CN107358635B - Color morphological image processing method based on fuzzy similarity - Google Patents
Color morphological image processing method based on fuzzy similarity Download PDFInfo
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Abstract
The invention provides a color morphological image processing method based on fuzzy similarity, and relates to the technical field of image processing. The method comprises the steps of firstly, enabling a color image to be processed to correspond to an RGB color space, determining a Fuzzy Similarity Measure (FSM) function representing the similarity degree between two color vectors, then taking a pixel as an index, obtaining structural units and color vector sets thereof one by one in the RGB color space, determining a supremum vector and a supremum vector of the color vector sets by taking the FSM as a reference, and constructing basic operations of color morphology and applying the basic operations to the color image. The invention applies the morphological thought to the color image processing, has the characteristics of good stability, strong practicability and the like in the actual color image processing, not only can smooth the color target, but also can well process the detail characteristics of pixel inconsistency of a homogeneous area, and finally achieves the aims of color image analysis and processing.
Description
Technical Field
The invention relates to the technical field of image processing, in particular to a color morphological image processing method based on fuzzy similarity.
Background
The basic concept of morphology, which first appeared in the 19 th century, applies morphology to the field of image processing, namely, extracting and collecting image information using structural elements (circles, squares, lines, etc.) for analyzing and recognizing geometric features and structures of image objects. As a nonlinear image processing and analyzing method, mathematical morphology is successfully applied to binary and gray level images, and a complete morphological theory is formed. The binary morphology regards binary images as sets, and the simplest set operation (such as intersection, union, complement, translation and the like) is used for detecting original images. Because the adopted operations are all based on the set, the binary morphology has the characteristics of clear principle, simple calculation, easy expansion, suitability for parallel calculation and the like, and is widely applied to the image processing fields of denoising, boundary detection, skeletonization, region segmentation and the like. The gray level morphology is developed from binary morphology, and only the intersection in the binary morphology needs to be respectively converted into the minimum value and the maximum value of the pixel gray level in the structural unit.
In recent years, color images have been widely produced and used in various fields of human production and life. In comparison with binary and grayscale images, color images contain color information that can be perceived by humans in addition to luminance information, and thus color image processing is receiving increasing attention. At present, the popularization of mathematical morphology to color images, and the implementation of filtering, segmentation, feature extraction, edge detection, image enhancement and restoration, etc. of color images, is an important research direction in the field of color image processing.
In general, the simplest way to extend the gray-scale morphology to the color morphology is to view an RGB color image as being composed of three monochromatic images of red, green, and blue, process the three monochromatic images by the gray-scale morphology, and finally restore the morphology processing result to the RGB color image. However, as a result of such processing, on one hand, the color in the original image is changed, and the original image information is lost or distorted; on the other hand, the correlation among the color image components is not considered, so that the red, green and blue images become independent images without connection. Another method for expanding the gray morphology to the color morphology is to sort the colors in the structural unit based on a multivariate data sorting criterion, such as edge order, conditional order, region order, degradation order, and the like, and define basic morphological operations by using the principle of the minimum and maximum values in the similar gray morphology, but it is difficult to find a proper and universal color vector sorting method for colorful color images, so the current color morphology methods have great limitations.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a color morphological image processing method based on fuzzy similarity, which defines a novel color morphological operation based on a fuzzy similarity measure concept describing the similarity degree between vectors in an RGB color space, not only can smooth color targets, but also can well process detail features of pixel inconsistency in homogeneous regions, and finally achieves the goal of color image analysis and processing.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a color morphology image processing method based on fuzzy similarity comprises the following steps:
step 1: reading a color image to be processed;
step 2: mapping the color image to be processed to an RGB color space, namely representing the pixels of the color image by using vectors of the color space, wherein each color vector consists of three color components of red (R), green (G) and blue (B);
and step 3: determining a Fuzzy Similarity Measure (FSM) function representing the similarity degree between any two color vectors in the color space, and determining parameters in the function; when the value of the fuzzy similarity measure is larger, the similarity of the two color vectors is higher, otherwise, the similarity of the two color vectors is lower;
and 4, step 4: acquiring a pixel in a color space, constructing a current structural unit as a moving window by taking the pixel as a center, and forming a color vector set in the current structural unit; the size of the current structural unit is selected according to actual needs;
and 5: determining a supremum vector and a infimum vector of a color vector set formed by the current pixel by taking the FSM as a reference;
step 6: constructing basic operations of color morphology by using the supremum and the infimum of the current pixel and the color vector set thereof, wherein the basic operations comprise expansion operation, corrosion operation, opening operation and closing operation;
and 7: applying the basic operation of color morphology proposed in the step 6 to the color image, and replacing the current color vector by the supremum vector or the infimum vector, namely replacing the current pixel by the supremum pixel or the infimum pixel, and outputting the current pixel as the morphology of the current structural unit;
and 8: and (4) judging whether all pixels of the color image to be processed are processed, if not, returning to the step (4) to process the rest pixels until all pixels are processed.
Preferably, in step 3, a fuzzy similarity measure FSM for describing the similarity between two color vectors is constructed and drawn together according to the distance and angle of the color vectors, as shown in formula (1), the function value is between 0 and 1, when the two color vectors are the same vector, the value is 1, and when the two color vectors are completely different, the value is 0;
wherein k is1═ 0, ∞) and k2＝[0，1]For the fuzzy control parameter, two fuzzy control parameters k are set artificially according to actual conditions1And k2Value of (a), parameter k1And k2Directly determines the degree of similarity of the two color vectors, as k is1、k2The similarity measure among the color vectors is reduced, and the similarity degree is reduced; otherwise, the degree of similarity increases; parameter k1Ratio k2The influence on the similarity measure is larger, the similarity measure is for k1Is more sensitive; d (v)i，vj) Representing any two colour vectors v in a colour imageiAnd vjThe vector distance between; theta (v)i，vj) Representing any two colour vectors v in a colour imageiAnd vjThe vector angle between;
when the two color vectors are closer in distance and angle, namely the distance and the included angle are smaller, the value of the similarity measure is larger, and the similarity of the two color vectors is higher; conversely, when the distance and the included angle between two color vectors are larger, the value of the similarity measure is smaller, and the similarity between the two color vectors is lower.
Preferably, the specific steps of step 5 are as follows:
step 5.1: calculating FSM function values between any two color vectors in a color vector set in a current structural unit according to a formula (1);
step 5.2: determining the most dissimilar color vector pair set in the current structural unit based on the FSM function value calculated in the step 5.1, randomly selecting a pair of the most dissimilar color vector pairs, and determining the maximum color vector and the minimum color vector according to the magnitude of the mode values of two color vectors in the most dissimilar color vector pairs, wherein the maximum mode value is the maximum color vector, and the minimum mode value is the minimum color vector;
step 5.3: dividing a color vector set formed by the current structural unit into two subsets by taking the maximum color vector and the minimum color vector as cores, namely a maximum color vector subset and a minimum color vector subset; for any color vector in the color vector set formed by the current structural unit, if the similarity measure of the any color vector and the maximum color vector is greater than the similarity measure of the any color vector and the minimum color vector, the any color vector belongs to the maximum color vector subset, otherwise, the any color vector belongs to the minimum color vector subset;
step 5.4: respectively calculating the highest similarity color vector in the maximum color vector subset and the minimum color vector subset;
step 5.5: and defining the highest similarity color vector obtained in the minimum color vector quantum set as a infimum vector, and defining the highest similarity color vector obtained in the maximum color vector quantum set as an supremum vector.
Preferably, when the pixels are taken in step 4, the pixels are taken one by one in the color image to be processed, from left to right, from top to bottom.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: the invention provides a color morphological image processing method combining color space fuzzy similarity, which defines a fuzzy similarity measure which is consistent with human perception and used for measuring color vector similarity relation in RGB color space, and accordingly provides a morphological method applied to color images. The invention really applies the morphological thought to the color image processing, not only avoids the problem of color vector sequencing, but also effectively solves the problem of losing or distorting the original image information in the color image processing, has the characteristics of good stability, strong practicability and the like in the actual color image processing, not only can smooth the color target, but also can well process the detail characteristics of pixel inconsistency of a homogeneous region, finally achieves the target of color image analysis and processing, and provides a new thought for the filtering, segmentation, characteristic extraction, edge detection, image enhancement, restoration and the like of the color image.
Drawings
FIG. 1 is a flowchart of a color morphological image processing method based on fuzzy similarity according to an embodiment of the present invention;
FIG. 2 is a color vector representation of RGB space corresponding to color image pixels in step 2 provided by an embodiment of the present invention;
FIG. 3 is a diagram illustrating the determination of FSM functions according to an embodiment of the present invention;
FIG. 4 is a diagram illustrating the influence of fuzzy control parameters of FSM functions on similarity according to an embodiment of the present invention;
FIG. 5 is a flowchart of step 5 according to an embodiment of the present invention;
fig. 6 is a high resolution remote sensing image according to an embodiment of the present invention;
FIG. 7 is a diagram of color morphology operation results, wherein (a) is a result of erosion operation, (b) is a result of dilation operation, (c) is a result of open operation, and (d) is a result of close operation;
fig. 8 is a schematic diagram of comparing (a) an average value of similarity measures of gray images corresponding to an original color image and (b) a schematic diagram of similarity degree comparison of gray images corresponding to the original color image according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
A color morphological image processing method based on fuzzy similarity, as shown in fig. 1, includes the following steps:
step 1: reading a color image to be processed;
in this embodiment, the color image to be processed is defined as X ═ X i1.. N }, where x isiI is the ith pixel, i is the pixel index, N is the total number of pixels, X is 150 × 150 pixels, and the total number of pixels N is 22500.
Step 2: the color image to be processed is mapped to the RGB color space, i.e. the pixels of the color image are represented by vectors of the color space, and each color vector is composed of three color components, red (R), green (G) and blue (B).
For the color image X to be processed, the color image X is corresponding to an RGB color space, and N pixels of the color image X form a color vector set VX＝{v i1,.., N }, wherein v ═ 1,.. N }, in which v ═ v ·i＝(viR，viG，viB) Is the color vector of the color pixel i, viR、viG、viBRespectively representing colour vectors viThe red, green and blue components of (a) as shown in fig. 2.
And step 3: a Fuzzy Similarity Measure (FSM) function describing the similarity degree between two color vectors is determined, parameters in the function are determined, and when the value of the fuzzy similarity measure is larger, the fuzzy similarity measure is considered to have higher similarity degree, namely the colors of two corresponding pixels are more similar, which is just consistent with the visual perception of human beings. The FSM function is shown in fig. 3.
In RGB color space, color vector v representing any two pixel points i and j in color imageiAnd vjThe similarity of (c) is represented by the inter-vector distance as:
d(vi，vj)＝((viR-vjR)2+(viG-vjG)2+(viB-vjB)2)1/2
when the distance d (v) between two color vectorsi，vj) The smaller the value is, the higher the similarity degree of the two vectors is, namely, the colors of the two pixel points i and j are closer visually, otherwise, the larger the difference between the colors of the pixel points i and j is visually represented. Similarly, the angle of the color vector (i.e. the relative direction of the vector) can also be used to describe the similarity, as shown in the following formula.
When the angle theta (v) between the vectors formed by the two pixel points i and ji，vj) The smaller the similarity between two pixel points is, the more similar the similarity isAnd when the angle between the vectors formed by the two pixel points i and j is larger, the similarity of the two pixel points is lower. However, both of the above function definitions have certain disadvantages and limitations due to consideration of only one aspect.
In this embodiment, the distance and angle of the color vectors are used together to construct and characterize a fuzzy similarity measure FSM of the similarity between two color vectors, which is defined as follows:
wherein k is1═ 0, ∞) and k2＝[0，1]Two fuzzy control parameters k are artificially and flexibly set according to actual conditions for the fuzzy control parameters1And k2Value of (a), parameter k1And k2The human adjustment of (2) can make the fuzzy similarity measure FSM not only visually depict the similarity between two vectors, but also be consistent with the visual perception of human blur, i.e. for the same two color vectors, different people have differences in their recognitions of the similarity. Assuming that the distance and angle of two color vectors are d-1 and theta-pi/4, respectively, the similarity measure between the two vectors is dependent on the parameter k1And k2As shown in fig. 4, it can be clearly seen that for the same two color vectors, the current parameter k is1And k2The fuzzy similarity measure obtained by equation (1) is different when different values are taken, with the parameter k1And k2Directly determines the degree of similarity of the two vectors, as k is1、k2Decreases the similarity measure between vectors and decreases the similarity measure, whereas the similarity measure increases and the parameter k1Ratio k2The influence on the similarity measure is larger, the similarity measure is for k1Is more sensitive to changes in the signal. From the above analysis, it can be seen that this is consistent with the characteristic that the similarity of the color vectors varies from person to person and from environment to environment, and can meet and conform to the uncertainty and ambiguity caused by the visual perception of the person in the color image processing process.
The FSM is similar to a fuzzy membership function,the function value is between 0 and 1. When two color vectors viAnd vjThe closer the distance and the angle are, the smaller the distance and the included angle are, the larger the value of the similarity measure is, and the higher the similarity between the distance and the included angle is; conversely, when the distance and the included angle between two color vectors are larger, the value of the similarity measure is smaller, and the similarity degree is lower. When two color vectors are superposed (namely, the same vector), the distance and the included angle are both 0, the similarity measure is 1, the similarity degree of the characteristics is the highest, the similarity measure and the characteristics are consistent with the actual visual perception, and the limitation caused by only defining the distance or the angle is overcome.
And 4, step 4: in the color space VXObtaining a pixel i, constructing a current structural unit as a moving window by taking the pixel i as a center, selecting the size of the current structural unit according to actual needs, and forming a color vector set in the current structural unit
Including the current center vector viThe q color vectors inside. In this embodiment, the color image V to be processed is obtained as pixels are acquiredXWherein pixels are taken one by one in left-to-right, top-to-bottom order.
And 5: the supremum vector and the infimum vector of the set of color vectors formed by the current pixel are determined by taking the FSM as a reference, as shown in fig. 5, and the specific steps are as follows.
Step 5.1: and (3) calculating the FSM function value between any two color vectors in the color vector set in the current structural unit according to the formula (1).
Step 5.2: determining the set V of color vector pairs that are least similar in the current structural element based on the FSM function values calculated in step 5.1idsRandomly selecting a pair of least similar color vector pairs from the color vector pairs, and determining the maximum color vector and the minimum color vector according to the magnitude of the modulus values of two color vectors in the least similar color vector pairs, wherein the maximum color vector is the modulus value larger, and the minimum color vector is the modulus value smallerIs the minimum color vector, which is defined as follows:
wherein p is ViAnd q is the number of color vectors in the set. According to the above definition, set VidsIs Vi×ViAnd all the color vector pairs are the vector pair set with the smallest similarity measure. At VidsIn (d), a vector pair is randomly selected as the least similar color vector pair, and is marked as (v)ids1，vids2)∈Vids. According to the size v of its mouldids1And vids2Respectively called maximum color vector (modulus is large) vimaxAnd minimum color vector (modulus value-minimum) vimin。
Step 5.3: taking the maximum color vector and the minimum color vector as the core, dividing the color vector set formed by the current structural unit into two subsets, namely a maximum color vector subset and a minimum color vector subset, namely respectively taking the maximum color vector v and the minimum color vector v as the coreimaxAnd viminAs a core, let ViAll color vectors are divided into two categories, denoted as CLimaxAnd CLimin. For arbitrary color vectors vip∈ViIf v isipAnd vimaxIs greater than vipAnd viminIs a measure of similarity of vipBelong to CLimaxOtherwise, vipBelong to CLiminNamely:
CLimin＝{vip，μ(vip，vimin)≥μ(vip，vimax)，vip∈Vi} (3)
CLimax＝{vip，μ(vip，vimax)≥μ(vip，vimin)，vip∈Vi} (4)
step 5.4: separately calculating the two subsets CLimaxAnd CLiminThe highest similarity color vector in (1).
At CLiminAnd CLimaxIn (1), define the color vector v with the highest similaritycliminAnd vclimaxRespectively as follows:
step 5.5: will subset CLiminThe highest similarity vector obtained in (c) is defined as the infimum vector, and the subset CL is defined as theimaxThe highest similarity vector obtained in (a) is defined as the supremum vector.
From the definition of the highest similarity color vectors of equations (5) and (6), the structural unit V can be constructediThe lower definite limit operation and the upper definite limit operation in (1) are respectively as follows:
∧Vi＝∧{vi1，vi2，...，viq}＝vclimin(7)
∨Vi＝∨{vi1，vi2，...，viq}＝vclimax(8)
as can be seen from the formulas (7) and (8), the output color vectors of the lower definite operation V and the upper definite operation V are respectively the color vector class CLiminAnd CLjmaxMedium highest similar color vector vcliminAnd vclimaxThey are each independently of CLiminAnd CLimaxThe sum of the similarity measures of all other color vectors in the set is the largest. In addition, the color vectors output by the defined supremum and infimum operations are all the color vectors in the structural units in the acquired color image, i.e. the operations do not generate new color vectors, and the original image information is effectively maintained to a great extent, which is also the basis for constructing the color morphology method.
Step 6: and constructing basic operations of color morphology by using the supremum and the infimum of the current pixel and the color vector set thereof, wherein the basic operations comprise expansion operation, corrosion operation, opening operation and closing operation.
For the color to be processedColor image X, color vector collection space V formed by color imagesXThe morphological operation of the color image defined in this embodiment includes a dilation operationXEtching operationXClosed operation chiXOn operation oXRespectively defined as:
X(VX)＝{∨Vi，i＝1，2，...，N} (9)
X(VX)＝{∧Vi，i＝1，2，...，N} (10)
χX(VX)＝X(X(VX)) (11)
oX(VX)＝X(X(VX)) (12)
as can be seen from the above color morphology operations, vector set V is aimed at color imagesXIs in the structural unit ViFinding the supremum of the color vector subset; similarly, the etching operation is carried out in the structural unit ViFinding the infimum of the subset of color vectors; the open and close operations are complex operations of expansion and corrosion, and only the sequence of the calculation of the infimum and the infimum is different each time. Therefore, morphological processing on the color image can be effectively finished, and basic characteristics of pixel color vectors of the original image are reserved to a great extent.
And 7: and (3) applying the basic operation of color morphology proposed in the step (6) to the color image, and replacing the current color vector by the supremum vector or the infimum vector, namely replacing the current pixel by the supremum or the infimum pixel, and outputting the current pixel as the morphology output of the current structural unit.
And 8: and judging whether all pixels of the color image to be processed are processed or not, if not, returning to the step 4, obtaining another pixel from left to right and from top to bottom, and performing the same processing on the rest pixels until all pixels are processed, so that the color image is processed, and the foundation is laid for the subsequent filtering, segmentation, feature extraction, edge detection, image enhancement, restoration and the like of the color image.
In this embodiment, the rulerThe remote sensing image with the high resolution and the degree of 150 x 150 pixels is used as a color morphology operation test image to observe and analyze the processing capacity and the effect of the remote sensing image on a color image, and the remote sensing image is shown in fig. 6. Parameter k in fuzzy similarity measure FSM10.001 and k2Theoretical and experimental simulations show that the image processing effect is better when the parameter is equal to 0.8. In specific implementation, specific values of the two parameters can be modified in real time according to actual image processing requirements. The structural unit is a square with 3 × 3 pixels in scale, and the color shape operation results are shown in fig. 7, where (a) is erosion, (b) is dilation, (c) is on operation, and (d) is off operation. As can be seen from fig. 7(a), the erosion operation expands the shadow (i.e., background) area in the original image, compresses other objects, fills the original small gaps, and smoothes the color and edges of each object; as can be seen from fig. 7(b), the result of the dilation operation is just the opposite of the erosion operation, the shaded (background) portion of the original image is compressed, the other objects are expanded, i.e., the light color is expanded, the dark color is compressed, the "burrs" in the original image are eliminated, and the color and edges of the objects are also smoothed. Similar to the erosion and dilation operations, as shown in fig. 7(c) and (d), the above operation results show that the color morphological operation proposed in this embodiment conforms to the basic principle of morphological operation, and can better solve the problem of pixel inconsistency in homogeneous regions, which makes color image segmentation, filtering, target extraction, etc. based on color morphology possible.
The color morphological operation proposed in this embodiment is compared with the color morphology expanded by the gray scale morphology and the morphology based on the region sorting, and the color remote sensing image shown in fig. 6 is still selected as the test image. The color morphology with expanded gray scale morphology is that the color image is regarded as being composed of three monochromatic images of red, green and blue, the three monochromatic images are respectively processed by utilizing the gray scale morphology, and finally the color image is restored by utilizing the morphological processing result. The morphology based on region sorting is to sort the gradient of the vectors in the current region (the region is 3 × 3 pixels) and output the vector with the minimum gradient and the maximum gradient as the morphology. Book (I)The parameter k of the fuzzy similarity measure in the color morphology operation is provided by the embodiment10.001 and k2The structural unit is 3 × 3 pixels, 0.8. From the theory of gray-scale morphology, the color image after the operations of erosion, expansion, opening, closing, etc. are performed by three different morphological methods is converted into the corresponding gray-scale image, and the average value of the similarity measure between the color image and the gray-scale image corresponding to the original color image is obtained, as shown in fig. 8(a), it can be clearly seen that the operations of erosion, expansion, opening, closing, etc. can change the gray-scale information corresponding to the original image. In addition, the average value of the fuzzy similarity measure of the morphological operation result and the corresponding pixels of the original image, i.e. erosion-original image, dilation-original image, opening-original image, and closing-original image, is compared from the perspective of similarity of the color image, and the similarity degree between the morphological operation result and the original image is evaluated, as shown in fig. 8(b), it can be seen that the original image can be changed by erosion, dilation, opening, closing, and other operations, but the similarity after the color morphological operation proposed in this embodiment is the highest, that is, when the same color image processing target is reached, the morphological operation proposed in this embodiment has the smallest change of the detail characteristics of the original image, so that the phenomenon of color image distortion caused by the operation can be greatly reduced. Through quantitative comparison, it can be seen that the proposed color morphology based on fuzzy similarity not only can be consistent with the classical binary and gray scale morphology theory, but also can well maintain the detail characteristics of the original image, has a better processing effect, and lays a foundation for the popularization and application of the color morphology.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.
Claims (2)
1. A color morphology image processing method based on fuzzy similarity is characterized in that: the method comprises the following steps:
step 1: reading a color image to be processed;
step 2: mapping the color image to be processed to an RGB color space, namely representing the pixels of the color image by using vectors of the color space, wherein each color vector consists of three color components of red (R), green (G) and blue (B);
and step 3: determining a fuzzy similarity measure function representing the similarity degree between any two color vectors in the color space, and determining parameters in the function; when the value of the fuzzy similarity measure is larger, the similarity of the two color vectors is higher, otherwise, the similarity of the two color vectors is lower; a fuzzy similarity measure function, namely FSM function;
the distance and the angle of the color vectors are used for jointly constructing and describing a fuzzy similarity measure FSM of the similarity between the two color vectors, as shown in formula (1), the function value is between 0 and 1, when the two color vectors are the same vector, the value is 1, and when the two color vectors are completely different, the value is 0;
wherein, mu (v)i，vj) For two colour vectors viAnd vjA fuzzy similarity measure FSM of the inter-similarity; e represents the base of the exponential function; k is a radical of1═ 0, ∞) and k2＝[0，1]For the fuzzy control parameter, two fuzzy control parameters k are set artificially according to actual conditions1And k2Taking the value of (A); d (v)i，vj) Representing arbitrary in a color imageTwo color vectors viAnd vjThe vector distance between; theta (v)i，vj) Representing any two colour vectors v in a colour imageiAnd vjThe vector angle between;
when the two color vectors are closer in distance and angle, namely the distance and the included angle are smaller, the value of the similarity measure is larger, and the similarity of the two color vectors is higher; on the contrary, when the distance and the included angle between the two color vectors are larger, the value of the similarity measure is smaller, and the similarity between the two color vectors is lower;
and 4, step 4: acquiring a pixel in a color space, constructing a current structural unit as a moving window by taking the pixel as a center, and forming a color vector set in the current structural unit; the size of the current structural unit is selected according to actual needs;
and 5: determining a supremum vector and a infimum vector of a color vector set formed by the current pixel by taking the FSM as a reference; the method comprises the following specific steps:
step 5.1: calculating FSM function values between any two color vectors in a color vector set in a current structural unit according to a formula (1);
step 5.2: determining the most dissimilar color vector pair set in the current structural unit based on the FSM function value calculated in the step 5.1, randomly selecting a pair of the most dissimilar color vector pairs, and determining the maximum color vector and the minimum color vector according to the magnitude of the mode values of two color vectors in the most dissimilar color vector pairs, wherein the maximum mode value is the maximum color vector, and the minimum mode value is the minimum color vector;
step 5.3: dividing a color vector set formed by the current structural unit into two subsets by taking the maximum color vector and the minimum color vector as cores, namely a maximum color vector subset and a minimum color vector subset; for any color vector in the color vector set formed by the current structural unit, if the similarity measure of the any color vector and the maximum color vector is greater than the similarity measure of the any color vector and the minimum color vector, the any color vector belongs to the maximum color vector subset, otherwise, the any color vector belongs to the minimum color vector subset;
step 5.4: respectively calculating the highest similarity color vector in the maximum color vector subset and the minimum color vector subset;
step 5.5: defining the highest similarity color vector obtained in the minimum color vector quantum set as a infimum vector, and defining the highest similarity color vector obtained in the maximum color vector quantum set as an supremum vector;
step 6: constructing basic operations of color morphology by using the supremum and the infimum of the current pixel and the color vector set thereof, wherein the basic operations comprise expansion operation, corrosion operation, opening operation and closing operation;
and 7: applying the basic operation of color morphology proposed in the step 6 to the color image, and replacing the current color vector by the supremum vector or the infimum vector, namely replacing the current pixel by the supremum pixel or the infimum pixel, and outputting the current pixel as the morphology of the current structural unit;
and 8: and (4) judging whether all pixels of the color image to be processed are processed, if not, returning to the step (4) to process the rest pixels until all pixels are processed.
2. The method for processing a color morphological image based on fuzzy similarity according to claim 1, characterized in that: when the pixels are obtained in step 4, the pixels are obtained one by one in the color image to be processed from left to right and from top to bottom.
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