CN107622488A - A method and system for measuring similarity of confocal image blocks - Google Patents

A method and system for measuring similarity of confocal image blocks Download PDF

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CN107622488A
CN107622488A CN201710892587.5A CN201710892587A CN107622488A CN 107622488 A CN107622488 A CN 107622488A CN 201710892587 A CN201710892587 A CN 201710892587A CN 107622488 A CN107622488 A CN 107622488A
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rectangular image
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image block
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何涛
黄海清
胡洁
戚进
沈健
胡方凯
陈集懿
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Shanghai Jiao Tong University
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Abstract

本发明提供了一种共聚焦图像块相似度测量方法及系统,包括:以第一像素为中心选取矩形图像块;以第一像素以外的若干像素为中心分别选取相似矩形图像块,计算两矩形图像块之间的距离,将若干相似矩形图像块按距离从近到远排序,并选取前K个相似矩形图像块;计算矩形图像块与相似矩形图像块的相似度函数,选取K个相似矩形图像块中相似度函数大于预定阈值的相似矩形图像块。本发明有效地加强了图像块相似度测量的鲁棒性,便于后续的分析,能有效提升算法的稳定性。

The invention provides a method and system for measuring the similarity of confocal image blocks, comprising: selecting a rectangular image block centered on the first pixel; selecting similar rectangular image blocks centered on several pixels other than the first pixel, and calculating two rectangular image blocks The distance between image blocks, sort several similar rectangular image blocks from near to far, and select the first K similar rectangular image blocks; calculate the similarity function between rectangular image blocks and similar rectangular image blocks, and select K similar rectangular image blocks A similar rectangular image block whose similarity function is greater than a predetermined threshold in the image block. The invention effectively enhances the robustness of image block similarity measurement, facilitates subsequent analysis, and can effectively improve the stability of the algorithm.

Description

一种共聚焦图像块相似度测量方法及系统A method and system for measuring similarity of confocal image blocks

技术领域technical field

本发明涉及图像处理技术领域,具体地,涉及一种共聚焦图像块相似度测量方法及系统。The present invention relates to the technical field of image processing, in particular to a method and system for measuring the similarity of confocal image blocks.

背景技术Background technique

随着移动互联网的高速发展,人们可以快速方便地获取图像资源,如何从这些海量的图像资源里找到一些相似的图像显得非常重要。1991年,Swain提出了颜色直方图算法,并且用它来进行图像检索。该算法的优点是计算简单,而且对图像不需要做太多的预处理,对图像的尺寸也没有严格要求,但是由于图像的颜色直方图表示的是每种颜色出现的概率,它没有指明某一种颜色在图像中的具体位置,因此当计算两幅图像块的相似度时,就会造成偏差;而且该算法对颜色比较单一的两幅图像块也不能做出很好的判断。With the rapid development of the mobile Internet, people can quickly and easily obtain image resources, how to find some similar images from these massive image resources is very important. In 1991, Swain proposed the color histogram algorithm and used it for image retrieval. The advantage of this algorithm is that the calculation is simple, and the image does not require much preprocessing, and there is no strict requirement on the size of the image. However, since the color histogram of the image represents the probability of each color, it does not specify a certain color. The specific position of a color in the image, so when calculating the similarity of two image blocks, it will cause deviation; and the algorithm cannot make a good judgment on the two image blocks with relatively single color.

发明内容Contents of the invention

针对现有技术中的缺陷,本发明的目的是提供一种共聚焦图像块相似度测量方法及系统。In view of the defects in the prior art, the object of the present invention is to provide a method and system for measuring the similarity of confocal image blocks.

根据本发明提供的一种共聚焦图像块相似度测量方法,包括:According to a method for measuring the similarity of confocal image blocks provided by the present invention, comprising:

矩形图像块选取步骤:以第一像素为中心选取矩形图像块;Rectangular image block selection step: select a rectangular image block centered on the first pixel;

相似矩形图像块选取步骤:以第一像素以外的若干像素为中心分别选取相似矩形图像块,计算两矩形图像块之间的距离,将若干相似矩形图像块按距离从近到远排序,并选取前K个相似矩形图像块;Steps for selecting similar rectangular image blocks: select similar rectangular image blocks around several pixels other than the first pixel, calculate the distance between two rectangular image blocks, sort several similar rectangular image blocks according to the distance from near to far, and select The first K similar rectangular image blocks;

相似度函数计算步骤:计算矩形图像块与相似矩形图像块的相似度函数,选取K个相似矩形图像块中相似度函数大于预定阈值的相似矩形图像块。Similarity function calculation step: calculate the similarity function between the rectangular image block and the similar rectangular image block, and select the similar rectangular image block whose similarity function is greater than a predetermined threshold among the K similar rectangular image blocks.

优选的,所述矩形图像块选取步骤包括:以像素i为中心,r为半径选取矩形图像块pi,矩形图像块pi内共包含(2r+1)×(2r+1)个像素。Preferably, the step of selecting a rectangular image block includes: selecting a rectangular image block p i with pixel i as the center and r as the radius, and the rectangular image block p i contains (2r+1)×(2r+1) pixels in total.

优选的,所述相似矩形图像块选取步骤包括:以像素i以外的若干像素j为中心,r为半径选取相似矩形图像块pj,相似矩形图像块pj内共包含(2r+1)×(2r+1)个像素,计算两矩形图像块之间的距离d(i,j),Preferably, the step of selecting a similar rectangular image block includes: taking several pixels j other than pixel i as the center and r as the radius to select a similar rectangular image block p j , and the similar rectangular image block p j contains a total of (2r+1)× (2r+1) pixels, calculate the distance d(i,j) between two rectangular image blocks,

将若干相似矩形图像块按距离从近到远排序,并选取前K个相似矩形图像块,Sort several similar rectangular image blocks according to the distance from near to far, and select the first K similar rectangular image blocks,

d(pi,p1)<d(pi,p2)<d(pi,p3)<…<d(pi,pK)。d(p i ,p 1 )<d(p i ,p 2 )<d(p i ,p 3 )<...<d(p i ,p K ).

优选的,所述相似度函数计算步骤包括:Preferably, the similarity function calculation step includes:

计算矩形图像块pi与相似矩形图像块pj的相似度函数I(i,j),Calculate the similarity function I(i,j) between the rectangular image block p i and the similar rectangular image block p j ,

设定阈值ε,选取K个相似矩形图像块中与矩形图像块相似度函数大于ε的相似矩形图像块。Set the threshold ε, and select the similar rectangular image blocks whose similarity function with the rectangular image block is greater than ε among the K similar rectangular image blocks.

根据本发明提供的一种共聚焦图像块相似度测量系统,包括:A confocal image block similarity measurement system provided according to the present invention includes:

矩形图像块选取模块:以第一像素为中心选取矩形图像块;Rectangular image block selection module: select a rectangular image block centered on the first pixel;

相似矩形图像块选取模块:以第一像素以外的若干像素为中心分别选取相似矩形图像块,计算两矩形图像块之间的距离,将若干相似矩形图像块按距离从近到远排序,并选取前K个相似矩形图像块;Similar rectangular image block selection module: select similar rectangular image blocks around several pixels other than the first pixel, calculate the distance between two rectangular image blocks, sort several similar rectangular image blocks according to the distance from near to far, and select The first K similar rectangular image blocks;

相似度函数计算模块:计算矩形图像块与相似矩形图像块的相似度函数,选取K个相似矩形图像块中相似度函数大于预定阈值的相似矩形图像块。Similarity function calculation module: calculate the similarity function between a rectangular image block and a similar rectangular image block, and select a similar rectangular image block whose similarity function is greater than a predetermined threshold among the K similar rectangular image blocks.

优选的,所述矩形图像块选取模块包括:以像素i为中心,r为半径选取矩形图像块pi,矩形图像块pi内共包含(2r+1)×(2r+1)个像素。Preferably, the rectangular image block selection module includes: selecting a rectangular image block p i with pixel i as the center and r as the radius, and the rectangular image block p i contains (2r+1)×(2r+1) pixels in total.

优选的,所述相似矩形图像块选取模块包括:以像素i以外的若干像素j为中心,r为半径选取相似矩形图像块pj,相似矩形图像块pj内共包含(2r+1)×(2r+1)个像素,计算两矩形图像块之间的距离d(i,j),Preferably, the similar rectangular image block selection module includes: selecting a similar rectangular image block p j with several pixels j other than pixel i as the center and r as the radius, and the similar rectangular image block p j contains (2r+1)× (2r+1) pixels, calculate the distance d(i,j) between two rectangular image blocks,

将若干相似矩形图像块按距离从近到远排序,并选取前K个相似矩形图像块,Sort several similar rectangular image blocks according to the distance from near to far, and select the first K similar rectangular image blocks,

d(pi,p1)<d(pi,p2)<d(pi,p3)<…<d(pi,pK)。d(p i ,p 1 )<d(p i ,p 2 )<d(p i ,p 3 )<...<d(p i ,p K ).

优选的,所述相似度函数计算模块包括:Preferably, the similarity function calculation module includes:

计算矩形图像块pi与相似矩形图像块pj的相似度函数I(i,j),Calculate the similarity function I(i,j) between the rectangular image block p i and the similar rectangular image block p j ,

设定阈值ε,选取K个相似矩形图像块中与矩形图像块相似度函数大于ε的相似矩形图像块。Set the threshold ε, and select the similar rectangular image blocks whose similarity function with the rectangular image block is greater than ε among the K similar rectangular image blocks.

与现有技术相比,本发明具有如下的有益效果:Compared with the prior art, the present invention has the following beneficial effects:

本发明有效地加强了图像块相似度测量的鲁棒性,便于后续的分析,能有效提升算法的稳定性。The invention effectively enhances the robustness of image block similarity measurement, facilitates subsequent analysis, and can effectively improve the stability of the algorithm.

附图说明Description of drawings

通过阅读参照以下附图对非限制性实施例所作的详细描述,本发明的其它特征、目的和优点将会变得更明显:Other characteristics, objects and advantages of the present invention will become more apparent by reading the detailed description of non-limiting embodiments made with reference to the following drawings:

图1为本发明的工作流程图。Fig. 1 is the work flowchart of the present invention.

具体实施方式detailed description

下面结合具体实施例对本发明进行详细说明。以下实施例将有助于本领域的技术人员进一步理解本发明,但不以任何形式限制本发明。应当指出的是,对本领域的普通技术人员来说,在不脱离本发明构思的前提下,还可以做出若干变化和改进。这些都属于本发明的保护范围。The present invention will be described in detail below in conjunction with specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

如图1所示,本发明提供的一种共聚焦图像块相似度测量方法,包括:As shown in Figure 1, a method for measuring the similarity of confocal image blocks provided by the present invention includes:

矩形图像块选取步骤:以第一像素为中心选取矩形图像块;Rectangular image block selection step: select a rectangular image block centered on the first pixel;

相似矩形图像块选取步骤:以第一像素以外的若干像素为中心分别选取相似矩形图像块,计算两矩形图像块之间的距离,将若干相似矩形图像块按距离从近到远排序,并选取前K个相似矩形图像块;Steps for selecting similar rectangular image blocks: select similar rectangular image blocks around several pixels other than the first pixel, calculate the distance between two rectangular image blocks, sort several similar rectangular image blocks according to the distance from near to far, and select The first K similar rectangular image blocks;

相似度函数计算步骤:计算矩形图像块与相似矩形图像块的相似度函数,选取K个相似矩形图像块中相似度函数大于预定阈值的相似矩形图像块。Similarity function calculation step: calculate the similarity function between the rectangular image block and the similar rectangular image block, and select the similar rectangular image block whose similarity function is greater than a predetermined threshold among the K similar rectangular image blocks.

矩形图像块选取步骤包括:以像素i为中心,r为半径选取矩形图像块pi,矩形图像块pi内共包含(2r+1)×(2r+1)个像素。The step of selecting a rectangular image block includes: selecting a rectangular image block p i with pixel i as the center and r as the radius, and the rectangular image block p i contains (2r+1)×(2r+1) pixels in total.

相似矩形图像块选取步骤包括:以像素i以外的若干像素j为中心,r为半径选取相似矩形图像块pj,相似矩形图像块pj内共包含(2r+1)×(2r+1)个像素,计算两矩形图像块之间的距离d(i,j),The step of selecting a similar rectangular image block includes: taking several pixels j other than the pixel i as the center and r as the radius to select a similar rectangular image block p j , and the similar rectangular image block p j contains (2r+1)×(2r+1) pixels, calculate the distance d(i,j) between two rectangular image blocks,

将若干相似矩形图像块按距离从近到远排序,并选取前K个相似矩形图像块,Sort several similar rectangular image blocks according to the distance from near to far, and select the first K similar rectangular image blocks,

d(pi,p1)<d(pi,p2)<d(pi,p3)<…<d(pi,pK)。d(p i ,p 1 )<d(p i ,p 2 )<d(p i ,p 3 )<...<d(p i ,p K ).

相似度函数计算步骤包括:The calculation steps of the similarity function include:

计算矩形图像块pi与相似矩形图像块pj的相似度函数I(i,j),Calculate the similarity function I(i,j) between the rectangular image block p i and the similar rectangular image block p j ,

设定阈值ε,选取K个相似矩形图像块中与矩形图像块相似度函数大于ε的相似矩形图像块。Set the threshold ε, and select the similar rectangular image blocks whose similarity function with the rectangular image block is greater than ε among the K similar rectangular image blocks.

根据上述共聚焦图像块相似度测量方法,本发明还提供的一种共聚焦图像块相似度测量系统,包括:According to the above confocal image block similarity measurement method, the present invention also provides a confocal image block similarity measurement system, comprising:

矩形图像块选取模块:以第一像素为中心选取矩形图像块;Rectangular image block selection module: select a rectangular image block centered on the first pixel;

相似矩形图像块选取模块:以第一像素以外的若干像素为中心分别选取相似矩形图像块,计算两矩形图像块之间的距离,将若干相似矩形图像块按距离从近到远排序,并选取前K个相似矩形图像块;Similar rectangular image block selection module: select similar rectangular image blocks around several pixels other than the first pixel, calculate the distance between two rectangular image blocks, sort several similar rectangular image blocks according to the distance from near to far, and select The first K similar rectangular image blocks;

相似度函数计算模块:计算矩形图像块与相似矩形图像块的相似度函数,选取K个相似矩形图像块中相似度函数大于预定阈值的相似矩形图像块。Similarity function calculation module: calculate the similarity function between the rectangular image block and the similar rectangular image block, and select the similar rectangular image block whose similarity function is greater than a predetermined threshold among the K similar rectangular image blocks.

矩形图像块选取模块包括:以像素i为中心,r为半径选取矩形图像块pi,矩形图像块pi内共包含(2r+1)×(2r+1)个像素。The rectangular image block selection module includes: selecting a rectangular image block p i with pixel i as the center and r as the radius, and the rectangular image block p i contains (2r+1)×(2r+1) pixels in total.

相似矩形图像块选取模块包括:以像素i以外的若干像素j为中心,r为半径选取相似矩形图像块pj,相似矩形图像块pj内共包含(2r+1)×(2r+1)个像素,计算两矩形图像块之间的距离d(i,j),The similar rectangular image block selection module includes: taking several pixels j other than the pixel i as the center and r as the radius to select a similar rectangular image block p j , and the similar rectangular image block p j contains a total of (2r+1)×(2r+1) pixels, calculate the distance d(i,j) between two rectangular image blocks,

将若干相似矩形图像块按距离从近到远排序,并选取前K个相似矩形图像块,Sort several similar rectangular image blocks according to the distance from near to far, and select the first K similar rectangular image blocks,

d(pi,p1)<d(pi,p2)<d(pi,p3)<…<d(pi,pK)。d(p i ,p 1 )<d(p i ,p 2 )<d(p i ,p 3 )<...<d(p i ,p K ).

相似度函数计算模块包括:The similarity function calculation module includes:

计算矩形图像块pi与相似矩形图像块pj的相似度函数I(i,j),Calculate the similarity function I(i,j) between the rectangular image block p i and the similar rectangular image block p j ,

设定阈值ε,选取K个相似矩形图像块中与矩形图像块相似度函数大于ε的相似矩形图像块。Set the threshold ε, and select the similar rectangular image blocks whose similarity function with the rectangular image block is greater than ε among the K similar rectangular image blocks.

本领域技术人员知道,除了以纯计算机可读程序代码方式实现本发明提供的系统及其各个装置、模块、单元以外,完全可以通过将方法步骤进行逻辑编程来使得本发明提供的系统及其各个装置、模块、单元以逻辑门、开关、专用集成电路、可编程逻辑控制器以及嵌入式微控制器等的形式来实现相同功能。所以,本发明提供的系统及其各项装置、模块、单元可以被认为是一种硬件部件,而对其内包括的用于实现各种功能的装置、模块、单元也可以视为硬件部件内的结构;也可以将用于实现各种功能的装置、模块、单元视为既可以是实现方法的软件模块又可以是硬件部件内的结构。Those skilled in the art know that, in addition to realizing the system provided by the present invention and its various devices, modules, and units in a purely computer-readable program code mode, the system provided by the present invention and its various devices can be completely programmed by logically programming the method steps. , modules, and units implement the same functions in the form of logic gates, switches, ASICs, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by the present invention can be regarded as a hardware component, and the devices, modules, and units included in it for realizing various functions can also be regarded as hardware components. The structure; the device, module, and unit for realizing various functions can also be regarded as a software module for realizing the method or a structure in a hardware component.

以上对本发明的具体实施例进行了描述。需要理解的是,本发明并不局限于上述特定实施方式,本领域技术人员可以在权利要求的范围内做出各种变化或修改,这并不影响本发明的实质内容。在不冲突的情况下,本申请的实施例和实施例中的特征可以任意相互组合。Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. In the case of no conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims (8)

  1. A kind of 1. Confocal Images block similarity measurement method, it is characterised in that including:
    Rectangular image block selecting step:Rectangular image block is chosen centered on the first pixel;
    Similar rectangular image block selecting step:Choose similar rectangular image respectively centered on some pixels beyond the first pixel Block, the distance between two rectangular image blocks are calculated, by some similar rectangular image blocks by distance from closely to remote sequence, and before selection K similar rectangular image blocks;
    Similarity function calculation procedure:Similarity function of the rectangular image block to similar rectangular image block is calculated, it is individual similar to choose K Similarity function is more than the similar rectangular image block of predetermined threshold in rectangular image block.
  2. 2. Confocal Images block similarity measurement method according to claim 1, it is characterised in that the rectangular image block Selecting step includes:Centered on pixel i, r is that radius chooses rectangular image block pi, rectangular image block piIt is interior to include (2r+1) altogether The individual pixels of × (2r+1).
  3. 3. Confocal Images block similarity measurement method according to claim 2, it is characterised in that the similar histogram As block selecting step includes:Centered on some pixel j beyond pixel i, r is that radius chooses similar rectangular image block pj, phase Like rectangular image block pjIt is interior to include the individual pixels of (2r+1) × (2r+1) altogether, the distance between two rectangular image blocks d (i, j) is calculated,
    <mrow> <mi>d</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> <mrow> <mo>(</mo> <mn>2</mn> <mi>r</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>&amp;times;</mo> <mo>(</mo> <mn>2</mn> <mi>r</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mfrac> </mrow>
    By some similar rectangular image blocks by distance from closely to remote sequence, and K similar rectangular image blocks before choosing,
    d(pi,p1) < d (pi,p2) < d (pi,p3) < ... < d (pi,pK)。
  4. 4. Confocal Images block similarity measurement method according to claim 3, it is characterised in that the similarity function Calculation procedure includes:
    Calculate rectangular image block piTo similar rectangular image block pjSimilarity function I (i, j),
    <mrow> <mi>I</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>&amp;times;</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mfrac> </mrow>
    Given threshold ε, choose the similar histogram for being more than ε in K similar rectangular image blocks to rectangular image block similarity function As block.
  5. A kind of 5. Confocal Images block similarity measurement system, it is characterised in that including:
    Rectangular image block chooses module:Rectangular image block is chosen centered on the first pixel;
    Similar rectangular image block chooses module:Choose similar rectangular image respectively centered on some pixels beyond the first pixel Block, the distance between two rectangular image blocks are calculated, by some similar rectangular image blocks by distance from closely to remote sequence, and before selection K similar rectangular image blocks;
    Similarity function computing module:Similarity function of the rectangular image block to similar rectangular image block is calculated, it is individual similar to choose K Similarity function is more than the similar rectangular image block of predetermined threshold in rectangular image block.
  6. 6. Confocal Images block similarity measurement system according to claim 5, it is characterised in that the rectangular image block Choosing module includes:Centered on pixel i, r is that radius chooses rectangular image block pi, rectangular image block piIt is interior to include (2r+1) altogether The individual pixels of × (2r+1).
  7. 7. Confocal Images block similarity measurement method according to claim 6, it is characterised in that the similar histogram Choosing module as block includes:Centered on some pixel j beyond pixel i, r is that radius chooses similar rectangular image block pj, phase Like rectangular image block pjIt is interior to include the individual pixels of (2r+1) × (2r+1) altogether, the distance between two rectangular image blocks d (i, j) is calculated,
    <mrow> <mi>d</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> <mrow> <mo>(</mo> <mn>2</mn> <mi>r</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>&amp;times;</mo> <mo>(</mo> <mn>2</mn> <mi>r</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mfrac> </mrow>
    By some similar rectangular image blocks by distance from closely to remote sequence, and K similar rectangular image blocks before choosing,
    d(pi,p1) < d (pi,p2) < d (pi,p3) < ... < d (pi,pK)。
  8. 8. Confocal Images block similarity measurement method according to claim 7, it is characterised in that the similarity function Computing module includes:
    Calculate rectangular image block piTo similar rectangular image block pjSimilarity function I (i, j),
    <mrow> <mi>I</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>&amp;times;</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mfrac> </mrow>
    Given threshold ε, choose the similar histogram for being more than ε in K similar rectangular image blocks to rectangular image block similarity function As block.
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