according to predefined criteria), coded within PURE BOXES (4.1.) already allows to find the spatial way of a point within a 30-picture sequence. f) Codings such very significant points PS, a kind of framework or skeleton is obtained, enabling to code less significant points top-down between them until the available bit rate stops the procedure, still enabling to interpolate then. 5. Statistical range prediction, bottom-up correction codes, range reduced HUFFMAN codes

6.1. Bottom-up nesting a) All kind of possible ranges are implicitely (statistic estimation) and explicitely codable, even DISPLACEMENTS. /3/ is already mentioning a too-down nesting of DISPLACEMENTS, statistically pra-dicting the range, Wide address ranges are chosen to prevent the worst case, the displacement not being codaole within the statistically predicted ADDRESS RANGE. This is of course avoided by

DIRECT PRECODING as utilized by SONY /5/ according to 2., in order to obtain a

"HIGH EFFICIENCY CODING APPARATUS"/Sd/, still having to amortize the overhead of the MIN-MAX-precodes and without reaching such very small boxes. b) According to /7 b/, both methods are usable. But, if a pre-dicted range R is wrong there, a BOTTOM-UP-NESTING of the mentioned boxes is chosen, exactly inverting method 3.1., also applied now with ranges of displacements: c) If a predicted range is FALSE (too small),it may be extsnded (e.g. doubled) subsequently by 1 bit-codes, until the UNEXPECTED EVENT is codable within.

Thus, method 3. and the components of equation 2.2a are optimizable for all kind of displacements, measurable like points in a combined FUNCTION-ADDRESS

SPACE, dynamic blocks being selectable new along nonlinear correlation. lines within a multidimensional space to result often in a quasi static problem, to be solved like this (see chapter 8.).

5.2. Using (range reduced) HUFFMAN codes according to pre-dicted cumulations

According to a DISTRIBUTION PROBABILITY (FIG.3), PROBABLE HUFFMAN- or RANGECODES(4.2) of short lenght are reserved for CUMULATIONS, longer words for less dense sections, even approximately quasi EMPTY RANGES R(i,j,k...) of a domain.

7. Implicite and explicite coding of empty ranges (empty scales, holes)

7.1. Saving the mentioned excessies bit rates at a (sharp) contour

Real objects contain sharp contours. An ideal contour selects two quantities, e.g. a quantity of white and a quantity of black points. In this case, there is no value existing between black and white! The whole range in between is an

EMPTY RESIDUAL QUANTITY(ERQ), because every value in between is not a real one!

Measurable SYSTEM TIME CONSTANTS T of the transmission help to eliminate them: a) As the falsifiec values will lie within the intervall T (see FIG.3: ERQ=RML) they are correctable by making them white or black. In reality already the first point diverging relevantly from one quantity, belongs to the other one! Conventionally unexact SUBJECTIVELY ADAPTIVE DPCM-predictors have the best coding exacthess within that ERQ, according to the MEAN VALUE of the PREDICTION, causing faults like "edge business" and "slope overload". b) The LOCALIZATION of an ERG is acniaved by method 3.1. resulting in small CHAINS OF RELEVANT BLOCKS, indicating the high EDGE DIFFERENCE along contours. c) Within those blocks of high relevance only, a 1/0-pattern localizes the edge. Thus, the new method codes for every point by 1bit/pel if it belongs to the "left" or the "right" side of ths edge. In greater blocks, e.g. of 3x3 pel, that 1 bit/pel-information would even be reducible by hierarchical block codings, e.g. one block containing 2x2 or 2x1 pels with that SIGN (LEFT/RIGHT). d) Each bit indicates, if the point is element of the RIGHT or LEFT QUANTITY. Instead of a coded value, the nearest RIGHT or LEFT point may be supposed to be the true function value (A-prediction). Each PREDICTION, made by a surrounding, evan DIRECTED to the edge, might prevent a kind of too abrupt jerkeyness. s) The procedure may be done as a completely independent coding of two AREAS, segmented by a contour chain as detected by c,d and algorithm 3.1. Like BLOCKS, such NATURALLY SEPARATED AREAS are SYNCHRONIZED by one BRIDGE (V = RW-MIN) only. f) The transmitter is able to code a measured range of such an ERQ in the same way as ths mentioned real ranges when using the LOCAL GRADIENT! Whenever such an ERQ is estimated from the coded past (e.g. along the contour!), a binary value codes ths event as TRUE or FALSE, followed by implicit or explicit range codes, R or CL even being estimated along the contour to code exact local differences! If the (not too small) estimated CL is FALSE, a simple bottom-up extention is made until the real (difference-) offset is enclosed to code it. g) Since such an ERQ is effective for a whole block, it reduces the quantity of possible values (the scale!) for the rest of the block, according to FIG. 3: For the whole initial block (t1 to t4) the DOUBLE RANGE EM21 and EM22 is valid after the exclusion of ERQ (=RML) by the time constant T along the edge. h) After having eliminated or coded the RELEVANCE CHAIN, residual quantities of values (of points) are codable like having no edges (see 4.3a : R = R3 + R5). Within a mole black-white region, neighbouring blocks are coded by 1bit/block! 7.2. Saving bit rates at (block-included) sharp and less sharp contours a) Each ERQ is some KIND OF HOLE in multidimensional solids,given by undeterminate (e.g. black/white) function and/or address values (where a CONSTANT VALUE or a SHARP EDGE is obtained one by the other by a 90 degree rotation). Such uncoded holes,obtained when coding the SHARED DOMAINS (see FIG.4: INTERNAL and EXTERNAL REGION) as sep rated by a CONTOUR (also: FIG. 3), and one synchronizing BRIDGE between them, will save data for usually coding all edge offsets, this type of EDGE ADAPTIVE coding being more exact than commonly linear distributed samples. b) Detecting less sharp contours (rising part longer than T) one or more additional bits will approximate better the contour than eqidistant samplss /5b/.

- Using a circle as a scals, where black and white or the two grey values S1 and S2 of an edge become adjacent values, the principle gets very clear:

- Each halfseals is directed to the other value, the highest densities near S1, S2. since small deviations only will be probable from each CUMULATION POINT HP selecting the direction of the other HP - (see FIG. 3) , inverting the SIGN.

- The surrounding of the edge is coded less dense when leaving a point HP. c) In monoton (rising/falling) functions, already coded (addressed) areas may be excluded to obtain a smaller address range for a further CL-reduction.

- If any MONOTON QUANTITY is coded within a HALF RANGE, the addresses of the following points are codable with 1bit less (like in a plane address block).

- This may be successively done.

- Rising/Falling edges are also representing such monoton functions (FIG. 7).

(*) FIG. 7

7.3. Eliminating transmission errors by redundant bridges

To eliminate faults, 2 redundant additional exact DELTA CODES at the border of greater blocks are to be used: If the computed result of one path differs from the result of all others, an error is detected and correctable, presumed the existence of at least 3 paths, values having to become equal for each path!

7.4. Prefix to chapter B: Multidimensional spaces

(*) FIG. B As mentioned in 3.3d, the values of a plane containing addressss and function values may be regarded as VECTORS, having 3 coordinatss. This is suitabls for MIN(i) and MAX(i), while the other vectors, as a set of parallels, are codable subsequently by making address information redundant (degenerated vectors).

In equivalence, in a 30-address space, 4 (reducible) components are to be coded. Real 30-vectors, e.g. displacements , are a (reducibl e) 6-component probl em. 6. New object: How to reach 1bit/pel in multi-dimensional spaces a) Static 30-blocks are selectable by known methods (z-sum of differences = 0). A supposed bit rate ef 4bit/pel is distributable upon a 30-block of at least 4 SUBSEQUENT STATIC PICTURE PLANES coming down _to a_ bit rate of_ 1bit/pel. In the pass of noise, the mean value of 4 picturss is computed along the z-axis. b ) In DYNAMIC REGIONS known and unknown methods are applied:

All kind of DISPLACEMENT VECTORS may be measured normally as known from frame to frame, resulting in virtual CORRELATION LINES (FIG. 9). The blocks may now be estimated,their range being represented by an angle: often becoming smaller if the estimation is true (TRUE: the point has been found within) and wider, if not, until TRUE. Thus the address range of all components may be minimized.

(*) FIG. 9 c) Another method works completely too-down:

A correlation point may be found again within subsequent pictures to compose a GREAT BOX OF SEVERAL SUBSEQUENT PICTURES (FIG.10), nestable in analogy to 3.1. Generally the highest deviation defines the size (CL!) of an initial "big box". Smaller, CURVED AREAS are selectable like edges (FIG.5) or between correlation lines, as shown by the black arrows (boxes/areas) all treatable according to 3, since their components are quite normal signal functions, RANGE PRE-DICTIONS being applicable for every block-function,treating components like a luminance. Such a measured (or even statistically) pre-dicted RANGE (BOX) OF SUBSEQUENT PICTURES is mentioned in /5d/,prior /7b/. Now (new) the EVENT of FIG. 10 is also advantageously nestable according to 3, FIG. 5 (FIG. 2, 3, 4) and FIG. 9!

(*) FIG. 10. d) In ACTIVE REGIONS, PCM-exactness is reducible, as known by the SONY-method /5b,c/ or is locally interpolated as known by RBN of BRITISH TELECOM /2/.

But, wheras those methods still produce more noise, by diminishing only planar (spatial) or functional exacthess /5/, pp.18-22 (SONY at BS-6x6 and 2.2bit/pel; 37.8d8 - RBN at BS(min)=3x3 and 6.43 bit/pel: 42.8d8), the new BOXES allow a n-dimensional DISTRIBUTION OF IN-/DECREASING EXACTNESS on all components x,y,z,F.

- Utilizing the predefined BOXES according to 2.1 and 4., the new method is able to reduce exacthess in subsequent coordinates (components) bit by bit:

- Reducing the FUNCTION EXACTNESS by 1bit, the X-EXACTNESS by 1pel and the

Y-EXACTNESS by 1pel, using interpolation between all such points, defined in the 30-matrix, the aim of 1 bit/pel is certainly reached with minimal noise, since the maximal distortion remains smaller than in the mentioned methods.

- In the worst case interpolations between boxes (MIN(i) and MAX(i)) may suffice. Within 2 pictures, (non)linear interpolation or TRANSPORT OF FORMS CF THE PAST from picture p to p+1, forms adjusted about MIN(k,p+1),MAX(k,p+2), is possible. 8. New object: How to reach 1 bit/pel in multi-dimensional spaces a) Static 3D-blocks are selectable by known methods (z-sum of differences = 0). A supposed bit rate of 4bit/pel is distributable upon a 30-block of at least 4 SUBSEQUENT STATIC PICTURE PLANES coming down to a bit rate of 1bit/pel. In the case of noise, the mean value of A pictures is computed along the z-axis. t) In DYNAMIC REGIONS known and unknown methods are applied:

All kind of DISPLACEMENT VECTORS may be measured normally as known from frame to frame, resulting in virtual CORRELATION LINES (FIG. 9). The blocks may now be estimated,their range being represented by an angle: often becoming smaller if the estimation is true (TRUE: the point has been found within) and wider, if not, until TRUE. Thus the address range of all components may be mininized.

(*) FIG. 9 c) Another method works completely top-down:

A correlation point may be found again within subsequent pictures to compose a GREAT BOX OF SEVERAL SUBSEQUENT PICTURES (FIG.10), nestable in analogy to 3.1. Generally the highest deviation defines the size (CL!) of an initial "big box". Smaller, CURVED AREAS are selectable like edges (FIG.5) or between correlation lines, as shown by the black arrows (boxes/areas) all treatable according to 3, since their components are quits normal signal functions, RANGE PRE-DICTIONS being applicable for every block-function, treating components like a luminance. Such a measured (or even statistically) pre-dieted RANGE (BOX) OF SUBSEQUENT PICTURES is mentioned in /5d/,prior /7b/. Now (new) the EVENT of FIG. 10 is also advantageously nestable according to 3, FIG. 5 (FIG. 2, 3, 4) and FIG. 9!

(*) FIG. 10. d) In ACTIVE REGIONS, PCM-exactness is reducible, as known by the SONY-method /5b,c/ or is locally interpolated as known by RBN of BRITISH TELECOM /2/.

But, wheras those methods still produce more noise, by diminishing only planar (spatial) or functional exacthess /6/, pp.18-22 (SONY at BS=6x6 and 2.2bit/pel: 37.8d8 - RBN at BS(min)=3x3 and 6.43 bit/pel: 42,8d8), the new BOXES allow a n-dimensional DISTRIBUTION OF IN-/DECREASING EXACTNESS on all components x,y,z,F.

- Utilizing the predefined BOXES according to 3.1 and A., the new method is able to reduce exacthess in subsequent coordinates (components) bit by bit:

- Reducing the FUNCTION EXACTNESS by 1bit, the X-EXACTNESS by 1pel and the

Y-EXACTNESS by 1pel, using interpolation between all such points, defined in the 30-matrix, the aim of 1 bit/pel is certainly reached with minimal noise, since the maximal distortion remains smaller than in the mentioned methods.

- In the worst case interpolations between boxes (MIN(i) and MAX(i)) may suffice. Within 2 pictures, (non)linear interpolation or TRANSPORT OF FORMS OF THE PAST from picture p to p+1, forms adjusted about MIN(k,p+1),MAX(k,p+2), ispossible. e) A nesting of 2D cr 3D-sqares is easy. But if the past indicates, that only one coordinate is relevantly changing (estimation!), this may be utilized now to diminish the pel specific overhead, dividing then that one coordinate only. Sines IR/RELEVANCE is automatically selectable, RELEVANCE CHAINS may localize now implicitely the displacements instead of former explicite codings. f) A valid BOX FOR ALL COMPONENTS, as FIG.10, is pre-dictable (by precodes or estimations with correction if FALSE) to use method 3, also meaning subsequent NESTINGS OF ALL FRAME DIFFERENCES, then of SINGLE FRAME-TO-FRAME DIFFERENCES! g)While'3 separate vector components, e.g. V = (20,5,10) still need a set of CL = (5,3,4) = 12 bits, its VOLUME (2x5x10) contains 1000 points, each point within being codable with only CL=10 bits. Its CL is also precodable by 4 bit. h) COLOUR VECTORS are treatable like displacements now, according to 3.

Using displacements, an exact but Iess dynamic, sometimes a quasi static information should be obtained according to FIG. 9 and/or FIG. 10. But the method discriminates other kinds of correlations:

6.1. New correlation types, obtained by the method a) In DYNAMIC REGIONS the pure block specific RANGE INFORMATIONS (3.1) result in CL-CORRELATION INFORMATION (CLC). To find correlations (points), CLC is a simple but efficient (first) reference. PURE BOXES (4.1) may already be used! b) Utilizing specific HIERARCHICAL CL-RELATIONS of CL(h), CL(h+1 )...CL(h+n), meaning to compute their coefficients by dividing one by the next, give a kind of SPECIFIC PATTERN, characterizing the region. c) CUMULATIONS are measurable thereby or by known methods, according to FIG.3, enabling an apparatus to find a same caracteristic within subsequent pictures. They are found as SORTED HIGH DENSITY F-CORRELATIONS of even different places of small function differences. A fine black-white-grey pattern has such points, without having small local x-y-differences! A discorrelation indicates singularities: Distortions or even defects of an element of the recorder, coarse distributions to be found within an ERQ of an edge, producing excessive bit rates, should be eliminated (interpolated) before transmissions. d) Utilizing also MIN(i) and/cr MAX(i), even if they are coded within PURE BOXES as single points, very exact references are obtained within a sequence. 9. Coding generalized gradient functions within nested deviation ranges

2.1. Boxes of higher dimension a) All kind of differences in a space given by functions and addresses will be called here a GENERALIZED GRADIENT /7b/, a normal gradient of adjacent points as well es a local (= correlational) or function displacement (= edgs!).

In subsequent planes, x-(y-) or z-gradients (DIFFERENTIAL AREAS) are applied to apply method 3., since the point-to-point differences need less bits than absolute values. But all detected small or great displacements are diminished hierarchically within the pre-dieted RANGE OF THE BOXES containing then /7b/, method 3. being also applicable to code a DIFFERENCE TO A PREDICTION (=surface). b) Within a plane, HIGH RELEVANCE may be given by a SET OF ABRUPT DIFFERENCES (offsets OFR), selecting contours of natural areas for an ARTIFICIAL VIEWING as well as for future RANGE PREDICTION by defining a FUNCTION CODE LENGTH CLF as well as an ADDRESS CODE LENGTH CLA(x.y) for "displacements", defining BOXES. - The primary boxes may be devided in all (three spatial and fuction) axes (components), using (together or separately) the rules R1 to R3 (FIG. 6).

9.2. Separate relevance dependent hierarchical division of components a) In every coordinate, relevance may be measured separetely, indicating the RELEVANCE DEPENDENT NEED of (a degree of) division. Such separate (axial case dependent) deviding of each address coordinate end/or function component is advantageous, wherever axial parallel structures occur (e.g. static regions along the z-axis). Since axial irrelevance is indicated for the whole OBJECT by 1 bit (division = FALSE) for a certain RUN LENGTH (indirectly by CL) in a certain coordinate, this avoids ths need to devide along that coordinate! b) PREDICTED CODE LENGTHS CL(x,y,z; i,j,k) may be taken es FIRST REFERENCES for DISPLACEMENTS, being correctable bottom-up as well as precisable top-down, defining (hierarchically nested) BOXES to contain all possible values! c) If a picture fades in or out, already relatively extreme valuss of CL give a good reference for a defined object, especially combined with CUMULATIONS, as mentioned above, while the conventionally defined correlation may even indicate maximal z-difference (meaning maximal disporrslationl) at the same place, e.g. when detecting a light which fades out within a dark plane. While imagss of flickering reflecting waves or fire prevent to obtain results by direct correlation measurement, the CL-CORRELATION method will still succeed. R e f e r e n c e s

/1/ DUSCHEK ADALBERT: Vorlesungen ϋber höhere Mathematik, Band 2, SoringerVerlag Wien, 1963, pp. 32-34.

/2/ WO 86/04757: International patent application by BRITISH TELECOM.

/3/ BIERLING M. , THOMA R.: Motion compensating field interpolation using a

Hierarchically structured displacement estimator, SIGNAL PROCESSING 11/86 pp. 387-404,

/4/ ZSCHUNKE WlLLMUT: DPCM picture coding with adaptive prediction,

IEEE TRANSACTIONS ON'COMMUNlCATIONS, Vol. Com-25, No.11, 1977, pp.1295-1301 Description of contour predictions: pp. 1295, 1297

/5/ SONY publications by T.KONDO et al.: a) Adaptive Dynamic Range Coding Scheme (ADRC).

- Picture coding symposium 1986: Range reduction by MIN and MAX. b) T.KONDO: Adaptive Dynamic Range Coding Scheme for Futura Consumer Digitai VTR,

- Source unknown, published (internally?) by SONY Corp.,Tokio, - 10/1988 ?)

1. Range reducing by MIN and MAX: p.219, chapter 1

2. Compressing data from 216 to 25 Mbps: p.223, by

3. Reducing exacthess (of the functional component only) p.222 c) I) HIGH EFFICIENCY TECHIQUE FOR CODING A DIGITAL VIDEO SIGNAL, SONY patent

US-4703352, application filed 17.12.85, prior.: 19.12 (2x) and 21.12.84.

1. ADCR: Range reducing by MIN and MAX: 2, line 1S ff. by also

2. Reducing exacthess 2, line 1 ff.

II) HIGH EFFICIENCY CODING APPARATUS, US-pat. 4,722,003 (2S.1.S3, prio. 19.11.86)

1. Utilizing MIN and RANGE: Summary, 3, line 26 ff.

2. Maximal distortion for decision: 3, line 38 ff.

3. Evaluation of 4 frames: 4, 18 ff, Range number: 6, 55ff for unexact code. d) HIGH EFFICIENCY CODING APPARATUS, pat. applicaticn (EP-0269189 prio. 29.05.87):

1. 3D-ADRC ranges incl.time axis: SUMMARY of the invention, p.1ff. - claim 1

2. Utilizing the frame-to-frame difference (= z-gradient! ), pp. 2,3

- movement detections in a picture block incl. time: cl. 1,

3. Non exact (coarse) range quant ization (2, line 31 ff .) Ref, bage 2

/6/ J. PINDER: Datenreduzierende Codierung von Videosignalen durch lokaladaotive Reduction des Dynamikbereichs. - THD (W.Zschunke) and FTZ Darmstadt, 3.2.88

/7/ W.KEHLER, patent applications for SIGNAL-RANGE ADAPTIVELY REDUCED CODING: a) EP-0091979-A1, 20.04.1982 (EP-Pat.-No. 0091979-81: see claims): Bereichsprädiktives Code Modulations Verfahren mit signaladaptiv reduzierter Bitrats.

1. Multidimensional domains with limited QUANTITY OF SIGNAL VALUES: p.8,S.

2. Object of the invention: "Centering" the QUANTITY between MIN and MAX:

p.9, under 4.1.2. (the introduction was placed at p.S by the EPO) determining an expective range for expected values to pre-dict the range.

3. Centering by at least 2 values: p.3, (3.1), distribution range: p.4.

4. Reducing code lengths according to the range: p.7 (III,5.).

5. Successively achieving (centered) range reduction: p.6, (III, 4.). b) EP-0244660-A2, published 11.11.87 (prio. 10.4.86): Relevanz- und irrelevanzanalytisch bereichsprädiktives Code-Modulations-Verfahren.

1. Generelized multidimensional gradients and displacements: p.10 (1b), p.19,20

- defined in the space of address and function values p.3 (5g)

- utilizing the planar x (y-) and temporal (z-) gradient information, p.7.

- with a "prediction" used as direct and/or statistical precoding p.2 (5a),

2. Too-down reduced ranges and displacements: e.g. p.5

- Bottom-up extended ranges (prediction = FALSE): p.3 (5g), p.16.

3. Hierarchical nesting p.3 (5e).

- of displacements: p.6 (5.5, 2. section), p.13 (3c)

4. Successive CL reduction p.5 (5.5d). c) PCT/EP-01021 (=EP-88-118356), published 18.05.89, priority claimed:

GENERALISIERT BEREICHSPRÄDIKTIVES CODE MODULATIONSVERFAHREN,

1. Code length coding: p.15, 16. - Special successive CL reduction p.19

2. Hierarchical relevance selection (p.14, 2a), with block synchronization by overlapping (p.19, 20) and searching correlations (p.28 ff.)

3. Shared ranges: p.16 to 18 tabls) example range reduced HUFFMAN, p.21 (3.).

4. CL-correlation: p.32 - Empty ranges: p. 17, 32

5. Successively coding multidimensional sharper (or coarser): p.32 (7.). P u b l i c a t i o n :

/8/ W.KEHLER: WISSENSBASIERTE SIGNALANAL YSE UND -CODIERUNG MIT BEREICHSPRÄDIKTIVER CODEMODULATION, NTZ-ARCHIV 3/89, VDE-Verlag, Berlin, pub lished : 21.07.89. P i c t u r e s

FIGURE 1 : Range of a planar area between its extremes MINIMUM and MAXIMUM.

FIGURE 2: Typical linear luminance function of an edge: A simple linear

division selects smaller and larger scales for the quantities EM(ij). according to "dynamic" ranges of the luminance function of a photo.

FIGURE 3: An addrsssing t(i), i = 1,2,3... may select the acress ranges for

previously defined larger and smaller scales. The delay, caused by the system when transmitting an ideal edge (small picture) is given by T. The CUMULATION POINTS HP(i) result in DISTRIBUTIONS EM(ij).

FIGURE 4: A given code length, e.g. CL=4 for the range of 15 PCM-values, is

chosen to select thereby RELEVANT and IRRELEVANT blocks (R/I).

Each time at least one common point P12 of at least two blocks should be included to build BRIDGES for the BLOCK SYNCHRONIZATION.

FIGURE 5: Hierarchical plane division of an area, by BRITISH TELECOM (modified).

called QUAD TREE or RECURSIVE BINARY NESTING (Image encoding by BT). The CONTINUATION PRINCIPLE is utilizing punctual values on the borders.

FIGURE 5: Block with positions of MIN and MAX in the 3D-FUNCTION+ADDRESS SPACE.

OR: Advantageous SPATIAL ADDRESS BLOCK with a large quantity of points.

FIGURE 7: Within monotonuously (not) rising or falling function values or address spaces or at an EDGE, a coded space (function part) may be excluded. The remaining address spacs is continuously diminishing.

FIGURE B: Different kinds of volumes, the first one showing the extremes

MIN,MAX and min,max of two vector components.

FIGURE 9: Following an object using its scales defined by CL and/or DISTRIBUTIONS of its CUMULATION POINTS within bottom-up and top-down varying angles (planes): If a statistically predicted range (box, angle) is FALSE, the angle (box, range) is widened, otherwise hierarchically diminished.

FIGURE 10: Image sequence with static and dynamic areas (white and dark arrows).

All displacsments must remain within a box being measursd and precoded or even statistically predicted and confirmed as TRUE, hierarchically diminishable according to FIG.4, 5 and 6.

Claims

C l a i m s

1. RANGE ADAPTIVE CODING METHOD (RAC) for the range adaptive coding of LIMITED PARTS of = SIGNAL, these SIGNAL SEGMENTS (domains, sections, regions, fields, blccks, parts, samoles) defined by (subseαuently) limited (multidimensional) spacss containing their relative FUNCTION VALUES and/or their relative ADDRESS VALUES, their extremes being used for CODINGS and DECCDINGS OF THE RANGES to define thereoy (subsequent ) INTERVALS or BOXES for the reconstruction of the segmented signal, the said method comp rising:

1.1. DIRECT PRECODING OF RANGES or their CODE LENGTHS CL(i) only, according to the determined (measured) ranges R(i) and/or their HIERARCHICAL CODING (step by step top-down, bottom-up nested codings) of predefined (implicitely/explicitely precoded) ranges, the ranges being defined by their minimum and maximum,

1.2. BITWISE and/or multi-bitwise explicite or implicite CODINGS of, even subsequent, CONFIRMATIONS or NEGATIONS of ranges or its code lengths or by codings of predefined NUMBERS of predefined ranges,

- having now precoded those defined BOXES (ranges) implicitely or explicitely to

1.3. CODE (even subsequently finer nested) SAMPLES or all values contained in the box, by known methods, even succeeeively more and more exact (coarser, then finer), to reconstruct the signal, especially by

1.3.1. hierarchically code-length-defined CODES OF SIGNAL VALUES according to obtained diminished cods lengths, especially range reduced codes of one or more EXTREMES (minimum, maximum), especially for INTERPOLATION,

1.3.2. RANGE REDUCED PULSE CODE MODULATION (RRPCM), or CUMULATION ADAPTIVELY SELECTED scales or other sampling methods.

- especially accomplished by a

1.4. SYNCHRONIZATION of the BOXES and/or thereby now CODED SIGNAL PARTS or SEGMENTS to reconstruct them to the complete or sampled SIGNAL by

1.4.1. ESTIMATING SURFACE DIFFERENCES TO OPTIMIZE ERROR CODES according to the given surface information of the signal segments, to RECONSTRUCT THE COMPLETE SIGNAL by its well ordered now coded signal segments according to the result, especially by CODING THE DEVIATION of the estimation to the real difference,

1.4.2. CODING BRIDGES between samples of the coded signal segments as offsets (differences) Between at least two coded points of different signal segments, espscially using an

1.5. ADJUSTING of the completely coded signal or signal parts, as segments, with

1.5.1. at least one exact (DELTA-/PCM-) code, especially a minimum or a maximum: espacially in a rangs adaptively reduced cods length,

1.5.2. a subsaquent SELF ADJUSTING by correction of impossible absoluta values union exceed the absolute or the reduced scales or their code lengths,

1.5.3. a subsequent SELF ADJUSTING by correcting those impossible absolute values which exceed the possible extremal values, the points 1.1, 1.2, 1.3, 1.4, 1.5, being applicated separately or combined, the method being also applied for multiple components of a signal, especiallly VECTORS with its components, including DIFFERENCES like DISPLACEMENTS, with its code lengths to be also valid to define run lengths in coordinates (components).

2. RANGE ADAPTIVE CODING METH0O (RAC) for the range adaptive coding of LIMITED PARTS of a SIGNAL, those SIGNAL SEGMENTS defined by limited spaces containing their relative FUNCTION VALUES and/or their relative ADDRES5 VALUES, their extremes being used for CODINGS and DECODINGS OF THE RANGES to define thereby INTERVALS or BOXES for the reconstruction of the segmented signal, comprising:

- CODINGS and DECODINGS OF THE RANGES to define subsequent INTERVALS (run lengths, even defined indirectly by CL), BOXES and SUBBOXES for the reconstruction of the segmented signal especially by:

- SHARINGS OF PREDEFINED RANGES(BOXES) to obtain at least two PARTIAL RANGES, to obtain PARTIAL RANGE REDUCTIONS for CODE LENGTH REDUCTIONS of codes, preceding the (number or group of numbers of the) partial range for its values, ths values especially to be coded within partly formerly reduced cods lengths of the partial ranges (within higher hierarchies).

3. Method according to claim 1. or 2., comprising : combinations one with eachother, and/or with other coding methods, as PCM, DPCM, TRANSFORM CODING and other range adaptive and not range adaptive codings, especially with subjectively and/or capacity dependent subjectively coarser or finer quantization and/or sampling of the points of the space, given by addresses and values as points of a multidimersional space, and/or

one of the claimed methods used for, or combined with COMPUTER VISION.

-