CA2106974A1 - Process for compressing video images - Google Patents

Abstract

Abstract of the disclosure Images are approximated by invariant densities of stochastic processes, e.g. by so-called fractals. The parameters of those stochastic processes whose invariant densities approximate the images to be compressed in the sense of a quality criterion to an optimal extent give a compressed representation of this image. These optimal stochastic processes are found with the aid of a sto-chastic optimization process, preferably with the aid of a genetic optimization process. The genetic optimization process makes use, in this case, inter alia of mutation, crossover and exchange of genes for the alteration of the genetic information. With the aid of the process, extremely high data compression factors, typically between 1000 and 10000, are attainable. The process is suitable both for the data compression of still images and also for the compression of images derived from moving image sequences.

Description

q'l ~/1 ? 6 ~

2 1 ~ 4 Process for compressing image data The invention relates to a novel type of process for the reduction of the required storage capacity in the storage of image data in electronic data processing systems or for the reduction of the data transmission rate in the transmission of image data in telecommunica-tions systems or other data transmission devices. Such processes have a great and still rapidly growing economic significance, also with respect to appropriate services in connection with digital message transmission in public communications networks (ISDN), or in connection with the mass storage of image data, for example in medical technology and in other areas of applied research.
Conventional processes reduce the required storage capacity for the archiving of still images and moving image sequences or the data transmission rate for a transmission of still and moving images by a selection and/or combination of essentially the following pro-cesses:
- spatial subsampling - temporal subsampling - run length encoding (eg. CCITT G3) - Huffmann encoding - Lempel-Ziv-Welch (LZW) encoding - hierarchical encoding (quadtrees and variants) - subsampling in color space - transformation encoding with quantization of the coefficients - motion estimation or motion prediction.
Depending upon the image material and the level of quality demanded in reproduction, in this case it is not possible to achieve compression factors in general exceeding 20 (in the case of still images) to 200 (e.g.
in the case of the encoding of moving image sequenceC for transmission over 64 kbit/s lines for the video tele-phone).
In an article in ~roc. of the National Acad. of Sciences USA, vol. 83, pp. 1975 - 1977, 1986, Barnsley 21Q697~

described the principles of a novel type of process, by which compression factors in image data compression of between 1000 and 10000 can be achieved. In this article, use is made of so-called iterated function systems, for the purpose of representing an image approximately as the superposition of a plurality of geometric figures with in most cases a fractal dimension. In the case of the formerly known examples of images which were compressed in this manner (see Barnsley and Sloan in the journal Byte, Jan. 1988, pp. 215 to 223) the encoding has however in all cases been generated interactively by experienced operators. The company Iterated Systems, Inc., which was founded by M.F. sarnsley for the technical realization and marketing of his ideas, is intensively occupied with processes for the automatic compression of images using these methods. To date, however, in this way only dis-appointing and technically unusable compression factors in the order of magnitude of 10 have been achieved.
The object of the invention is to provide a process for the compression of image data, by means of which process the automatic compression of image data is possible, even without the collaboration of a human operator, with the achievement of extremely high data compression factors in the range between 1000 and 10000.
This object is achieved by means of a process for the compression of image data having features according to claim 1.
In this process, the image data are approximated by invariant densities of stochastic processes, where the carriers of these invariant densities, i.e. those regions o~ subsets of the image plane on which these invariant densities assume non-vanishing values, are likewise of in most cases fractal dimension. As also in the case of the Barnsley process, the parameters of those stochastic processes whose invariant densities approximately repres-ent the image are utilized as a compressed representation of the image, or are employed for a compressed represen-tation of this image. However, the decisive difference from the Barnsley process resides in that the stochastic 210697~

processes are found not by an experienced human operator, but by means of an automatically proceeding optimization process. This optimization process seeks that stochastic processes which optimizes a quality function for the assessment of the quality of the approximation of the image to be compressed by the invariant densities of stochastic processes. The values of the parameters of the stochastic process found in this manner give a compressed representation of the image to be compressed.
Thus, for the first time a process has been provided, with which the compression of image data is possible with the achievement of extreme data compression factors within the range from 1000 to 10000 in an auto-matic manner. The process is suitable for the compression of any type of digital raster images, and especially for the compression of digital raster images comprising temporal sequences of such raster images. The image data to be compressed may especially also have been created in the implementation of other image data compression processes, such as for example image data in the trans-formation range of a transformation encoding process, difference image data in the performance of a difference pulse code modulation process, spatially or temporally subsampled images or motion-compensated images. The compression process proposed here for image data may as a result be combined with a multiplicity of known com-pression processes for image data.
The process i8 especially also suitable for the compre~sion of colored image data, binary image data or gray image data. In the event that the image data to be compre~sed are colored image data, the proce~s must be separately applied to each color component. Binary images can be regarded as special cases of gray tone images, whose gray tones can assume only two (extreme) values, namely nblack" or "white".
It has proved to be particularly advantageous for the compression of image data to utilize a particular class of stochastic processes, which arise through randomly controlled sequential execution of affine 21 0697il transformations of the image plane. Each stochastic process selected from this family is unambiguously characterized by the indication of the transformation parameters of the employed affine transformations, as well as by the indication of the relative frequencies with which these affine transformations are executed. A
specified stochastic process of this family, the in-variant density of which specified stochastic process approximates particularly well a given image in the sense of a quality criterion, can be employed for the compres-sion of this image, in that the parameters characterizing this stochastic process, i.e. all transformation para-meters of its affine transformation and all pertinent frequencies, are employed for the compressed representa-tion of this image. The quality criterion employed in theselection of such a process is preferably a suitably selected metric, i.e. a distance measure on the density or image space.
It has proved to be particularly advantageous, for the selection of this stochastic process, to employ a stochastic optimization process. So-called genetic algorithms are particularly suitable for this purpose, in which a population of stochastic processes, whose para-meters form their genotype and whose associated invariant densities form their phenotype, find themselves in Darwinian competition.
Since the process for the compression of image data is associated with a not inconsiderable computing effort, it is in general advantageous if the image to be compressed is present in various planes of resolution of a pyramid of resolution, and if the resolution is increased stepwise with the progression of the optimiza-tion process which selects the stochastic process employed for the compression.
Advantageous further developments of the inven-tion are evident from the subclaims.
In the text which follows, the invention is described with reference to a preferred illustrative embodiment.

2.1 ~

The invention is based, by way of principles, upon two quite different relatively recent mathematical methods: on the one hand, the theory of iterated function systems, and on the other hand the theory of genetic algorithms. Since both methods are not necessarily familiar to the average person skilled in the art in the field of image data compression, but are essential for the representation of the process according to the invention, in two introductory sections these two funda-mental mathematical methods are described so far asrequired for an understanding of the process. However, in principle all methods and terms required here can also be inferred from the publications by Barnsley in 1986 or from the book by Goldberg: "Genetic Algorithms in Search, Optimization, and Machine Learning,~ Addison Wesley, Reading, MA, USA 1990.

Iterated function systems.

An iterated function system IFS comprises a set W of affine mappings or transformations w(i), where i =
1, ..., n as well as an equally large set P of relative frequencies (or alternatively probabilities) p (i), where i = 1, ... n:

W = {w(l), ..., w(n)}
P = {p(l), ..., p(n)} where p(i) 2 0 (1) and p(l) + p(2) + ... + p(n) = 1 An affine mapping w(i) is a linear transformation of the image plane into itself, which transformation maps each point x of the image plane into the point w(i,x) of the image plane in accordance with formula 2):

w(i,x) - A(i) . x + B(i) where a(i) b(i) e(i) A(i) = , ~(i) = (2) c(i) d(i) f(i) in this case, A(i) is a 2 x 2 transformation matrix - 6 _ 2106~7~
appropriate to w(i) and B(i) is a translation vector appropriate to w(i~.
The ~et of the affine transformations forms a group in the algebraic sense. If affine transformations executed sequentially, then the result is, in turn, an affine transformation. If affine transformations w(i) in a random sequence are executed sequentially in each instance with probabilities p(i), then the result is a stochastic process, whose properties are dependent both upon the parameters A(i), B(i) of the affine transforma-tions and also upon the probabilities or relative fre-quencies p(i), with which these transformations are selected. Subject to the condition which is represented in formula (3) ¦A(1)¦P(1) . ¦A(2) ¦P~2) ... IA(n) IP(n) < 1 (3) in which the product of the determinants, raised to the power of the relative frequencies p(i), of the transformation matrices A(i), must be genuinely smaller than 1, a stochastic process of the type represented here possesses an invariant density, i.e. there is a function on the image plane, that is, an image, which is converted into itself by this stochastic process or iterated function system.
The carrier of this invariant density, i.e. that region or subset of the image plane on which this density is different from zero, can be generated by the following simple experiment:
To this end, the fixed point of one of the mappings w(i), i.e. a point which is mapped on itself by the mapping w(i) is selected as starting point x(O). To this starting point x(O) there are applied in succession the mappings w(j) with the relative frequencies p(j) and the result of this i8 a set of points in the image plane which covers the carrier of the invariant density of the stochastic process or iterated function system appropriate to this parameter the better, the more this iteration proces~ is repeated. The carrier of the invariant density of the 7 21Q~971' stochastic process is in this case generated as an image.
This carrier is also designated as attractor of the iterated function system. The condition described in formula (3) is designated as contractivity condition.
Each point of the attractor is in this case produced with a relative frequency of the stochastic process, which frequency corresponds to the value of the invariant density of this stochastic process at this point. The entire attractor is invariant under the stochastic process which corresponds to the parameters which are given by the sets W and P respectively.
Since the attractors of such stochastic processes or iterated function systems usually possess a fractal dimension, their images are usually also designated as fractals.

Genetic algorithms In recent times, so-called genetic algorithms have increasingly been employed to solve difficult optimization tasks, and especially non-convex optimiza-tion tasks. An introductory presentation of the field ofgenetic algorithms may be found, for example, in the book by Goldberg: "Genetic Algorithms in Search, Optimization, and Machine Learning", Addison-Wesley, Reading, MA, USA
1990. In these processes, specified principles which led, in the natural evolution according to Charles Darwin, to the evolution of the species, are taken up in order to optimize technical systems or processes. The most import-ant principles of evolution are explained below using the biological nomenclature, to the extent that this is necessary for an understanding of genetic algorithms as they are employed to carry out the process according to the invention:
1) Each individual is characterized by a genotype and a phenotype. The genotype is given by the sum of the hereditary elements, and the phenotype by the physical characteristics and the behavior of the individual. In this case, the phenotype is almost exclusively determined - 8 _ 2 1 06 9 7 by the genotype.
2) In the reproduction of individuals, the genotype is passed on. The genotype of the descendants is modified by a few processes which are subjected only to chance and in particular are not dependent upon the phenotype:
a) mutation by incorrect copying of the genes or externally triggered processes;
b) genetic crossover;
c) mutual exchange of individual genes deriving from father and mother;

3) Individuals are characterized by a specified degree of adaption ("fitness") to their environment. The degree of this fitness is in this case determined only by the phenotype of the individual and the environment itself;

4) Individuals who possess a higher degree of fitness have a greater number of descendants than those with lower fitness (differential reproduction).
In terms of the result, these mechanisms of evolution lead to a fitness of the members of a popula-tion for the environmental conditions which grows from generation to generation, with which the less fit indivi-duals are displaced by those of higher fitness. A genetic opt;~;zation process is understood accordingly as referr-ing to a stochastic optimization process, i.e. an optim-ization process which is controlled by chance, in ~hich a statistical ensemble of suboptimal solutions of the optimization problem, represented by a population of individuals, is subjected to certain changes, controlled by the mechanisms of biological evolution, with the objective of obtaining an altered statistical ensemble of suboptimal solutions, the members of which are charac-terized by an improved degree of fitness, i.e. by better values of a quality criterion.
In the text which follows, the process according to the invention is de~cribed in part using the biologi-cal terminology, since it serves for better understanding. In this case, the following correspon-dences exist between term~ of the biological terminology 2~ O~g7'~
g on the one hand and the theory of iterated function systems or stochastic processes on the other hand:
Genotype - Parameters of an iterated function system or of a stochastic process Phenotype - Invariant density of an iterated function system or stochastic pro-cess Individual - Member of a statistical ensemble (population) of stochastic processes or iterated function systems Fitness - Quaiity of the approximation of an image by the invariant density of a stochastic process Performance of the process for image data compression In the text which follows, a possible implementa-tion of the process for image data compression is des-cribed with reference to a preferred illustrative embodi-ment: in the first instance, an initial population of K
individuals having a standard genotype is generated. One possible way of achieving this is to select a genotype whose phenotype is selected to be a uniform coverage of the entire image plane with N pixels in width and M
pixels in height. These invariant densities which assume constant values everywhere within the image plane are, for example, generated by an iterated function system which is given by four affine transformations with parameters and relative frequencies according to Table 1:

i a~ bl cl d~ ei fl Pl 1 0.00 0.25 0.00 0.25 0.00 0.00 0.25 2 0.00 0.25 0.00 0.25 N/2 0.00 0.25 3 0.00 0.25 0.00 0.25 0.00 M/2 0.25 4 0.00 0.25 0.00 0.25 N/2 M/2 0.25 Table 1 Since all individuals of this 1st generation have the same genotype and consequently also the same 210697~

pheno-type, there is no distinction between them in fitness. The 2nd generation now comes into being by "crossing of individuals of the 1st generation; in this case, mutation, crossover and exchange of genes from father and mother (in each instance with a specified probability of occurrence) alter the genotype.
The individuals of the second generation will therefore differ from one another in their genotypes, and thus also in their phenotypes, and accordingly in their fitness. Henceforth, in procreation those parents who have a higher fitness in comparison with the remainder of the population will be preferred. From generation to generation there will accordingly arise, on a preferen-tial basis, descendants whose genotype was formed from the genotype of the fittest individuals of the parental generation. In each instance, only a specified limited number of the individuals having the best fitness will be accepted into the population of the next generation. In this way, an explosive growth of the population is prevented. This may take place, for example, by a strict limitation of the number of individuals per population.
After a sufficiently large number of generations, i.e.
when the approximation quality - assessed by the fitness - of an image has reached an appropriately high value by the invariant densities of the members of the instan-taneous population, the genotype of the individual (i.e.
the parameters of the iterated function system) with the best fitness will be employed as a compressed representa-tion of the image.
The variation of the genotype is achieved by meanR of the mechanisms ~mutation , gene exchange" or "genetic crossover . To this end, it is in the first instance necessary to indicate probabilities for the occurrence of these two mechanisms in the generation of a descendant: the mutation rate, the gene exchange rate and the crossover rate. In the event that they occur, the respective processes cause the following:

21~697~
~utation: sy mutation, one or more of the parame-ters a(i), b(i), c(i), d(i), e(i), f(i) and - in the event that gray tone or col-ored images are to be encoded - the rela-tive frequencies p(i) of the iterated function system are altered. This may happen, for example, by a random walk process. In this case, attention must be paid to the unaltered observance of the boundary condition of the contractivity (formula 3).
Crossover: By crossover, the number n of affine transformations which characterize an iterated function system may be altered.
The first j affine transformations of a parent are combined with the last k affine transformations of the other parent. In this way, an iterated function system is formed with n = k + j affine transformations. In the event of a crossover, it is of course necessary to ensure that the sum of the relative frequencies is subsequently renormalized to 1.
Gene exchange: One or more of the parameters ai to p~, which the individual has accepted from one of the parents, are replaced by the corresponding parameter or parameters of the other parent. In this case also, where appropriate, the set of probabil-ities Pi must be renormalized.
The set of individuals of a current population can be kept constant or alternatively can be varied according to the progression of evolution (optimization).
Thus, for example, the number of individuals of a popula-tion may be increased in order to increase the bandwidth of the gene pool in the event of stagnating fitness values. On the other hand, it is appropriate to reduce the size of A population in the event that development is - 12 - 21~697~
progressing adequately faster, in order by this means to reduce the computing effort. In any event, only the best individuals of a population are accepted. In this case, two modes of procedure are possible for the temporal development of a population:
Synchronous evolution: from the population at time t, having regard to the differential reproduction, a specified number of descendants are grown. Into the population at time t + 1, there are accepted a corres-ponding number of the best individuals, who may originateboth from the new group of descendants and also from the old population (i.e. from the older generation).
Asynchronous evolution: from the population at time t, having regard to the differential reproduction, one descendant is generated. The latter immediately becomes part of the new population if his fitness is adequate. In this case, in certain circumstances one or more individuals with the weakest fitness are removed from the population, in order to match the size of the population to the desired value.
The technical suitability of the described optimization process for image data compression is decisively dependent upon the selection of a suitable fitness function. The latter assesses the quality of the approximation of an image by the invariant density of an iterated function system or of a more general stochastic process. In this case, the fitness function, i.e. the quality criterion, must, like any cost function, satisfy the customary continuity and monotonicity conditions.
Relying upon customary modes of procedure, it is for example possible to make use of the sum, ext~nded over all image points of the image plane, of all squares of differences between the gray tones of the image to be compressed and the values of the invariant density. The process may however in certain circumstances be improved, if in this case squared differences in those image regions which are visually critical are multiplied (in the center of the image or in regions with high contra~t) by for example, h~gher weighting factors.

~ 13 -The compression of an image can additionally be assisted by the use of pyramids of resolution: in this case, the image to be compressed is fed, in different planes of resolution of a pyramid of resolution, to the optimization process to seek the best iterated function system: the fitness of the first generations of the evolution is in this case in the first instance tested by means of a coarse image resolution (e.g. using the third step of a quadtree representation), or for example by means of an image which has been subsampled by an appro-priate factor. In the case of the following generations, the resolution can be improved at appropriate points in time, e.g. when the fitness values vary only slowly, stepwise up to the resolution of the original image. In this way, it is possible to achieve considerable savings of computing time and thus a more rapid performance of the process.

Decompression of a compressed image The decompression of an image compressed by this process is actually a simple matter: for this purpose, the invariant density of the iterated function system or stochastic process employed for the compression of the image is simply computed. This takes place, for example, by means of the process which is presented in the section "iterated function systems" and in which - proceeding from a starting point in the image plane of the attractor and thus the invariant density of an iterated function system by repeated application of the affine transforma-tions appropriate to it with the relative frequencies appropriate to it, to the created points of the image plane - the computation is made. The aforementioned company Iterated Systems Inc. has developed hardware with which images in the format 256 x 256 image points can be reconstructed in 1~30 second from their compressed representations in the form of the parameters of an iterated function system. In this way, it is shown that the image data compressed by means of this process can be 210 ~ 9 14 decompressed at a speed which permits the application of the described process for the decompression of temporal sequences of compressed images in real time.
Both the compression of image data and also the decompression of image data can easily be performed in parallel and with low expenditure on hardware. In the case of image decompression, by way of example the computation of a random number, two multiplications and three additions are required per iteration of an image point. In the case of the performance of the compression, it is possible to have recourse to standard image pro-cessing hardware for the computation of the quality function.
In any event, the performance of the image compression with appropriate approximation quality does in general require substantially greater computing times than the performance of the decompression, so that the described process appears to be particularly suitable for application in those cases in which the time employed for the compression of the image data is not particularly critical, as long as the decompression of the image data is possible sufficiently rapidly, for example in real time. Accordingly, the process is particularly suitable for application in the compression and decompression of medical image data or other image archives.
The process can also be carried out with the aid of a computer program which is attached as annex A to the present patent application.

- 15 - 210697~

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::-- Cd _ -e:e:.-:.d..:s .:~ :..e :FS i~:_?a~__::_es d-.r.
:: :-.e : - :a::ve ?:C?dr: ::y c:s::_~-: c.-Ise:' la-e' I: S-rie: :.e-'FS) :) 1.--.dX - . ~
aDs ~ )a:e' I: ;-a :`ie-:~;) .) ~a:e' ~:-s-~ :-e-:.-;S
1~ Id:e' I:FS-D :.e-:FSi s) id:e' (:FS-: .-e- .~I
~? sn ~- I:d: :-?::Ps) ~d:e' ~: S-:e: :-.e-:Fs) : ~~: :?s ) ~:..:. :)) ~se:' :-?::?s-rc:- ~:a: :-?:Ps)) ~se:' ~iFS-~?::? :.~e- FSI
n..aF:a~ a-.~-a Ixl (/ x c-prr?s-r.r:~
~:-: I:eve:se C-?-cps~
Ida::.-es (i 2'i) ~ 'al i~e:a:ions 'c: x a.... C ~ - d a ~ S--i?-po...: :.ne-:Fs)) ; IDe~:e:: _alc a ':xeC p~ :' r..e ::~
:ne-'FS)) ~Ce'_r. ~ut-t--lFS (:he-7Fs) :: --_--_--_--__________________ :; selec:s a ?a:a2e:e: anC rep:aces s~
:: Dy a .~c-a~eC va'_e. ?ay:r.3 a:_ei~ion :o :; :ne cDr.s:rasr.. s-s-a!?ha<l ;; r.-_:a~:o-. Dy arcc.. ~a:k c' genes ;: WCR'~S C~i v F5R ~FS ^-F~ k:nC-:c~
;: ------------------____________________ ~r.er (c (-a~c~. :.0) ~-o:a:e-?-i?~) le:- ((7eie (r.:h (:ar.cr..-. (lens:~ FS-?-!:s: :`.~-;FS))) FS-?-::s: :-e-;FS) ) ) ~ ?a: I:ar.Dr-. 5I~) ca 5e par o ;sca1e 'ac:r.:
se:' (S::s: Se-.e) (-ax C (~ (~;:s: ~ene) (- -3.1 (:a-.Cc2 0.2))))) se:' (se-:.-c -er.e) ~-:r. ~secor.d 7e.~e) (/ (- ('::5: Sene) ('::s Se.ne) ) ) ) ) ) (: ;y-s::e:c`.:r7 (se:s (sec:~._ ?e-e) ~-ax 0 (~ (se~ C Se^e) 1- -;.l ( ar.cri ^.2)))1) se:' ('::s: -,e^.e) (-:-. (~::s: ~,j;er.e ~eX?: (seC^nC ;e..e) -O.j))) 2 ;snea::-.7 se-' (:h_:: ;e-e) 1- -:.S (:a^cro :.C)))) 3 ;:o:a::or s~ .. ;e.-e) I=:c (~ (:ol.::.- ger.e) (- -:S (:-r.:o-. 31))) 360))I
l~i ;x-::a.~sla:ion ~ :r se.~e) (- -2 (:arco~si S))l) (5 ;y-t:ans`a::or (:~.:' (:_::`. ;e-.-) I- -2 (:anco~i ~ I)~I)) :.-e-!FS) ;:e:_:n :..e -.::a:eo :__;

:e' r ero~ov-r-~i~S ('a:.^e: -.o:`.e: C5.:
;; ------------__________________________ ;; p<:'o:-.s :ne eq :va!~ o' a ;e-.-::c ::ossove:
~ v--n th- p-::S:s _: :-.e cvo ;FS i..s:-nc-s.
:: chilC e-n oe also :-:.e: o: .-.o:.~ :sel:
~ :s: ?a:: c' ?-`:s: :s :a~ ':o-. 'a:^.e:
:: (- :ota` O~ S-S?::C- e:-re~-:s)~ - se:ond :: '::~ :`.- ..o:hi-: Is:a:: r.; ~ r.:h r-s?`-ce .-~-~enes) :: ----------_______________________ Ic-s-r.~s ~cDpy-::-- ll.S-p-!is: ~th - :l ~ ~ ~ :d-i'-_:: Sen-s ~v~-n 1< ~:aiCoi-i '.0) '::ossov-r-pro?') I~-geres ~copy-:r-e (;F5-p-':st r..o:h-:~

~ 1 8 - 2 1 0 6 9 7 '-.~-s_ -e ~ g--:- ^-~e-es :--s_. :~ ~.a~ . e..-:- ---e-ss.)) :^ a:e :--e-.es se:_ - a:e ~ ---: f-s- ::e ? ~:e)~
~se:. ---e-ss 1C:~ -s? :e ~- e^es~
~: ~> -~s?:::e C~
~:~ a^d ~ d:e .. -cenesl :s?i::e ~e-es ::;e:r.e:
se:g :--e^.es .--5e-.esl11~ :d:op 'a:.~e:'s senes a ::~e:-e ~se:' ~:PS-?-_:s: c-.::d~ ~- eres~
_.-_ :~) :re:~r.- :he ?oss_a'y -:::' e- :-_e'... ~xch~ns~-IFS ~ -.e- .-~ er c-.::d1 ;: ?e:'-:-s :.~e ec~ :a e-.: _' a ge.~e erc.~dnge :; De:~ee.~ :^e p-::s:s c' :..e :~o ;.S :.-s:ances.
~ :'d :an De a:s~ 'a:^.e: o: -::.~e: ::sel' :: --------------------------___________________ .-e-. ~< Irancc- '.0) ~exc~ Se-?rO?'~
:: -- :h:s ' ^.c::on :5 c_~:er:!y only a 5 ..L' I
C.`:!d) ~ce':~ n-v-I~S ('ather ~o:her) ~:e: ~1C ~ld ~a~e-'.S))) :ossove:-i.S 'a:ne: ~.o:'.e: :h~ld) s:ve ch:ld a set 0' Se.~es ~e~c~ange-~.5 fa:~e: rlc:ne: ch:Id) :exchange genes -.::a:e-~.5 ch'!-) :.. ::a:e :he Ser.es 1se:_?-:r5 cn~!d))) :~sn:cSenes:s~ :e:u-n r.e~ -- :
Ice' - lt-r~t--I~S ~:he-;.5 -.) zec:are ~:n' re .S--.a?-?c:~._) (:?:~ 2e lspeed 3) (safety C))) c:::.-.es ~
1: 5-.-.a?-?^:..: :-.e-;.5))) ~Ce' n ~ et-IFS ~) :: ------_________________________ :: se'ec:s an :.S ':c~ :.e ^~^::a::on ac:c:-:.s :o ::s f::.-ess :: :-.-:v:C_a!s are C:a~r. ?-efe:a_:y ':o~ :~.e ':::er ?d:: c' :-.e :: _o^ la::c-. I:-.e e-.d c' :~.e ::s: IFs-?^?~
:: _________________________________ ~-.:.- ~-`~c: ~ 5-pc?-s:2e~
~ exp: ~:d.-:-.- ~ C.2;1)1 ' --5-^:?' ::e' -. t-~-IFS ~:.-e-I~5 :: ----------_ _____________________ :: exa. pie ':: a c:^.^a::s--. :~ a.~ S :-aSe ~::h :.~e ;:~e-. :.-aSe :: :n a::ay ~:T.age~ ~:ses a c:?y cf ~:.-.age~ :n -eas~:e~) :: ::era:e- :~S :.c:e-e-: '::-.ess 'o: ac~ ^o:n: o' :.~e :T.age :: :ha~ !s h:: cy :-e ?:~e: va:.e :hen s~o::ac: l ':C.T. :ne p:xel va: e :: :n:~ tavc:s :he ::..re-.::a::o~ o' ~aFoed po:-.:s :n dar~
ar--~ ' h~ :--Ç-, :_: '- 5ar~ - s?:-ads :.e po:..:s :c e-- :r.-: a:- -:: ~e: :^v-:eo eno_g.~
:: -- -- -- -- -- -- -- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ~:e: ~:au~.: C1 pc:. :~
(: o:: ~- s ~ :: c . s - ) ~s--:q pc:.~ s---~-~-pc~ sl ) (ir.c~ co-:nt ~a~ eas.re' :aCd :eCuced p:xe! va: ~ a: :::-.:
-.~x O (-.:n ~e-s-_:--vid:h' Ic~: ?:-:)~) I.-ax 0 1-:-. -.-as::e-he;;`.:- Icdr pc:n:))))) 10-~ su:e- :d-c:e~er.t p;x-; va`:e l.-ax O !.-:~ ~-as_:c-v::t.- ~ea: po:..:))) (-ax O ~.-.:n -.-asu:--he.~.lt- (cd: poir.:1 :: - - - -- r- ~ s L r~ -IS--:;p; ~9--) : :esto:e :!~e :.T.~9--s-:' I:'S-'::ness ~.ne-:.S~ :c~.:1)) - 19- 2106~7-1 ?-:~'5- ' :: _- es :.-e --a~- e~e ~-a_e :.-d: :s :: _e ~c:e-:: -.:o :.ke d-:ay -eas -e- se~ :es:-:~d e :: -- -- -- -- -- -- _ _ _ _ _ _ _ _ _ _ _ _ _ _ ~eS ! 1~ 2_e-v:=~
i-_-:-es ( 1:- :-a e-ne~
(Se:' ~a-e' -e2s_:e- : ;1 (2:e' :.-a7e- : ))1~
-e'~J~ 1n1t-1~-g- 11 ___________________ :: a-c_::es 2.. :=2se ::2.-5'e:5 ~ o d::~y :-2se-:: ca!c_ a:es :.~e o_:_=al va! e o' :.e :~S-'::r.ess :: va!ue ;.~a: Cd.- oe :eac~.e- v~ :e:a::c-.s- c' :: an op::..a! i S rd??:n3. ?u:s i: :-.:o c~::.Ta1-': .-ess-:: (:.~:s oe?er.cs o.~ :ne alsc:~ sed 'c: :~e co.-.?a::so.n :: c~ :~e :.-age v::~. an !FS-:cd:ns (i.e. on :.~e 'u..c::o.. :es:-:.-.d-e~
:: ----------------------______________________ r.::~
-e'J~ ~vol~-IFS-popl (.~:c~es -~ eSS ~key ne~) :: ---- -- -------- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ :: Do~..ea:y canC:::or.: ccns:an: ?o?u-a:ion cS IFS-?c?-s; e- nd:v:- 2:s :: async.-~ o~s evc_-_::c-.: each c''s?::-.s :..~ed a e!y Deco~es a -.e-.ce:
:: o' t`e ?op_`a::cn :: ------------------------_____________________ le: (c::rene- FS
...:n-'::ress 99999) ~ax-~ ess) v.en nev :se:u? a r.ev ?o?_:a::c.
~se::p-:sa~e) ~se:? -e-.e:a::c-.-^c -.:- O ::.- s is ac:-a!!y :`.e -. .-.De: c' ?:_- :e- -'';-. ---FS-p?' ~
c~ .es 1: ;FS-?op-s re-) se:q c_::e-.:-:FS Ise::?-:FS
.-a~e-:~S :?-!:s:
' ( ~ C. S ~ C
0.5 ' ~ ~ C o~) ^.; 1 ^ i` 64 ~) .; : ~ ~ 6~ 6;~
~-es:-:FS -:::en:-'FS) :s.. ~_::e^.:-!FS ':FS-?Cp'~)) I::_p I:~.c' ge--:a::o.--:_J.. -I
ls-:q ::::e-:-~.S (-.e~-:~S ~se'ec:-:FS) :::ea:e r.ev :FS
~se:e-:-lFS))) :esc-..S c_::e-.:-:.S
~s-cq .~ ess e :.~ -.:.-'::ress l!F5-'::.ess cu::e.-:-:~SIIl ~vlen ~>- ~:FS-~;:.-~ss c-_::enc-!FS) :c~::en: FS ~s ':::e: :na-. ~ed~es:
:, s-'::.-ess 1'::5: ~-Fs-po?~) ) ) ~P~? '!FS-pe;-~ ;re.tove :.~e veak-s:
1?'-~' c-~ -.:-!F5 :FS-?c?~) ::.nse:: :~.e nev ISe:~ -FS-pep ~s::- ~-FS-pop~ -c :key '!FS-'~ sslll s-:q .tax-'::n-ss l!rS-'::~ess lc-r ll-s: ~:FS-pop~)))) ~v~e~ .a~-' :^ess ~.:3.~es:-'::Aess) rn~
:d sene:a:_o~ o:n:- i S-po?-s:2e-~ 0 I'o:.s.~: s -~-A -~ -A -.2F -A~

5-~ :o^.-:o~:.:-_ ._~ ^e5 'FS-'::-.-ss l'::s: 'FS-po?~
c::~ -l!a.-.~J~ s~ :~v~:~3- ' P~?':
l- x l.FS-'i:ne5s :'s))) 'IFs-p:?~ :in:: a'-va!u- O) ! S-pc -S:S-' s.~x-S':. ~ss) ~ ss 999999))))) - 20 - 210~97'~

- - - .volv.-I~S-pop2 ~ es~ ess i<ey .1e~) :: -- -- ------_----__ _______ __________ ~ -a.y c:...... c ~ :a..... s:a.. : ?cc ~ c' ' ss-?c^-s:~e~ :: a s.
:: ;,^:~ ~.-c s e~-- :::-: -.c- :e :.S-?:~-s :e :'~s.-~
:: -:? a:~ :es: eac-. ~ee? ':.-S-_c--s::e~ oes: _-. v a a s ~^a-e-.-s --:: -e~- :''s~.:-.;) :^ :.~e po-'a::c.-:: -- -- -- -- -- --_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ e: ~c ::e.:-:.-S
l- .-'::.-ess 3S3S;~
-ax-'~ ess) .-e-. ~.e~ :se::? a .~e~ -cc a~
(se: ?-~-a;e) se:q ?ene:a~:c^-co~n:' O
~:- S-pc^~
~C:::..es ~_ :.S-?cp-s:2e-) ~se:q c ::e-.:-;FS ~se~ p-:FS
17.dse--FS :?-!:s:
.5 1 0 0 0 O) / O.S I O O 0 64) C.; 1 0 0 64 O) ~ O.S ~ O ~ 64 6C~)))) l~es~-;^S cc::er.:-iFS) ~p~sh c_.ren:-;FS -;FS-pop-))) ~se~q ~:FS-pop- ~sc-~ ;FS-po?~ ~'< :key ~''FS-fi:~.ess)) ( loop ~:-.c' gene:a: on-co~r.:-) (se~q ~o''sc::~.gs- '()) ~cc::.. es ~ FS-pop-s:ze~) :cr~a:e an c''sp:ing pc~_la:::-.
~se:q ~.:.-'::r.ess 9g93S9) :: --- c:ea~e a nev :FS
~sesq c:::e..:-:FS ~..e~-:FS ~se:ec~-:FS) ~seiec:-:FS))) ~:es:-;-S c ::e-:-:^S) (se:c, ..:n-'::-.ess ~sin r~ :ness (;FS-':~ess c :-er.:-:.5 ~?Cs- cc::e-:-;FS ~o''5?:i~gs~)) Ise:c. ~C''s?::-.7s- (so:: ~C'~s?::-,s- 4~< :~ey ':FS-';:-ess~
:: --- -e:a~r, :.'e bes~ c' bc:.' ?a-en~s o: c-.:_Cs ~se;5 ~;FS-?c? (-.: cC: 25 I.~:se 'lis. ~o~sp:i~Ss~ '-'S-PC?' ~< :~cey I~'FS-~ ess))I
se:q ~ax-'i:.-ess (:FS-~ ess Ica: llas: ~S-?OD~
~'~:.-.a: : ~ -A -A -A -, 2F -A"
gene:a::o..-co_-.:-:-.ess :.~in '::3ess o' c ~5_ -.7 I:~;-'::-.ess ~'::s: ~ S-?c^~)) : -:: '::-ess c' ,C_,C '3::--ec _e 'lla.-._ca (x :'s) :ave:age '::ness c' Co ~- x (:FS-'::ness :'s) ) ) ~:.;-_:p~ ::-.:::ai-va' e O) -FS-pc?-s:2e-~ax--::.~ess) ~h-n 1>- m-x-'::-ess ~:;.'es:-'::ness) (:e: :r.))))) !ce~ ncod--l~av- Iscp:i:na! ~ el::y 0.9)) ;: -- _______________________________ :; volv-~ an .'F5 ?:p~l~:_cn ~n::l a a~s:r-d coc;.~q -_ai y cs ~ a7- in ::-y ~s.-.-;-~
:: :s :e-c.~o ~::oe`::y~ ea~s pe:'e~ a:c~) :; ------------____________________________ ~ S-) :s-t~p ~:.~-9-~ ~op~ l-'::.e-s~
IS-:; '::-:a:ions~ ::00) :oe~er-.ines spe-d .-o _ a:::y r' ~:: -.
I C: J ~ 5t3:: :FS v~ :h a '::n--s goal o' -A"
~' :- ::Y ~:?::~a!-'::n-ss~) ) 5-.~ cn ~o:s: -:.n avg ~x :_:ness-') ev: ~ F5-popi 1~ r.d-li:y op~ a!-':~.~ess-)

Claims (10)

Patent Claims

1. A process for compressing image data, in which process - images are approximated by invariant densities of stochastic processes;
- these stochastic processes belong to a family of stochastic processes whose elements can be identified by indication of the values of specified parameters;
- the stochastic processes employed for the compression of an image are found with the aid of an optimization process which optimizes a quality function for an assess-ment of the quality of the approximation of this image by the invariant densities of stochastic processes;
- the values of the parameters of the stochastic pro-cesses employed for the compression of an image give a compressed representation of this image.

2. The process as claimed in claim 1, in which digital raster images are compressed.

3. The process as claimed in one of the preceding claims, in which digital raster images of a temporal sequence are compressed.

4. The process as claimed in one of the preceding claims, in which - the family of the stochastic processes is characterized by a number n, which indicates the number of affine transformations w(i), i = 1, ..., n of the image, from which transformations each element of the family emerges by sequential execution of the affine transformations w(i) with relative frequencies p(i), and - each stochastic process of this family can be identi-fied by the values of its parameters, namely the trans-formation parameters of the n affine transformations w(i) as well as the relative frequencies p(i).

5. The process as claimed in one of the preceding claims, in which the quality of the approximation of an image by an invariant density is assessed by means of a quality function which is given by a metric on the density space.

6. The process as claimed in one of the preceding claims, in which a stochastic optimization process is employed.

7. The process as claimed in one of the preceding claims, in which a genetic algorithm is employed as stochastic optimization process.

8. The process as claimed in claim 6, in which genetic changes are effected by mutation, crossover, gene exchange or a combination of these mechanisms.

9. The process as claimed in one of the preceding claims, in which the optimization process proceeds from a stochastic process or from a plurality of stochastic processes, whose invariant densities are constant within the image plane.

10. The process as claimed in one of the preceding claims, in which the image to be compressed is present in various planes of resolution, e.g. a pyramid of resolu-tion, and in which the resolution is increased stepwise with the progression of the optimization process.