CN109360199B - Blind detection method of image repetition region based on Watherstein histogram Euclidean measurement - Google Patents

Blind detection method of image repetition region based on Watherstein histogram Euclidean measurement Download PDF

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CN109360199B
CN109360199B CN201811197053.1A CN201811197053A CN109360199B CN 109360199 B CN109360199 B CN 109360199B CN 201811197053 A CN201811197053 A CN 201811197053A CN 109360199 B CN109360199 B CN 109360199B
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histogram
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杜振龙
叶超
李晓丽
马芸
宋国美
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Nanjing Tech University
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    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
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Abstract

The invention discloses a blind detection method of an image repetition region based on Watherstein histogram Euclidean measurement, which comprises the following steps: step A, dividing an image to be detected into a plurality of small blocks; b, calculating the Wtherstein barycentric coordinate of each small block obtained in the step A to obtain a Wtherstein barycentric coordinate set of the image to be detected; and C, selecting the block with the maximum Wtherstein barycentric coordinate measured by the Euclidean distance (removing the block per se) as an initial block, and searching the suspected repeated block by using a patch search matching PatchMatch algorithm until a repeated area is searched. Compared with the prior art, the algorithm can accurately detect the repeated objects in the image, and has better robustness.

Description

Blind detection method of image repetition region based on Watherstein histogram Euclidean measurement
Technical Field
The invention relates to a Wtherstein image repetition region blind detection method, and belongs to the technical field of image processing.
Background
With the rapid development of information technology and the popularization of intelligent electronic devices, it becomes easier for people to acquire and modify images. Meanwhile, the appearance of various image modification software provides convenience for random tampering of image contents, and also brings huge challenges for image use in media, news, criminal investigation, judicial law and other aspects. Therefore, there is a need to develop image detection and forensics methods and techniques that make images convenient for people's life while providing a secure guarantee of content authenticity.
Copy-paste image forgery is a common image forgery means, and copies and pastes a certain part of an image to other areas of the same image to achieve the purpose of hiding or adding new content. The current counterfeit detection method for duplicated moving images includes: traversal searching method, image block autocorrelation matrix method, image block matching method and the like.
Firstly, partitioning an image to be identified by an image block traversal search method, taking each image block as a retrieval template, and traversing the rest image blocks to judge whether the image blocks same as the template exist or not; and if the similar image blocks exist, increasing the size of the image block, and searching again until the identical image block cannot be searched. The method has a simple principle, but has large operation amount and poor noise robustness.
The image block autocorrelation matrix rule detects a repeated image area according to the fact that the copied and pasted image block has high autocorrelation. The method comprises the steps of firstly partitioning and setting a self-correlation judging threshold, searching all image blocks in a traversing mode, and if the image blocks exceeding the set threshold are searched, determining that copy and paste operations exist among the image blocks. The algorithm has a smaller calculation amount than that of the traversal method, and the defect is that only the condition that the size of the copied sticking block is small can be detected.
The image block matching method expresses image blocks by using matrixes, and compares all the image block matrixes to find out the same image block. The detection effect of the method is good, but the calculated amount of the algorithm is O (m)2) (m is the number of image blocks) and, in addition, the block feature dimension is high, resulting in a large algorithm space consumption.
Disclosure of Invention
The technical problem to be solved by the invention is to overcome the defects of the prior art, and provide a blind detection method for an image repetition region based on the Euclidean metric of a Wtherstein histogram, so as to detect a copy-paste counterfeit region in an image.
The invention discloses a blind detection method of an image repetition region based on Watherstein histogram Euclidean measurement, which comprises the following steps:
step A, dividing an image to be detected into a plurality of small blocks;
step B, calculating the Wtherstein barycentric coordinate of each small block obtained in the step A, so as to obtain a Wtherstein barycentric coordinate set of the image to be detected;
step C, according to the Wtherstein barycentric coordinate, from the beginningStarting blocks, calculating | · | | | non-calculation between blocks except self and other blocks in turn2Norm, finding out the block with the minimum distance as the initial detection block according to the norm measurement distance; after the initial block is determined, searching image blocks around the initial block by using a PatchMatch algorithm, expanding a search range and positioning an image repetition region;
and D, outputting a repeated region detection result of the image.
As a further detailed scheme of the method of the present invention, the wotherstein barycentric coordinate set of the image is calculated in step B, specifically according to the following steps:
step B1, for any image block piA handle piDividing into B, G, R three color channels, and calculating a histogram of each channel;
step B2, respectively calculating the Wtherstein gravity centers of B, G, R channel histograms;
and step B3, calculating the Wtherstein barycentric coordinates of the image blocks by using a Wtherstein barycentric coordinate regression method according to the calculated Wtherstein barycentric.
As a further detailed scheme of the method of the present invention, the calculation of the wotherstein barycentric coordinates of the histograms of the respective channels in step B2 is performed by using an extended Sinkhorn algorithm, specifically as follows:
the centre of gravity of the wotherstein is defined as,
Figure BDA0001829049080000021
therein, sigmaNIs a simplex of the normalized histogram; p is a radical ofsIsNThe s-th histogram of (i), p being ∑NAn inner histogram; w (p, p)s) Is a histogram p, psThe OT distance is normalized by the entropy of (1); w (p, p)s) Is defined as
Figure BDA0001829049080000022
Where C is the cost of quantizing the transmission quality between histogram bins and γ is a regularization parameter; t is the N positive definite matrix representation of the histogram, H is the negative entropy of T;
obtaining the Wathers according to the differentiation calculation of the Sinkhorn algorithmThe specific formula of the Stant gravity center is as follows: for all S ≦ S,
Figure BDA0001829049080000023
for l is more than or equal to 0, S is less than or equal to S, and S represents the total number of the histogram, the following iteration is carried out:
Figure BDA0001829049080000024
and is
Figure BDA0001829049080000026
Wherein K is e-C/γThen, then
Figure BDA0001829049080000025
The exact center of gravity of the wotherstein is thus obtained.
As a further detailed embodiment of the method of the present invention, step B3 is specifically as follows:
step B301, according to the formula of the Wtherstein barycentric coordinate:
Figure BDA0001829049080000031
the formula is non-convex, and a stable point of the formula can be obtained by a gradient descent method;
step B302, utilizing a chain type derivation rule to solve partial derivation for lambda of the Wtherstein barycentric coordinate formula to obtain a P (lambda) gradient formula:
Figure BDA0001829049080000032
wherein
Figure BDA0001829049080000033
Is that
Figure BDA0001829049080000034
The jacobian matrix of (a) is,
Figure BDA0001829049080000035
is psA gradient at P (λ);
step B303, utilizing P (lambda) given in step B302) Gradient formula, performing one iteration of the center of gravity P of avostasentan(l)(λ) instead of P (λ); the formulas in steps 301, 302 are changed to:
Figure BDA0001829049080000036
ε(λ)＝L(P(l)(λ),ps)，
Figure BDA0001829049080000037
step B304, using backward recursive computation
Figure BDA0001829049080000038
Thereby obtaining
Figure BDA0001829049080000039
The specific algorithm is as follows:
firstly, defining:
Figure BDA00018290490800000310
and is
Figure BDA00018290490800000311
Figure BDA00018290490800000312
And is
Figure BDA00018290490800000313
Figure BDA00018290490800000314
Can be calculated by the formula, i.e.
Figure BDA00018290490800000315
Wherein v is(L)Initial value is
Figure BDA00018290490800000316
The following inverse recursive calculation is used:
Figure BDA00018290490800000317
and step B305, calculating the Wtherstein barycentric coordinates of each image block to obtain a Wtherstein barycentric coordinate set of the image.
Compared with the prior art, the blind detection method for the image repetition region based on the Oldham's metric of the Wtherstein histogram has the following beneficial effects:
the method provided by the invention can accurately detect the copy-paste counterfeit area of the image and has better robustness for detecting the rigid target object.
Drawings
FIG. 1 is a flow chart of the blind detection method of the Wtherstein image repeat region of the present invention.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings:
it will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The idea of the invention is to use the Wtherstein barycentric coordinates of the image block as a descriptor and a plurality of orthogonal Gaussian kernels as Wtherstein representation bases. The representation of the image blocks under the walstein base is taken as the walstein barycentric coordinates and used as its image features. According to | · |. non-woven phosphor between image block features2And (4) norm determination, namely determining the position of the initial block, and expanding a search area by utilizing a PatchMatch algorithm to obtain an image repeated area detection result.
For the convenience of public understanding, prior to the detailed description of the technical solution of the present invention, the related prior art related to the technical solution of the present invention will be briefly described below.
1. Wtherstein distance
The image, which is data having a high dimensional characteristic, has geometric information between dots, edges, and sides in addition to information characteristics of dots in general data, such as color and brightness. The feature extraction or learning algorithm based on the Euclidean measurement system cannot effectively retain geometric information on features. The Waterstein measurement does not simply regard the image as a common high-dimensional feature vector, but regards the image as a statistic, and geometric information of sample distribution can be reserved in the solving process. The Wtherstein distance in the invention is an entropy regularization optimal transmission distance, and is specifically defined as:
Figure BDA0001829049080000041
matrix Ci,j＝(Ci,j)i,jCost for quantifying transmission quality between histogram bins if the bins are at a certain position (x) in Euclidean spacei)iSampling, then C is usually Ci,j＝||xi-xj||α(α is usually a positive number). Here the regularization parameter y is usually a positive number, which ensures that the optimal solution is unique, and parallel computation is faster and easier. (where q is p)sRepresents the s th histogram, the same below)
2. Wo se Stant center of gravity
The Wtherstein center of gravity, also known as optimal transmission interpolation. The Optimal Transport is the Optimal Transport theory (Optimal Transport) which considers the probability histogram as a sand heap and quantifies the distance between the two by considering the cheapest method of moving all the sand grains from one histogram to reform them into another histogram. If the two distributions are compared to two states of a pile of sand, the theory of optimal transmission roughly reflects the "work" that is done to move the pile of sand from one state to another. In the working process, the geometric state of the sand can be reserved, and the distributed geometric property in the interpolation process cannot be damaged. The detailed definition of the centre of gravity of wotherstein is:
Figure BDA0001829049080000051
the uniqueness of P (λ) is determined by the strong convexity of the energy defined on the right side of equation (2). And the Wtherstein center of gravity and the usual linear average ∑sλspsIn contrast, the linear average corresponds to l2The center of gravity in the sense does not reflect the geometric characteristics, whereas the Wtherstein center of gravity does not have this problem.
3. Improved PatchMatch algorithm
Barnes et al propose a fast block matching search algorithm PatchMatch, which is most characterized by using the correlation between adjacent blocks to propagate domain information. The PatchMatch algorithm matches image blocks in two images by random initialization, propagation, and random search. The method utilizes the Wtherstein barycentric coordinate to initialize the random initialization replacing the PatchMatch algorithm, and then transmits and searches in the same image to determine the repeated area.
The invention relates to a blind detection algorithm of an image repetition region based on the Euclidean histogram of Watersstein, the flow of which is shown in figure 1, and the blind detection algorithm specifically comprises the following steps:
step A, dividing an image to be detected into a plurality of small blocks by utilizing a block code;
step B, extracting the characteristics of each small block for each small block divided in the step A:
the present invention provides an image copy and paste counterfeit detection algorithm based on Discrete Cosine Transform (DCT) coefficient features, which is provided by Fridrich et al [ FridrichJ, Soukal D, Lukas J.Detectinggofcopy-move for identification images, Proceedings of digital Forensic research Workshop,2003], and has the disadvantages of high calculation speed and high mismatching rate and serious performance degradation when a flat region exists in an image. Mohammad et al [ HashmiMF, Anand V, KeskarAG. copy-move ImageForgeryDetectionUsing and Effect and Robusted method combining and not having a detailed wavelet Transform feature Transform [ J ]. AASRIProcedia,2014,12(9):84-91 ] propose an image forgery detection algorithm of a dynamic wavelet Transform coupling scale invariant feature Transform, and locate a forgery region in a space domain, are difficult to reduce image feature dimensions, have the defect of high time complexity, are difficult to detect the forgery region in an affine geometric Transform falsification form, and reduce the algorithm robustness. The application of WDT and SIFT to the detection of image tampering by Anand and Hashmi et al [ AnandV, HashmF, KeskarAG. ACOPyMoveForgeryDetectiono Overcom Sun attacksUingDyadic wavelet transform and SIFT systems.2014:530 542 ] has higher detection accuracy, extracts key points of image features through SIFT transformation, and has the defect that the false forms such as blurring, rotation and the like are difficult to effectively identify. Liu Xiao Xia et al [ Liu Xiao Xia, Li Feng, bear soldier ] based on the image stitching detection of Weber local characteristics [ J ] computer engineering and application, 2013,49(12): 140-. Application research of RANSAC algorithm in copy and identification of the same picture, computer application research, 2014,31(7): 2209-. Li rock et al [ lie rock, liu zi, zhan bin, etc. ] after FI-SURF algorithm [ J ] in image mirror image copy paste tamper detection, in the communication report, 2015,36(5):54-65 ] using SURF method to extract feature points and generate feature descriptors, the copy paste area is turned over, and then feature matching is performed.
In view of the defects of the prior method, the invention provides a blind detection algorithm of an image repetition region based on the Euclidean measurement of a Wtherstein histogram, which uses the barycentric coordinates of the Wtherstein as an image feature descriptor, uses the Euclidean measurement block distance of the Wtherstein histogram and uses the PatchMatch method to expand and search the repetition region. The method can well consider the geometric characteristics of the image, effectively detect a plurality of repeated regions in the image, and has better robustness for the image containing Gaussian noise and lossy compression. The method comprises the following specific steps:
step B1, for image block piA handle piDecomposition into B, G, R three-channel image pib、pigAnd pir；
Step B2, calculating pib、pigAnd pirThe Wtherstein barycentric coordinate of (1) is taken as piThe characteristics of (1). And calculating the Wtherstein barycentric coordinates by adopting an extended Sinkhorn algorithm. The specific method is (taking B channel as an example, the method of other channels is the same as that):
step B201, calculating pib、pigAnd pirHistogram and normalization;
step B202, calculating the barycentric coordinates of the histogram according to the definition of the Wtherstein barycentric.
The centre of gravity of the wotherstein is defined as,
Figure BDA0001829049080000061
wherein ∑NIs a simplex of the normalized histogram; p is a radical ofsIsNThe s-th histogram of (i), p being ∑NAn inner histogram; w (p, q) is the entropy regularization OT distance of the histograms p, q. W (p, q) is defined as
Figure BDA0001829049080000071
Where C is the cost of quantizing the transmission quality between histogram bins(ii) a Gamma is a regularization parameter. (where q is p)sRepresenting the s-th histogram) because the definition of the barycenter of the waltherstein is not a closed expression, the barycenter of the waltherstein is obtained by differentiation calculation according to a Sinkhorn algorithm, and the specific formula is as follows: for all S ≦ S,
Figure BDA0001829049080000072
for l is more than or equal to 0 and S is less than or equal to S, iteration is carried out as follows:
Figure BDA0001829049080000073
and is
Figure BDA00018290490800000717
Wherein K is e-C/γThen, then
Figure BDA0001829049080000074
The exact center of gravity of the wotherstein is thus obtained.
Step B3, calculating the Wtherstein barycentric coordinate of a small block image by using a Wtherstein barycentric coordinate regression method according to the calculated Wtherstein barycentric, which comprises the following specific steps:
step B301, according to the formula of the Wtherstein barycentric coordinate:
Figure BDA0001829049080000075
the formula is non-convex, and a stable point of the formula can be obtained by a gradient descent method;
step B302, utilizing a chain type derivation rule to solve partial derivation for lambda of the Wtherstein barycentric coordinate formula to obtain:
Figure BDA0001829049080000076
wherein
Figure BDA0001829049080000077
Is that
Figure BDA0001829049080000078
The jacobian matrix of (a) is,
Figure BDA0001829049080000079
is the gradient of q at P (λ).
Proposition 001: assuming that the wotherstein center of gravity P (λ) can be accurately calculated, for simplicity, the function (Φ, Ψ) is first introduced and the wotherstein center of gravity iterative calculation in step B202 is written as:
P(l)(λ)＝Ψ(b(l)(λ), λ) wherein
Figure BDA00018290490800000710
P(l+1)(λ)＝Φ(b(l)(λ), λ) wherein
Figure BDA00018290490800000711
And is
Figure BDA00018290490800000712
Defining:
Figure BDA00018290490800000713
Figure BDA00018290490800000714
wherein
Figure BDA00018290490800000715
And
Figure BDA00018290490800000716
corresponding to the partial derivative of phi (b, lambda) (psi (b, lambda)) with respect to its first and second components. In practice, an exact computational approach is not used, since these vectors can only be approximated by iterating a sufficient number of times to converge to sufficient accuracy. And is
Figure BDA0001829049080000081
The calculation of (A) needs to be solved forN x N linear systems, where N is typically on the order of 10^ 6.
Step B303, taking into account the iterative computation P (λ) given in proposition 001, using the l iterations of the Tavotherstein center of gravity P proposed in step B202(l)(λ) instead of P (λ). The formulas in steps 301, 302 become: ,
Figure BDA0001829049080000082
step B304, using backward recursive computation
Figure BDA0001829049080000083
Thereby obtaining
Figure BDA0001829049080000084
The specific algorithm is as follows: firstly, defining:
Figure BDA0001829049080000085
wherein
Figure BDA0001829049080000086
Figure BDA0001829049080000087
Wherein
Figure BDA0001829049080000088
Figure BDA0001829049080000089
Can be calculated by the formula:
Figure BDA00018290490800000810
wherein u is(L)Is defined in step B303, v(L)Is initialized to
Figure BDA00018290490800000811
Figure BDA00018290490800000812
The following inverse recursive calculation is used:
Figure BDA00018290490800000813
computing
Figure BDA00018290490800000814
The method of (1) is to first perform a forward loop to calculate the Wtherstein center of gravity P(l)(λ), then performing an inverse loop to achieve v(l)And are accumulated to obtain
Figure BDA00018290490800000815
The method comprises the following specific steps:
inputting:
Figure BDA00018290490800000816
Figure BDA00018290490800000817
(w,r)←(0S,0S×N)
for l＝1,2,...,L
Figure BDA00018290490800000818
Figure BDA00018290490800000819
Figure BDA00018290490800000820
Figure BDA0001829049080000091
for l＝L,L-1,...,1
Figure BDA0001829049080000092
Figure BDA0001829049080000093
g←∑srs
return
Figure BDA0001829049080000094
and step B305, calculating the Wtherstein barycentric coordinate of the image block to obtain a Wtherstein barycentric coordinate set.
And step C, searching the image block by utilizing PatchMatch expansion according to the calculated Wtherstein barycentric coordinate set to obtain a repeated region of the image.
Step C1, calculating | | · | | luminous component except itself and among other blocks in turn from the first block according to the Wtherstein barycentric coordinate obtained by calculation2And (4) norm, finding out the block with the minimum distance according to the norm measurement distance, and taking the block as a detection initial block.
And step C2, after the initial block is determined, searching image blocks around the initial block by using a PatchMatch algorithm, thereby expanding the search range and positioning the image repetition region.
It will be understood by those within the art that each block of the block diagrams and/or flowchart illustrations, and combinations of blocks in the block diagrams and/or flowchart illustrations, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the methods specified in the block or blocks of the block diagrams and/or flowchart block or blocks.
The embodiments of the present invention have been described in detail with reference to the drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.

Claims (2)

1. A blind detection method of image repetition regions based on the euclidean metric of a waltherstein histogram, characterized by comprising the following steps:
step A, dividing an image to be detected into a plurality of small blocks;
step B, calculating the Wtherstein barycentric coordinate of each small block obtained in the step A, so as to obtain a Wtherstein barycentric coordinate set of the image to be detected;
step C, calculating I | · | | non-calculation light calculation between blocks except self and other blocks in sequence from the first block according to the Wtherstein barycentric coordinate2Norm, finding out the block with the minimum distance as the initial detection block according to the norm measurement distance; after the initial block is determined, searching image blocks around the initial block by using a PatchMatch algorithm, expanding a search range and positioning an image repetition region;
step D, outputting a repeated region detection result of the image;
b, calculating a Wtherstein gravity center coordinate set of the image, and specifically comprising the following steps:
step B1, for any image block piA handle piDividing into B, G, R three color channels, and calculating a histogram of each channel;
step B2, respectively calculating the Wtherstein barycenter of the B, G, R channel histogram, specifically adopting an extended Sinkhorn algorithm, and specifically comprising the following steps:
the centre of gravity of the wotherstein is defined as,
Figure FDA0003180942510000011
therein, sigmaNIs a simplex of the normalized histogram; p is a radical ofsIsNThe s-th histogram of (i), p being ∑NAn inner histogram; w (p, p)s) Is a histogram p, psEntropy regularization ofThe OT distance; lambda [ alpha ]sA distance adjustment coefficient representing the s-th histogram from the other histograms,
Figure FDA0003180942510000012
representing the optimal probability coordinates of finding the center of gravity of Watherstein;
W(p,ps) Is defined as
Figure FDA0003180942510000013
Where C is the cost of quantizing the transmission quality between histogram bins and γ is a regularization parameter; t is the N positive definite matrix representation of the histogram, H is the negative entropy of T; r+Represents a positive real number and a negative real number,<T,C>represents inner product operation, 1 represents unit vector, and T1 represents T multiplied by unit vector;
obtaining the Wtherstein gravity center according to the differentiation calculation of the Sinkhorn algorithm, wherein the specific formula is as follows: for all S ≦ S,
Figure FDA0003180942510000014
for l is more than or equal to 0, S is less than or equal to S, and S represents the total number of the histogram, the following iteration is carried out:
Figure FDA0003180942510000015
and is
Figure FDA0003180942510000016
Wherein K is e-C/γAnd l represents the first iteration,
Figure FDA0003180942510000021
the value of the variable a representing the s-th histogram at the i-th iteration, P(l)(λ) represents the state of the centre of gravity of wotherstein at the first iteration;
according to
Figure FDA0003180942510000022
Thereby obtaining the accurate gravity center of the Waterstein,
Figure FDA0003180942510000023
the state of the Wtherstein gravity center tends to be optimal when the iteration number l tends to infinity;
and step B3, calculating the Wtherstein barycentric coordinates of the image blocks by using a Wtherstein barycentric coordinate regression method according to the calculated Wtherstein barycentric.
2. The method of claim 1, wherein step B3 is specifically as follows:
step B301, according to the formula of the Wtherstein barycentric coordinate:
Figure FDA0003180942510000024
the formula is non-convex, and a stable point of the formula can be obtained by a gradient descent method;
Figure FDA00031809425100000219
a norm measure is represented that is,
Figure FDA00031809425100000220
representing Wtherstein centre of gravity and histogram psThe measurement value of (a);
step B302, utilizing a chain type derivation rule to solve partial derivation for lambda of the Wtherstein barycentric coordinate formula to obtain a P (lambda) gradient formula:
Figure FDA0003180942510000025
wherein
Figure FDA0003180942510000026
Is that
Figure FDA0003180942510000027
The jacobian matrix of (a) is,
Figure FDA0003180942510000028
is psA gradient at P (λ);
step B303, executing I iterations of the gravity center P of the avostasentan by using the gradient formula of P (lambda) given in the step B302(l)(λ) instead of P (λ); the formulas in steps B301 and B302 are changed into:
Figure FDA0003180942510000029
∑Srepresents all histograms, L (P)(l)(λ),ps) Representing the Wolstein centre of gravity and histogram p at the l-th iterationsThe value of the measured value of (c) is,
Figure FDA00031809425100000210
the partial derivative of the gravity center of the Votherstein at the first iteration is calculated;
step B304, using backward recursive computation
Figure FDA00031809425100000211
Thereby obtaining
Figure FDA00031809425100000212
The specific algorithm is as follows:
firstly, defining:
Figure FDA00031809425100000213
and is
Figure FDA00031809425100000214
Figure FDA00031809425100000215
And is
Figure FDA00031809425100000216
Figure FDA00031809425100000217
The partial derivative to x is represented as,
Figure FDA00031809425100000218
representing the partial derivative, phi (b), of the variable b(l)(λ), λ) represents the adjustment factor λ offset, Ψ (b), of the variable b from the center coordinate at the ith iteration in a histogram(l)(λ), λ) represents the adjustment factor λ offset of the variable b from the center coordinate at the ith iteration in the other histogram;
Figure FDA0003180942510000031
can be calculated by the formula, i.e.
Figure FDA0003180942510000032
Wherein v is(L)Initial value is
Figure FDA0003180942510000033
Figure FDA0003180942510000034
The following inverse recursive calculation is used:
Figure FDA0003180942510000035
l represents the number of iterations;
and step B305, calculating the Wtherstein barycentric coordinates of each image block to obtain a Wtherstein barycentric coordinate set of the image.
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