CN102708554B - Method for converting digital color images to grayscale images - Google Patents
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Abstract
The invention provides a method for converting digital color images to grayscale images. The method includes: mapping each pixel of a color image to a RGB (red, green and blue) space, and zoning a space zone so as to obtain a classification prototype; classifying points on the RGB space corresponding to the pixels of the digital color image to the classification prototype; and taking the classification prototype as a node of a one-dimensional spring system, establishing an optimal example by the aid of a mountain climbing law, and computing a grayscale value of each pixel by the aid of an inverse distance weighting method. Based on distribution density of the pixels of the converted color image in the color space, the corresponding points of the image on the color space are classified, mapping from three-dimensional space points to one-dimensional space points is achieved by the aid of the spring system according to the energy minimization principle, and the grayscale value of each pixel is computed finally. The method is good in robustness for different images, highly adaptive and low in computing resource utilization ratio, adjustment on manual parameters is not needed, and good conversion effects are obtained actually.
Description
Technical Field
The invention belongs to the field of digital images, and particularly relates to a method for converting a digital color image into a gray image.
Background
In the field of digital images, color images and grayscale images have different application ranges in real life. At present, the core algorithm of many image processing products takes a digital gray image as input data, and especially when gradient and edge information of an image is needed, the gray image is very important, because the gradient and edge calculation only needs single-channel image information. The gradient and edge information is important information for image enhancement and image identification, and is widely applied to video monitoring, human-computer interaction, computer intelligence and other aspects. Meanwhile, the storage space occupied by the gray image of the same image is only 1/3 of the color image, and the gray image is needed to be used in many cases, so that a large amount of storage space can be saved.
It is currently common practice to convert a color image into a grayscale image by calculating the luminance of each pixel in the color image, i.e., the modulus of the RGB values of the pixel in a three-dimensional color space. However, the biggest problem of this method is that different colors may have the same brightness value, and after conversion into a gray-scale image, the difference and edges between the colors disappear, thus causing a serious loss of information. Therefore, some scholars propose different gray-scale image conversion methods, some based on the global features of the image, and some based on the regional features of the image. At present, the conversion effect of the method based on the global feature is not ideal, and the method based on the regional feature can generate the negative effect of the low-frequency regional fluctuation of the image. Amy Gooch et al propose an improved regional method, called Color2gray method, which is relatively effective. However, this method is too computationally expensive to process high resolution images and is not very practical.
Disclosure of Invention
The present invention addresses the above-mentioned deficiencies of the prior art and provides a method for converting a digital color image into a grayscale image, which is implemented based on the global characteristics of the color distribution of the input color image and has a desirable conversion effect.
The invention is realized by the following technical scheme:
a method of converting a digital color image to a grayscale image, comprising the steps of:
(1) mapping each pixel of the digital color image to an RGB space to obtain a three-dimensional histogram, and performing Gaussian filtering smoothing processing on the three-dimensional histogram to form a continuous non-zero space region;
(2) partitioning the non-zero space region obtained in the step (1) according to density distribution to obtain a plurality of independent high-density regions, and selecting a plurality of high-density regions as classification prototypes according to the volume size of the high-density regions;
(3) classifying points corresponding to each pixel of the digital color image in the RGB space into the classification prototype selected in the step (2) by using a space expansion method;
(4) taking the classified prototype as a node of a one-dimensional spring system, randomly establishing a plurality of one-dimensional spring system examples, and selecting an example with the minimum pressure sum in a dynamic balance state from the plurality of one-dimensional spring system examples as an optimized example;
(5) establishing a corresponding relation between each node in the optimization example and the gray value of 0-255 to obtain the gray value corresponding to each classification prototypeu i ；
(6) Calculating any pixel in the digital color image using the following formulaxGray value ofu(x)：
Wherein, Nin order to classify the number of prototypes,i、jin order to classify the number of the prototype,，d(x,x i ) p is a pixelxIn RGB space with its classified prototypeiIs measured with respect to the distance between the centroids,pin order to be an index parameter, u i for classifying prototypesiThe corresponding gray-scale value of the image,，d(x,x j ) p is a pixelxIn RGB space with its classified prototypejIs measured in the center of mass.
Further, in the step (2), a space density estimation method is adopted for partitioning.
Further, the flow of the spatial dilation method described in step (3) is as follows:
(3.1) all classification areas are indicated by different non-zero numerical labels, and points in the same classification area have the same label. Points in space that do not belong to any classification region are labeled 0.
(3.2) setting status flagf=1, setting the current point as any vertex of the whole space;
(3.3) if the current point label is 0, marking the statef=0；
(3.4) checking all adjacent points of the current point, if one adjacent point label is not 0, setting the current point label to be the same as the label of the non-zero point, and classifying the current point into a classification area where the adjacent point is located;
(3.5) judging whether an unclassified point still exists in the space, if so, entering the step (3.6); if not, the step (3.7) is carried out;
(3.6) taking the current point as the next point, and repeatedly executing the steps (3.3) - (3.5) until all points of the whole space are traversed;
(3.7) judging status flagfIf yes, turning to the step (3.1); if not, ending.
Further, the sum of the pressures of the one-dimensional spring system in the step (4) is,m,nis a reference number for a node that is,Mis the total number of the nodes and,d mn (X)is the distance between the two nodes and is,≥0 is a weight coefficient whose value is a nodemAndnthe product of the number of points each has;δ mn is a nodemAndnthe ideal distance between the centroids of each classified prototype in the three-dimensional space;is a nodemAnd nodenThe pressure in between.
Further, in the step (4), an optimized example is selected from a plurality of one-dimensional spring system examples by adopting a hill climbing rule.
The method for converting the digital color image into the gray level image is characterized in that corresponding points of the image on a color space are classified according to the distribution density of pixels of the converted color image in the color space, then a spring system is used for realizing the mapping from three-dimensional space points to one-dimensional space points according to the energy minimization principle, and finally the gray level value of each pixel is calculated. The method is a global method based on the color distribution characteristics of the input images, has good robustness to different images, strong adaptability and low utilization rate of computing resources, does not need manual parameter adjustment, and obtains a good conversion effect in practice.
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FIG. 1 is a schematic flow chart of a conversion method according to the present invention;
FIG. 2 is a schematic view of a non-zero spatial region;
fig. 3 is a two-dimensional representation of the spatial density estimation method.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the method for converting a digital color image into a grayscale image according to the present invention comprises the following steps:
(1) mapping each pixel of the digital color image to a corresponding RGB space to obtain a three-dimensional histogram, and performing Gaussian filtering smoothing processing on the three-dimensional histogram to form a continuous non-zero space region. The non-zero space region refers to a region composed of all non-zero points in space, and the block-shaped region shown in fig. 2 represents the non-zero space region. The Gaussian filter operator in the Gaussian filter smoothing processing is a three-dimensional operator of 3 × 3, and the filter calculation formula is as follows:
wherein, Din order to obtain a smoothed three-dimensional histogram,Iin order to obtain a three-dimensional histogram before smoothing,hgaussian operator of 3 x 3.(x,y,z)Is the coordinates of a point of the three-dimensional histogram,（i,j,k）coordinates of the points of the gaussian operator.
(2) And (2) partitioning the non-zero space region obtained in the step (1) according to density distribution to obtain a plurality of independent high-density regions, and selecting a plurality of high-density regions as classification prototypes according to the volume size of the high-density regions.
Since the distribution density of the points in the space is different, some places are more concentrated and some places are more sparse, and the points in the density concentrated after filtering are represented as high-value points and are represented as vertexes (or peaks) in the three-dimensional histogram. The invention divides the area with each point concentration into high density areas. That is, the high density region is a region in which the number of points included in the non-zero space region is high relative to other regions, and is often a region near the vertex of the histogram. The volume of the high-density region is substantially the number of dots in the region, and the region having a large number of dots has a large volume. Of course, the concentration and the dispersion of the point distribution are relative meanings, no absolute standard exists, different partition methods can correspond to different estimation modes, and the obtained partition results are different.
The invention sorts the volumes of all high-density areas from large to small, and then selects a plurality of high-density areas from large to small as classification prototypes. The number of the classification prototypes depends on specific application and objects, the value range is 5-50, and the number equal to the number of the types of the colors in the color image can be generally selected. Too many classifications can result in large gray level fluctuations in the output result in regions that should be low frequency; too few classifications may result in color edges between different colors in the color image becoming less visible or even disappearing in the grayscale image. The latter spring system of the invention is somewhat tolerant to the above-mentioned problems, but should still be based as much as possible on the number of colors in the image when selecting the number of classifications. Setting the number of classes to 10 is a more compromised and feasible approach, except for some extremes.
There are many methods for partitioning the non-zero space region according to the density distribution, and a complete linkage method, a threshold method, a watershed method, and the like in the prior art can be adopted. The present invention employs a spatial density estimation method for estimating the density between two sets of points in digital space to determine whether two regions can be merged into one. Specifically, as shown in FIG. 3, let the set of two points in space beG 1 、G 2 ， G 1 AndG 2 respectively has a center of mass ofC 1 、C 2 Will beC 1 AndC 2 is divided into six equal parts, and the six equal division points are fromC 1 ToC 2 Are marked sequentially withC 6 、C 4 、C3、C5、C7(ii) a Respectively pass throughC 1 、C 4 、C 5 、C 2 Make perpendicular toC 1 C 2 Is marked byP 1 、P 2 、P 3 、P 4 (ii) a Marking the space regions between two adjacent planes asZ 1 、Z 2 、Z 3 。
To pairZ 2 AndZ 1 、Z 3 are compared to determine whether the two sets can be linked together. First, we first count the number of points in each region, i.e. the number of points between two adjacent vertical planes. Judging whether a point is between two planes, and judging by the following method:
consider a plane equation
WhereinA、B、C、DAre all real numbers.
Due to the fact thatP 1 、P 2 、P 3 、P 4 All parallel, in the above four planesA、B、CAre all equal. So for any adjacentP i AndP j the equations are respectively:
dotp 0 The distances to these two planes are:
if it is not goodp 0 In thatP i AndP j in between, thent i *t j < 0。
The method can count the regionZ 1 、Z 2 、Z 3 Number of midpointsn i Whereini=1,2,3。
In order to estimate the density of the points, the volume of the point distribution in each region needs to be calculated, however, the calculation of the distribution volume is very difficult, and the invention uses the average distance from the points to the center instead. All points in each region to the center point (i.e., the center point)Z 1 、Z 2 、Z 3 Respectively correspond toC 6 、C 3 、C 7 ) Is recorded as the average distanced 1 、d 2 、d 3 The density of each area can then be written as
Whereini=1,2,3，pIs an exponential parameter and is a positive real number.
Then, the densities of the regions are compared according to a preset comparison strategydens 2 ~f(dens 1 , dens 3 )Wherein-represents a comparison sign, a functionf()Representing the way in which the two densities are weighted.
For example, the predetermined comparison policy may be
dens
2
≥f(dens
1
, dens
3
)
f(dens 1 , dens 3 )=(dens 1 +dens 3 )/2
That is, the comparison sign is greater than or equal to, and the weighting mode is an average value. Of course, other comparison strategies may be used with the present invention. If the density of each region satisfies the comparison policy, it is considered that the two sets can be merged into one. And (4) processing the set of all points in the non-zero space region by adopting a space density estimation method to realize the partition.
(3) And (3) classifying the points corresponding to each pixel of the color image in the RGB space into the classification prototype selected in the step (2) by using a space expansion method.
Assuming that there are several independent classification regions in the finite digital space, the spatial expansion method means that these classification regions are expanded simultaneously so that they contact each other and fill the entire finite digital space. Spatial dilation is used to quickly classify discrete points in space into the nearest classification region. Specifically, the flow of the spatial dilation method is as follows:
(3.1) all classification areas are indicated by different non-zero numerical labels, and points in the same classification area have the same label. Points in space that do not belong to any classification region are labeled 0.
(3.2) setting status flagf=1, setting the current point as any vertex of the whole space;
(3.3) if the current point label is 0, marking the statef=0。
And (3.4) checking all adjacent points of the current point, if one adjacent point label is not 0, setting the current point label to be the same as the label of the non-zero point, and classifying the current point into a classification area where the adjacent point is located.
(3.5) judging whether an unclassified point still exists in the space, if so, entering the step (3.6); if not, the step (3.7) is carried out;
and (3.6) taking the current point as the next point, and repeatedly executing the steps (3.3) - (3.5) until all points of the whole space are traversed.
(3.7) judging status flagfIf yes, turning to the step (3.1); if not, ending.
(4) Taking the classified prototype as a node of a one-dimensional spring system, randomly establishing a plurality of one-dimensional spring system examples, and selecting an example with the minimum pressure sum in a dynamic balance state from the plurality of one-dimensional spring system examples as an optimized example;
according to the spring system theory, the concrete data in the step (3) are used for establishing a one-dimensional spring system example. The spring system is a one-dimensional system and consists of a plurality of nodes and connecting lines between each pair of nodes, and each node corresponds to a classification prototype in an RGB three-dimensional space. Each link can be considered a spring such that there is pressure between each two nodes.
Summation of pressure in a spring systemσ(X)Given by the formula carrousel pressure (Kruskal's stress):
wherein,m, nis a reference number for a node that is,Mis the total number of the nodes and,d mn (X)is the distance between the two nodes and is,≥0 is a weight coefficient whose value is a nodemAndn(i.e., the product of the number of points owned by each of the two classification models);δ mn is a nodemAndnthe ideal distance between the centroids of each classified prototype in the three-dimensional space;is a nodemAnd nodenThe pressure in between.
The specific method for calculating the sum of the pressures of the one-dimensional spring system example in the dynamic equilibrium state is as follows:
(4.1) having a one-dimensional spring systemnEach node, calculating the distance between every two nodes and calculating the pressure sumσ(X)。
(4.2) running one-dimensional spring System example, i.e. using the ideal distanceδ mn Minimizing the sum of the pressure, and the specific method comprises the following steps:
(a) calculating pressures between the nodes, and applying the pressures to each node; because each node is connected with a plurality of nodes, one node can be simultaneously subjected to a plurality of pressures. The pressure sum of each node can be calculated by the mechanics principle, and the node can move according to the pressure sum. According to the energy minimization law, the spring system will change towards a configuration in which the sum of the pressures is minimal.
(b) After the nodes move, updating all node distances and pressure sums; since the node distance and pressure sum are constantly changing due to the movement of the node, the node distance and pressure sum are updated every time the node moves.
(c) Repeating the steps (a) to (b) until the whole system reaches a dynamic balance state; at this point all nodes are no longer moving and the sum of the pressures of the one-dimensional spring system is minimal.
The invention adopts hill-climbing law to select the optimized example from a plurality of one-dimensional spring system examples. The specific method comprises the following steps:
(A) one spring system example is selected from a plurality of one-dimensional spring system examples to serve as a foreground spring system example, the rest spring system examples serve as background spring system examples, and all the examples are initialized randomly.
(B) All one-dimensional spring system examples were run in parallel.
(C) When the sum of pressure of a certain background instance is smaller than that of a foreground instance, deleting the current foreground instance and pushing the background instance to the foreground;
when a background instance still cannot obtain a smaller pressure sum than a foreground instance after running for a certain time (the time is a preset parameter), stopping the background instance and starting a new background instance;
when the foreground instance runs for a certain time (the time is also a preset parameter), the foreground instance can be replaced by the non-background instance, and then the foreground instance is used as an optimized instance.
(5) And establishing a corresponding relation between each node in the optimization example and the gray value of 0-255 to obtain the gray value corresponding to each classification prototype in the optimization example.
According to the invention, the numerical range of the node distance of the one-dimensional spring system corresponds to the range of 0-255 of the gray value, so that each node of the spring system corresponds to one gray value, namely each classification prototype corresponds to one gray value in the one-dimensional spring system, and the position of the classification prototype in the three-dimensional space can be mapped to the one-dimensional gray space.
Specifically, a node at the end of the one-dimensional spring system is selected as a head node, a node farthest from the head node is selected as a tail node, the head node corresponds to the gray value 0, and the tail node corresponds to the gray value 255. Setting any node inside one-dimensional spring systemαAt a distance from the head node ofLThe distance between the head node and the tail node isHThen nodeαGray value of 255 ×L/H。
The gray value corresponding to each node in the optimized example is used as the gray value of the classification prototype to be mapped to the one-dimensional spring system, and the gray value corresponding to the classification prototype in the one-dimensional spring system is obtained.
(6) And calculating the gray value of each pixel in the color image by using an inverse distance weighting method (inverse distance weighting) of Shepard (Shepard) according to the gray value corresponding to each classification prototype in the optimization example, thereby obtaining a gray image.
Calculating a pixelxThe specific formula of the gray value of (a) is as follows:
wherein,，Nthe number of classification prototypes selected in the step (2),i、jin order to classify the number of the prototype,d(x,x i ) p is a pixel pointxThe distance in RGB space from the centroid of the classification prototype in which it is located.u i For classifying prototypesiThe corresponding gray value in the optimization example described in step (5).，d(x,x j ) p Is a pixelxThe distance in RGB space from the centroid of the classification prototype in which it is located.pIs an exponential parameter, and is generally preset to be 1.
Example (b):
the present invention uses the digital image of the oil painting sunrise of monen as the conversion object of the embodiment. The digital image has a resolution of 1000 × 769 and is in the format of RGB 24 bits. In the oil painting, indigo is used to indicate the water surface, and vermilion is used to indicate the sun and its reflection at the water surface. If the gray scale image is obtained according to the brightness of the image, the contents of the sun and the reflection completely disappear in the gray scale image due to the close brightness of vermilion and indigo in the image. The present method can well show the difference between vermilion and indigo. The specific treatment process comprises the following steps:
(1) mapping each pixel of the color image to a corresponding RGB space to obtain a three-dimensional histogram, and performing Gaussian filtering smoothing processing on the three-dimensional histogram to form a continuous non-zero space region.
Each pixel in the image is mapped into 256 × 256 three-dimensional space, and the RGB value of the pixel is the coordinate of the corresponding point. Since there may be a plurality of pixels having the same RGB value, the coordinates of the corresponding point are the total number of pixels having the same RGB value. For example, assuming that the RGB values of 5 pixels are (0, 0, 0), the value of the point (0, 0, 0) in the three-dimensional space is 5. This is equivalent to creating a three-dimensional histogram of the RGB values of the image.
In order to speed up the processing, the present embodiment uses a three-dimensional space of 64 × 64 instead of a three-dimensional space of 256 × 256. This is equivalent to compressing the original 256 × 256 space, where each point in the space corresponds to an RGB value region. For example, the point (0, 0, 0) corresponds to 64 values of RGB values (0 to 3 ), and the value of the point is the number of pixels in the RGB value region.
And then, Gaussian filtering smoothing processing is carried out on the obtained three-dimensional histogram by adopting a Gaussian operator to form a continuous non-zero space region.
(2) And (2) partitioning the non-zero space region obtained in the step (1) according to density distribution to obtain a plurality of independent high-density regions, and selecting a plurality of high-density regions as classification prototypes according to the volume size of the high-density regions.
Because the image is large, the use of the full link method and the space density estimation method for partitioning consumes a large amount of memory (larger than the total memory amount of a common computer), the invention uses the watershed method which occupies relatively less resources to partition the non-zero space region, the number of the classification prototypes is set to be 10, and the centroid coordinates and the pixel number of each classification prototype are obtained, as shown in table 1.
TABLE 1
(3) And (3) classifying the points corresponding to each pixel of the color image in the RGB space into the classification prototype selected in the step (2) by using a space expansion method.
(4) Randomly establishing a plurality of one-dimensional spring system examples, and selecting an example with the minimum pressure sum in an equilibrium state from the plurality of one-dimensional spring system examples as an optimization example;
data between each node of the one-dimensional spring system is shown in table 2, wherein an ideal distance between two nodes is a centroid distance, and a weight between two nodes is a product of the number of pixels included in the two corresponding classification models. A number of one-dimensional spring system examples can be built from the data in table 2.
In the embodiment, a foreground instance and a background instance are established. When a background instance runs 2000 cycles, i.e. after 2000 updates of the system state, a smaller pressure sum than the foreground instance is still not available, the background instance is ended and a new one is started. When 100 background instances run and are finished and still cannot replace the foreground instance, the foreground instance is considered as the optimized instance.
TABLE 2
(5) And mapping all the classification prototypes to the optimization example to obtain the gray value corresponding to each classification prototype in the optimization example.
The bit positions of each node in the optimization example were converted to corresponding gray scale values, with the results shown in table 3.
TABLE 3
(6) And calculating the value of each pixel by a distance inverse weight weighting method of Shepard to obtain a gray level image.
The present invention is not limited to the above embodiments, and those skilled in the art can implement the present invention in other various embodiments according to the disclosure of the present invention, so that all designs and concepts of the present invention can be changed or modified without departing from the scope of the present invention.
Claims (5)
1. A method of converting a digital color image to a grayscale image, comprising the steps of:
(1) mapping each pixel of the digital color image to an RGB space to obtain a three-dimensional histogram, and performing Gaussian filtering smoothing processing on the three-dimensional histogram to form a continuous non-zero space region;
(2) partitioning the non-zero space region obtained in the step (1) according to density distribution to obtain a plurality of independent high-density regions, and selecting a plurality of high-density regions as classification prototypes according to the volume size of the high-density regions;
(3) classifying points corresponding to each pixel of the digital color image in the RGB space into the classification prototype selected in the step (2) by using a space expansion method;
(4) taking the classified prototype as a node of a one-dimensional spring system, randomly establishing a plurality of one-dimensional spring system examples, and selecting an example with the minimum pressure sum in a dynamic balance state from the plurality of one-dimensional spring system examples as an optimized example;
(5) establishing a corresponding relation between each node in the optimization example and the gray value of 0-255 to obtain the gray value corresponding to each classification prototypeu i ；
(6) The gray value of any pixel x in the digital color image is calculated using the following formulau(x)：
Wherein, Nin order to classify the number of prototypes,i、jin order to classify the number of the prototype,，d(x,x i ) p is a pixelxIn RGB space with its classified prototypeiIs measured with respect to the distance between the centroids,pin order to be an index parameter, u i for classifying prototypesiThe corresponding gray-scale value of the image,，d(x,x j ) p is a pixelxIn RGB space with its classified prototypejIs measured in the center of mass.
2. The method for converting a digital color image into a grayscale image according to claim 1, wherein the partitioning in step (2) is performed by using a spatial density estimation method.
3. The method for converting a digital color image into a grayscale image according to claim 1, wherein the flow of the spatial expansion method in step (3) is as follows:
(3.1) all the classification areas are represented by different non-zero numerical labels, points in the same classification area have the same label, and the label of the point which does not belong to any classification area in the space is 0;
(3.2) setting status flagf=1, setting the current point as any vertex of the whole space;
(3.3) if the current point label is 0, marking the statef=0；
(3.4) checking all adjacent points of the current point, if one adjacent point label is not 0, setting the current point label to be the same as the label of the non-zero point, and classifying the current point into a classification area where the adjacent point is located;
(3.5) judging whether an unclassified point still exists in the space, if so, entering the step (3.6); if not, the step (3.7) is carried out;
(3.6) taking the current point as the next point, and repeatedly executing the steps (3.3) - (3.5) until all points of the whole space are traversed;
(3.7) judging whether the state identifier f is equal to 0, if so, turning to the step (3.1); if not, ending.
4. The method for converting a digital color image into a grayscale image according to claim 1, wherein the sum of the pressures of the one-dimensional spring system in step (4) is
Wherein,m, nis a reference number for a node that is,Mis the total number of the nodes and,d mn (X)is the distance between the two nodes and is, ≥0 is a weight coefficient whose value is a nodemAndnthe product of the number of points each has;δ mn is a nodemAndnthe ideal distance between the centroids of each classified prototype in the three-dimensional space;is a nodemAnd nodenThe pressure in between.
5. The method for converting a digital color image into a grayscale image according to claim 1, wherein the step (4) selects an optimized instance from a plurality of instances of the one-dimensional spring system by using hill-climbing.
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