JPH01239678A - Binary threshold value deciding system - Google Patents

Abstract

PURPOSE:To decide the optimum threshold value to binarize a light-and-shade picture by using two two-dimensional cumulative histogram calculating means to calculate the value of an image element after passing a differential filter and a memory effectively. CONSTITUTION:The title system is provided with a concentration gradient calculation part 1 to calculate the size of concentration gradient in a picture by using a window differential filter, and a minimum value filter 3 to replace a central image element by the minimum image element in a window. The threshold values theta1 and theta2 to generate the output of first and second two-dimensional cumulative histogram calculation parts 17 and 18 to calculate the number of image elements whose image element value after passing filter 1 exceeds the threshold value theta1 and whose image element after passing a filter 3 and the one of an original picture value exceed the threshold value theta2 for all of the theta1 and theta2, and cumulative histogram calculation parts 9, 10, and 16 so as to set at the maximum degree of coincidence are detected by a coincidence calculation part 19 and an optimum threshold value decision part 15. Therefore, it is possible to decide the optimum threshold value by performing one time of scan of the picture.

Description

[Detailed Description of the Invention] [Summary] This invention relates to image processing for processing specific shapes of grayscale images, and particularly relates to a threshold value determination method for binarization. Determining threshold values quickly and with high precision 2
The purpose of the present invention is to provide a method for determining a threshold value for value conversion, and in an image processing system that processes gray scale images, the present invention provides a density gradient calculation means for calculating the magnitude of a density gradient in an image for each pixel, and a density gradient calculation means for calculating the magnitude of a density gradient in an image for each pixel. order filter means for outputting pixel values in a certain predetermined order when the pixel values in a window of a certain shape containing are arranged in order of size; The total number of all θ2
a first cumulative histogram calculation means for calculating the
a second cumulative histogram calculation means that sequentially calculates the total number of pixels whose pixel values after passing through the filter means are equal to or higher than the threshold value 02 for all θ2; a third cumulative histogram calculation means for calculating the total number of pixels for all 01, and a third cumulative histogram calculation means for calculating the total number of pixels for all 01; A first two-dimensional cumulative histogram calculation means that calculates the total number of pixels that are equal to or greater than θ2 for all θ1 and θ2, and a pixel value after passing through the δ gradient calculation means that is equal to or greater than the threshold value 01 and is the original image. The total number of pixels whose pixel value is greater than or equal to the threshold value 02 for all θ
A second two-dimensional cumulative histogram calculating means calculates for 1 and θ2, a second and a third cumulative histogram calculating means, and a concentration gradient calculation process from the results of the first and second two-dimensional cumulative histograms. Matching degree is calculated for all combinations of θ1 and θ2 between edges obtained by binarizing the subsequent image with threshold value θ1 and i4 and boundaries of figures obtained by binarizing the original image with threshold value θ2. Calculation means and θ1 and 02 where the degree of coincidence is maximum are set to 1! i! and optimum threshold value determination means for determining the threshold values θ1 and 02 at the same time.

[Industrial application field]

TECHNICAL FIELD The present invention relates to image processing for processing specific figures in grayscale images, and particularly to a binarization threshold determination method.

A digital image created by AD converting an analog image input from an IM image camera or the like is a two-dimensional still image, and is expressed as a grayscale image in which pixels exist on a grid. The gray value of each pixel corresponds to any level from 0 to 255, for example, and in this case is expressed in 8 bits in binary representation. Digital image processing, which quickly performs recognition of specific objects and figures in a given grayscale image, is
For example, it will be extremely important for factory automation technology, such as visual robots recognizing and picking up objects carried on a conveyor belt. When recognizing an object in a grayscale image, a binary figure obtained by converting the original image into a threshold C binarization is used, but in this case, it is required to quickly determine the optimal threshold. .

[Conventional technology]

The conventional binarization threshold determination method uses an edge image in which candidates for the outline of the object, that is, edges are extracted from the original image;
Binary values obtained by binarizing the original image with the threshold values ``The degree of coincidence of the boundary image extracted from the boundary of the figure is calculated for all threshold values, and the threshold value with the maximum degree of coincidence is adopted. Was.

FIG. 9 is a processing flow of the first conventional method.

In the figure, a density gradient calculating section 1 calculates the magnitude of the differential at each pixel, an edge detecting section 2 detects pixels for which the magnitude of the differential is greater than or equal to a predetermined threshold value,
For example, the threshold temporary setting unit 3 sets 256 values from O to 255.
The threshold processing section 4 binarizes the ζ input image according to the provisionally set threshold value, and the boundary point detection section 5 sets the integer value as a temporary threshold value. A coincidence calculation unit 6 that detects a boundary of a converted binary image, that is, a boundary image consisting of pixels whose pixel value is 1 and at least one pixel in its 8 neighboring pixels has a pixel value of 0. is used to calculate the degree of coincidence between the edge image from the edge detection section 2 and the boundary image from the boundary point detection section 5, and the degree of coincidence table 7 is used to calculate the degree of coincidence between the edge image and the boundary image for each temporarily set threshold value. The optimal threshold value determining unit 8 determines the threshold value that maximizes the degree of coincidence from the degrees of coincidence saved in the degree of coincidence table 7, and calculates that value. This is output as the optimal threshold value. In addition, in the matching degree calculation unit 6, the matching degree is calculated by the following equation (11 or (2)).

FIG. 10 is a block diagram of the second conventional system disclosed by the present inventor in Japanese Patent Application No. 8462/1983.

The b5 degree gradient calculation unit 1 calculates the magnitude of the differential at each pixel, and the edge detection unit 2 detects pixels where the magnitude of the differential is greater than a predetermined threshold, that is, candidate points for the outline of the object in the image. do. The minimum value filter 3 outputs, for each pixel, the minimum value of the pixel value within a predetermined neighborhood centered on that pixel. This is one of the order filters that selects gray values in a predetermined order.

The cumulative histogram calculation units 9 to 12 each calculate the cumulative histogram, that is, the total number of pixels whose pixel value is equal to or higher than the density for each 95 degree value from 0 to 255. The boundary point number histogram calculation units 13 and 14 calculate the difference for each z-degree value of the two inputted cumulative histograms, and the output of the boundary point Hino and Togerum calculation unit 13 is a boundary point. It represents the total number of pixels, and the output of the boundary point histogram calculation unit 14 represents the total number of pixels that are edges and boundary points.

The optimal threshold determination unit 15 determines the total number of pixels that are boundary points,
The threshold value that maximizes equation (1) is selected and output from the total number of pixels that are edges and boundary points, and the total number of pixels that are edges.

[Problem to be solved by the invention]

In the first conventional method, for example, for all temporary thresholds from O to 255, the threshold processing unit 4 and the boundary point detection unit 5
Since the binarization process in step 1 and the match degree calculation process in match degree calculation section 6 are required, the first problem arises in that an enormous amount of processing time is required.

The second conventional method quickly determines the optimal threshold value for binarizing the original image without setting a temporary threshold value, which solves the first problem of requiring a huge amount of processing time. However, it is necessary to set a threshold value for edge detection in advance, and a second problem arises in that if the threshold value for edge detection is not appropriate, the processing results will be poor.

SUMMARY OF THE INVENTION An object of the present invention is to provide a binarization threshold determination method that quickly and accurately determines an optimal threshold for binarizing a grayscale image.

[Means to solve the problem]

FIG. 1 is a block diagram of the present invention.

The density gradient calculating means 1 calculates the magnitude of the density gradient in an image. For example, the density gradient calculating means 3 calculates the magnitude of the density gradient in an image. When the pixel values in a window of a certain shape containing that pixel are arranged in order of size, the pixel values are output in a predetermined order.For example, 3
Scan the image with a ×3 window and 9111 in the window
The first cumulative histogram calculating means 9 uses a minimum value filter that replaces the center pixel with the minimum value among the pixel values of i1. The second cumulative histogram calculation means 10 calculates the total number of pixels whose pixel value after passing through the sequential filter means 3 is equal to or higher than the threshold value 02.
The third cumulative histogram calculation means 16 calculates the total number of pixels whose pixel values after passing through the density gradient calculation means 1311 are equal to or higher than the threshold value 01 for all 01. Dimensional cumulative histogram, calculation means 1
7 calculates, for all θ1 and θ2, the total number of pixels whose pixel value after passing through 1 m of concentration gradient calculating means is equal to or greater than the threshold value 01, and whose pixel value after passing through the order filter means 3 is equal to or greater than the threshold value 02. The second two-dimensional cumulative histogram calculating means 18 calculates the total number of pixels whose pixel values after passing through the density gradient calculating means 1 are equal to or higher than the threshold value 01, and whose pixel values in the original image are equal to or higher than the threshold value 02. The coincidence calculation means 19, which is calculated for all θ1 and θ2, is the first one. From the results of the second and third cumulative histogram calculation means 9 and 10.16 and the first and second two-dimensional cumulative histogram calculation means 17.18, the image after the 'b1 degree gradient calculation process is binary-valued at the threshold value θ1. Optimum threshold determining means 15, which calculates the degree of coincidence of the boundary of the figure obtained by binarizing the resulting image and the original image with a threshold value θ2 for all combinations of θI and θ2.
The method detects θJ and θ2 that have the maximum degree of coincidence, and the present invention is characterized in that the threshold values θl and θ2 are determined simultaneously.

[Function] In the present invention, the pixel value after passing through the differential filter is the threshold value 01.
and a first two-dimensional cumulative histogram calculating means for calculating the total number of pixels whose pixel values are equal to or higher than the threshold value 02 after passing through the minimum value filter for all 01 and θ2, and passing through the differential filter. A second two-dimensional cumulative histogram calculation f that calculates the total number of pixels whose subsequent pixel value is equal to or greater than the threshold value 01 and whose pixel value in the original image is equal to or greater than the threshold value 02 for all θ1 and θ2. By configuring the stages using memory effectively, it is possible to scan the image once,
Two threshold values θ1 and θ2 are determined.

〔Example〕

Next, embodiments of the present invention will be described with reference to the drawings.

The present invention calculates the degree of coincidence of equation (1) for two thresholds, θ1 for edge detection and 02 for binarizing the original image, and calculates the optimal thresholds θ1 and θ2. First, the method for determining θ2 will be briefly described.

FIG. 5 is a conceptual diagram of the binarization process for the gradation curve r(x) of the original figure. For simplicity, a one-dimensional curve is used here. At the discrete coordinate x1, the gray value f(x+
) has any value between 0 and 255, but depending on the threshold value θ2, when f(xl)≧θ2, B(x+)=1f(x+)<θ
2, then B(x+)-〇, in the figure, B(x+) =OX1≦X≦x for xl×xl
B(x+)=IX for 2? <B for XI (x
+) = 0, and the binarized series of the original figure (B(x+)
) will be shown in ■.

The gray value at discrete coordinate x1 is f(x+) and its neighborhood x
The gray values at 1-1 and x+++ are f (x
+−+), f (x+++), if the original figure is passed through a minimum value filter, the shading value f(x
+) is mix (f (x l+ +), f (x
+).

f(x+++)). Here, min is a symbol that means selecting the minimum value. Moreover, when the original figure is passed through a maximum value filter, the gradation value f(xI) at XI is max (f (x+-1), f (x+).

f (Xl+1)). Here, max is a symbol that means to select the largest one. If the discrete curve f(x+) is now passed through a minimum value filter, the figure after passing through the minimum value filter is represented by a dotted discrete curve g(x+). When this curve g(x+) is binarized with the same threshold value θ2, the binarized series (B, n (x +)) after passing through the minimum value filter is:
It will be as shown in ■.

The binarized series of the original figure shown in ■ (B (x +) 1
, the bits of the three neighboring points (B(XI-i), B
(x+), B (x+++))
When at least one is O, setting 13(x+)=0 is called "contraction," and when at least one is ■, setting B(xI)=1 is called "expansion." Further, a filter that performs contraction processing is referred to as a logical contraction filter, and a filter that performs expansion processing is referred to as an expansion logical filter. When the binarized series (B(xI)) of the original figure shown in ■ in FIG. 5 is passed through a contraction filter, the binarized series C(B(x
I)) is obtained, and this sequence is clearly equivalent to the binarized sequence (B, (x +)l after passing through the minimum value filter of O. That is, (B111(x +) ) = C(B (x +)
).

Also, in the binarized series (B(xI)) of the original figure, b (x +) = B (x + -+)○B(xI)
The binary series (b(xI)) generated by is a boundary binary figure. Here, 0 is exclusive OR.

Therefore, in Fig. 5, the binary series of ■ (B(xI))
From is the series of boundary binary figures shown in e (b(xI))
is obtained. The number of bits “1” in a binary series is the “area”
That's what it means. The bits of the boundary binary figure series (b(xI))
The number of 1", that is, the area is called the "number of boundary pixels." Fifth
In the figure, the number of boundary pixels for the series (b(xI)) is 2, and clearly the number of boundary pixels = the surface area of the binarized series (B(xI)) of the original figure - the figure after passing through the minimum value filter. Binarized series (Bln(
xI)) area, or: Number of boundary pixels - Area of the binarized series of the original figure (B(XI)) - Binary series C (B(xI)) contracted after the binarization of the original figure
The area of , holds true. That is, property l After minimum value filter processing, the figure obtained by binarization (B,
, (X l)) and the figure C(B(xI)l obtained by applying a contraction logic filter after binarization) are the same.

Property 2 The number of boundary pixels of the figure is Number of boundary pixels - Area of original figure - Area of figure after contraction It can be calculated from

Next is the histogram of the gradation values and the cumulative histogram of the gradation values!・Explain about Durham.

FIG. 6 is a histogram of the gradation values f(xI), and shows the frequency (number of pixels) of each gradation value. Also, the seventh
The figure is a cumulative histogram of gradation values f(xI), which shows the frequency of gradation values that exceed the threshold value θ2. For example, in the histogram of FIG. In the cumulative histogram shown in FIG. 7, the value at the point θ2 is S. Considering in Figure 5, since this S is the number of coordinate points in the interval (XI, X2), the area of the binary series (B(xI)) of the original figure of
equal to the number of “1”).

Therefore, the following property holds.

) υ1 The area of the figure obtained by binarizing the grayscale image changes depending on the threshold value, but the relationship between the threshold value and the area can be expressed by the cumulative histogram of the original image, which is equivalent to the area.

Property 4 The number of boundary pixels of a figure obtained by binarizing a grayscale image changes depending on the threshold value, but can be calculated by: Number of boundary pixels - Cumulative histogram of original image - Cumulative histogram after minimum value filter processing.

In other words, to summarize the above, the number of boundary pixels - the area of the original figure - the area of the figure after contraction - the area of the original figure - the cumulative histogram of the original image - the surface of the figure after contraction, bond = image after minimum value filtering Cumulative histogram boundary pixel number = original image cumulative histogram - cumulative histogram after minimum value filter processing.

Furthermore, the following property also holds true.

Property 5: The number of boundary pixels in a certain pre-set quadrant area is calculated by calculating the cumulative histogram J within that area, in other words, by manipulating areas other than that area. can.

In addition, the constant flow of the degree of coincidence between the edge IIj image and the boundary image is (
As shown in formula 1), ・ ・ ・ ・ (1) gives 2.

From property 4 and property 5, the molecule in the above formula is equivalent to the number of boundary pixels of the original image in the edge image chain acid, so the total number of pixels that are edges and boundary points - the cumulative histogram in the edge image area of one original image J. - All threshold values can be calculated simultaneously using the cumulative and product histograno in the edge image area for the image after minimum value filtering has been applied to the original image.

Further, the denominator of equation (1) is the total number of pixels that are edges or boundary points (AtJB) = the total number of pixels that are edges (A )
It can be calculated by subtracting the number of pixels that are edges and boundary points (AnB) from the number of pixels that are edges and boundary points (AnB). Here, U and mouth are symbols representing the sum and intersection of sets, respectively.

However, in the above explanation, the number of boundary pixels is accurately determined when changing the threshold value θ2 for binarizing the original image, but the number of boundary pixels when changing the threshold value θ1 for edge detection is determined accurately. The +9 number of pixels that is +9 has not been determined. Therefore, in the following, the threshold value θ1 for edge detection is also changed at the same time, and θ1. A method will be described in which equation (1) is calculated for all combinations of θ2 and θI and θ2 with the maximum degree of coincidence are determined simultaneously.

A cumulative histogram is a histogram in which the horizontal axis represents the density and the vertical axis represents the total number of pixels whose pixel value is greater than or equal to that density.The minimum value filter is a 3x3
It is a filter that scans an image in a window and replaces the center pixel with the minimum value of the nine pixel values within the window. Also, a differential filter calculates the magnitude of the density gradient at each pixel. For example, this is a filter that calculates a differential value in the X direction and a differential value in the Y direction, and outputs the square root (positive square root) of these values. In addition, a two-dimensional histogram is a histogram representing the IB behavior of pixels such that the pixel value of one image is 01 or more and the pixel value of the other image is θ2. Using these words, symbols for detailed explanation of the present invention will be defined below.

The cumulative histogram of the original image is I-((θ2)1, and the cumulative histogram after minimum filter processing is M(θ2), i2
The cumulative histogram after & minute filter processing is E(θ1),
The image after differential filter processing and the original image (the two-dimensional cumulative histogram of the elephant is EH (θl, θ2), and the two-dimensional cumulative histogram of the image after differential filter processing and the image after minimum filter processing is EM (, θ1.θ2) shall be.

2 pixels whose pixel value is 1 and at least one pixel value of 8 pixels adjacent to that pixel is O.
When defined as a boundary pixel of a value image, the following Theorem 1, which is equivalent to Property 4, holds true.

The number of boundary pixels when binarized with the threshold value θ2 is given by the number of boundary pixels−H(θ2)M(θ2) (2).

A general proof of this theorem is given at the end as an appendix.

Further, the number of pixels that are edges can be determined by calculating the 0 degree gradient for each pixel and finding the number of pixels for which the value is 01 or more, so the cumulative histogram is obtained after differential filter processing. Accordingly, the following Theorem 2 holds true.

The number of pixels that are the edges when the main threshold value θ1 starts is given by the number of edges - E(θ1) (3).

now,? 2 obtained by binarizing a light image 8 with threshold value θ2
Let B be the value image 1, C1 be the image obtained by applying the minimum value filter to 8, and D be the image obtained by applying the differential filter to 8. In addition, 'J' of the pixel whose pixel value is 62 or more in 8
The sum is Σ, the set of pixels whose pixel value is 02 or more in C is Δ, and the set of pixels whose pixel value is 01 or more in D is . In this case, H(θ2)−M(θ2) of Theorem 1
is a set of pixels whose pixel value in the original image is 62 or more, but whose pixel value after the minimum value filter is not 02 or more, so using symbols, it is equivalent to (Σmouth λ). Become. Therefore, the iL combination of pixels that are edges and boundaries is 1'1rl (Σmouth Δ) ... (5
). Furthermore, since the pixel having the minimum value is an element of a pixel set, the set Δ of pixels whose value is θ2 or more after the minimum value filter is included in Σ. In other words, (Σ")λ) is the number of elements of Σ minus the number of elements of Δ. Therefore, equation (5) is calculated by subtracting the number of elements of (nnΔ) from the number of elements of (n-mouth Σ). The total number of pixels that are edges and boundaries is the total number of pixels that are n and Σ El ((θ1.θ
From 2), the total number of pixels EM (θ1.θ2) that is ■ and Δ
is equal to minus Therefore, the following Theorem 3 holds true.

When edges are detected using a threshold value θ1 and the original image is binarized using a threshold value θ2, the number of pixels that are edges and boundaries is as follows: Number of edges and boundaries = EH (θ1.θ2) − EM (θ
l, θ2)...(6) It is given by:

Furthermore, referring to the diagram showing the set relationship in FIG. 8, the total number of pixels that are edges or boundary points is the total number of pixels that are edges (E (θ1)), the number of boundary pixels (H (θ2) - M (
θ2)] - number of pixels at the error and boundary (EH(θ1.θ2
)−EM (θ1.θ2)). That is, the following Theorem 4 holds true.

Theorem 4 When edges are detected with a threshold value θ1 and the original image is binarized with a threshold value θ2, the number of pixels that are edges or boundaries is: Number of edges or boundaries − E (θ, ) + H (θ2)M(θ2) −(El((θl, θ2)−EM (θ1.θ2))]・
...(7) is given by.

Formula (1) for calculating the degree of coincidence from these four theorems is...
・It can be calculated using (8).

FIG. 2 is a configuration diagram of this embodiment. In the same figure, the first
The same symbols are used for the same items as in the figure.

Image data representing the gray scale value of each pixel of the original image is inputted as shown in FIG. The concentration gradient calculation unit 1 calculates each pixel (xt, y
The magnitude of the gradient of the gray value at each pixel (x+,'y+) is calculated using a 3×3 window differential filter consisting of eight neighboring pixels centered on pixel (x+, 'y+). For example, the magnitude Δ■ of the gradient of the gray value can be calculated from (9). For example, if the gray value at the coordinates (xt, y+) is f (xt, y+), then the difference Δf (xt, y+) in the X direction is Δf (x l+ y
+ )−f (fx++, y+) (xt, y
+), and the sum Σ is given by Δ for a 3×3 window
represents the sum of f.

The minimum value filter 3 scans a 3×3 window, calculates the minimum value of the grayscale values of nine pixels in the window for each pixel, and calculates the grayscale value f (xt, y+) of each pixel (xt, y+). )
is replaced with the minimum gray value g(xt, y+) within the window (corresponding to g(xt) in FIG. 5 in one dimension).

Figure 9.10. and 16 correspond to a cumulative histogram calculating section. The bond histogram calculation unit (1) 9 first calculates 2
A cumulative histogram is calculated by scanning the original image input from 0. FIG. 3 is a configuration diagram of the cumulative histogram calculating section (1) of the present invention.

Specifically, the histogram image 21, which has addresses from 1 to 256 corresponding to the gray level, is first cleared to all zeros, the input image 20 is scanned, and each pixel (x+
, y+), 1 is added to the contents of the address corresponding to the gray value r (x+, y+). The contents of the histogram memory 21 when the entire image has been scanned expresses a histogram of gray values. In other words, the contents of address N represent the t8 number of pixels whose gray value is level N. That is, the pixel value histogram calculation control unit 22 accesses the hiss I/gram memory 21 with the input θ value N, adds 1 to the read content, and executes control to write it to the address N again. Next, the cumulative histogram calculation unit 23 accumulates the gray value histograms from the highest gray value to calculate the cumulative histogram J2. Specifically, the contents of address 256 of the histogram memory 21 are left as they are, and the following calculations are performed sequentially starting from address 255 and ending with address 1: contents of address N - contents of address N, contents of address N+1, 00). I can be photographed by doing.

Cumulative histogram calculation unit (2) 10 is minimum value filter 3
The same processing as that of the cumulative histogram calculation unit (1) 9 is performed on the output of the cumulative histogram calculation unit (1) to calculate the cumulative histogram of the image after the minimum value filter processing, that is, the area of the figure after contraction.

The cumulative histogram calculation unit (3) 16 inputs the pixel values of the image after the differential filter, and the cumulative histogram calculation unit (1)
A cumulative histogram is calculated by performing the same process as in step 9.

Two-dimensional cumulative histogram calculation unit (1) 17 is
The density gradient calculation unit 1 scans each of the image after differential filter processing and the image after minimum value filter processing to calculate a two-dimensional density histogram.

Figure 4 shows the two-dimensional cumulative histogram calculation unit (1) of the present invention.
FIG. In the figure, 24 is a two-dimensional histogram memory, 25 is a register for storing θ1 and θ2 and serves as a counter, and 26 is an i
Reference numeral 27 is a control unit, which is an incrementer that adds 1 to the content (i) of address and an addition increment unit that adds content (i) of address i and content (j) of address j.

First, in order to obtain a two-dimensional density histogram, the address control section 25 is operated as a register for setting gray values, and the addition increment section 26 is operated as an incrementer. Specifically, an integer value θ from 0 to 255
Same as 1 (set of integer values θ2 from 0 to 255 (θ1.θ2
), the two-dimensional histogram memory 24 whose address is determined by IFf is first cleared to all zeros, each of the two images is scanned simultaneously, and the string of pixel values of each pixel is stored in the address control unit 25. The contents of the two-dimensional histogram memory 24 at the address corresponding to the set of pixel values are read out, the addition increment unit 26 adds 1, and writes the result to the same address. If this is done for all pixels, when the image scanning is finished, the two-dimensional histogram memory 24
The content of represents a two-dimensional density histodarum. That is, the contents of the address specified by (θ1.θ2) represent the total number of pixels, with the pixel value of one image being 01 and the pixel value of the other image being 02. Next, in order to obtain a two-dimensional cumulative histogram, the address control unit 25 operates as a counter, the addition increment unit 26 operates as an adder, and the two-dimensional density histogram is converted into a two-dimensional density histogram using the two-dimensional histogram memory 24. A two-dimensional cumulative 1-bond histogram is calculated by accumulating from the highest value. Specifically, in the two-dimensional density histogram, the two-dimensional cumulative histogram is the same as the contents of the address that is 1 blue at (255°255), (255, θ2); θ2 = 0 to 254, (255, The process of replacing the contents of 02) with the contents of (255, θ2 - tl) is performed in order from the one with the largest θ2.

For (θI, θ2) other than the above, when 02 is 255, replace the content of (θ1.θ2) with the content of (θ+, 255) + (θ+1.255), and when θ2 is 254 or less, (θ1.θ2
) content + content of (θ1+1.θ2) + content of (θ1.θ2+1) - content of (θ1+1.θ2+1) The process of replacing the internal milk mi with θ1. From the side with larger θ2.

Do it in order.

In addition, the two-dimensional cumulative histogram calculation unit (2) 18 calculates the two-dimensional density histogram by scanning each of the original image and the image after differential filter processing. - Same as calculation unit (1) 17.

In the coincidence calculation unit 19, the cumulative histogram calculation unit (1) 9
output, that is, the cumulative histogram H, (θ2) of the original image
, the output of the cumulative histogram calculation unit (2) 10, that is, the cumulative histogram M(θ2
), the output of the cumulative histogram calculation unit (3) 16, that is, the cumulative image after 1-distribution filter processing, and the bond histogram E(
0, two-dimensional cumulative histogram, the output of the calculation unit (2) 18, that is, the two-dimensional cumulative histogram EH (θ1, θ2) of the image after differential filter processing and the original image, the two-dimensional cumulative histogram calculation unit (1) 17 The output, that is, the two-dimensional cumulative histogram EM (θ1°θ2) of the image after differential filter processing and the image after minimum value filter processing is input. Then, each θ1. Ell(θ1.θ2)EM(θ1.θ2)E (θ +
)+H(θ2)-M(θ2)-(Elf(θ1.
θ2)EM(θ1.θ2)] ・ ・ ・ ・ (8) Calculate.

The optimal threshold determination unit 15 selects θ1. θ
2 is output as the optimal threshold value. As a result, θ1 is the optimal threshold value for the edge coal mine, and θ2 is the optimal threshold value for binarizing the original image.

In this embodiment, for example, the minimum value filter 3, cumulative histogram calculation unit (1, 2, 3) 9, 10° 16.2-dimensional cumulative histogram calculation unit (1, 2) 17, 18 are realized by dedicated hardware. However, the matching degree calculating section 19 and the optimal threshold determining section 15 can be expressed by an algorithm using a microprocessor.

Further, when the properties 1.2.3.4 described above are expanded and generalized, the following results are obtained.

Property 1 The figure obtained by binarizing after maximum value (minimum value) filtering is the same as the figure obtained by applying an expansion (contraction) logic filter after binarization.

Here, the maximum value filter scans an image in a 3×3 window and replaces the center pixel with the maximum value of the 9 f[lil pixel values within the window.

Property 2 The number of boundary points of a figure can be calculated using the following three methods.

+11 Surface of original figure, bond - Area of figure after contraction (2)
Area of the figure after expansion - Area of the original figure (3) (Area of the figure after expansion - Area of the figure after contraction) / 2 Property 3 The area of the figure obtained by binarizing the grayscale image changes depending on the threshold value. However, the relationship between the threshold value and the area can be expressed by the cumulative histogram of the original image, which is equivalent to the area.

Property 4 The number of boundary pixels of a figure obtained by binarizing a grayscale image changes depending on the threshold value, but the relationship between the threshold value and the number of boundary pixels is as follows.
According to the three methods described in the section of Tt2, (3) It can be calculated as: histogram after maximum value filtering - cumulative histogram after minimum value filtering.

Based on property 4(2), the minimum value filter 3 in this embodiment may be replaced with a maximum value filter. At this time, if the cumulative histogram after maximum value filtering is X(θ2), then the number of boundary pixels X(θ2)−H
(θ2). Further, if the two-dimensional cumulative histogram of the image after the differential filter processing and the image after the maximum value filter processing is EX (01° θ2), the degree of coincidence can be calculated in the same way as in the case of the minimum value filter. In other words, if the pixel value is O, and the endogeneity of the 8 pixels adjacent to that pixel is at least 1
If a pixel with one pixel value of 1 is defined as a boundary point of a binary image, then from the same consideration as above, we can further calculate the number of boundary points by the number of boundary points according to the above two types of constant τ When defined as an average, an order filter that outputs the second largest pixel value or second smallest pixel value within a window may be used instead of the maximum value filter or the minimum value filter. In this case, results that are not affected by isolated noise can be obtained.

Further, as for the shape of the window, it is also possible to use a window consisting of a central pixel and pixels that are connected to the central pixel in the sense of 4-connection (3×3 or more). That is,
If the 8 adjacent pixels (up, down, left, right, and diagonal directions) in the boundary definition are replaced with 4 VA pixels (up, down, left, and right), the window shape of the maximum value (minimum value) filter will be changed to 3 accordingly.
All you have to do is change the shape from ×3 to a cross shape (excluding the four corners of 3×3). Furthermore, the window shape may be made variable.

Further, as still other implementation forms, a spatial filter (concentration gradient calculation unit), an order filter (minimum value filter), 1
Functions such as dimensional and two-dimensional histogram calculation (cumulative histogram calculation part) are constructed using dedicated hardware or software on a general-purpose computer, and functions of a coincidence calculation part and an optimal threshold determination part are added, and the overall This can also be achieved by providing software to control the

Finally, as an appendix, we provide a detailed proof of Theorem 1 (Proof of Theorem 1). We apply a minimum value filter to B and A of the binary image obtained by binarizing a great grayscale painting with threshold value θ2. The resulting image is called C. In addition, the set of pixels whose pixel values are 02 or more in 8 is Σ, and the set of pixels whose pixel values are 02 or more in C is Δ. Furthermore, let the set of boundary points be r.

Now assume that pixel ω is a boundary point of B. At this time B
, the pixel value of ω is 1, and at least one of the eight adjacent pixels has a pixel value of 0. Therefore, in the grayscale image A, the pixel value of ω is 02 or more, and at least one of the eight pixels adjacent to ω has a pixel value of less than 0. This means that in the grayscale image A, the pixel value of ω is 02 or more, and in the image C after the minimum value filter processing, the pixel value of ω is less than 02. In other words, if ω is a boundary point of B, the pixel value of ω is 02 or more in the gray-scale painting master, and the pixel value of ω in the image C after the minimum value filter processing is less than 02. On the other hand, if the pixel value is 02 or more in the grayscale painting great person, and the pixel value is 0 in the image C after the minimum value filter processing,
Pixels that are less than 2 (not 02 or more) are B boundary points.

r=ΣmouthΔ On the other hand, it is clear that if the pixel value in the image C after the minimum value filter processing is 02 or more, the pixel value of the next pixel is also 02 or more. In other words, Δ is included in Σ.

Therefore, the number of boundary points is equal to the number of pixels that are Σ and not Δ, but this number is the total number of pixels that are Σ H (θ2) minus the total number of pixels that are Δ M (θ2) equal.

〔Effect of the invention〕

Conventionally, in order to obtain the same effect as the present invention, the image was
x 256 times, but according to the present invention,
By scanning the image once, you can quickly and efficiently find the optimal threshold value that best matches the edge obtained by binarizing the image after differential filter processing and the boundary of the figure obtained by binarizing the original image. You can get it in bulk.

[Brief explanation of the drawing]

Fig. h'1,1 is a 11179 diagram of the present invention, Fig. 2 is a block diagram of this embodiment, Fig. 3 is a block diagram of the cumulative histogram calculation unit (1), and Fig. 4 is a two-dimensional cumulative histogram calculation of the present invention. Part (1)
The IR configuration diagram in Figure 5 is 2 for the 'bl light curve f (x) of the original figure.
Figure 6 is a histogram of gray values, Figure 7 is a cumulative histogram of gray values, Figure 8 is a diagram showing set relationships, and Figure 9 is a processing flow of the first conventional method. , Figure 10 is the second
FIG. 2 is a block diagram of a conventional method. DESCRIPTION OF SYMBOLS 1... Concentration gradient calculation means, 3... Order filter means, 9... First cumulative histodrum calculation means, 10...
Second cumulative histogram calculating means, 15... Optimal threshold determining means, 16... Third cumulative bond histogram calculating means, 17.
...First two-dimensional cumulative histogram/calculation means, 1 day...Second two-dimensional cumulative histogram/grab calculation means, 19... Matching degree calculation means, Patent applicant: Fujitsu Limited Kinoe B Moon) 577 Figure 1 $ 2k [Tsuba i (G11 17 Kin YA Figure 2 Shade I Straight Cumulative 1 Kanmi Mata Togerum Figure 7

Claims (1)

[Claims] 1) An image processing system that processes a grayscale image, comprising: a density gradient calculation means (1) that calculates the magnitude of a density gradient in the image for each pixel, and a shape that includes the pixel for each pixel. order filter means (3) for outputting pixel values in a predetermined order when the pixel values in the window are arranged in order of size; a first cumulative histogram calculation means (9) that calculates the value for all θ_2, and a pixel value after passing through the sequential filter means (3) is a threshold value θ_2
a second cumulative histogram calculation means (10) which calculates the total number of pixels that is above for all θ_2; and a pixel value after passing through the density gradient calculation means (1) is a threshold value θ_1.
A third cumulative histogram calculation means (16) that calculates the total number of pixels that is above for all θ_1, and a pixel value after passing through the density gradient calculation means (1) is a threshold value θ_1
a first two-dimensional cumulative histogram calculation means (17) which calculates the total number of pixels whose pixel value after passing through the order filter means (3) is equal to or higher than the threshold value θ_2 for all θ_1 and θ_2; The pixel value after passing through the concentration gradient calculation means (1) is the threshold value θ_1
The second step is to calculate the total number of pixels whose pixel value of the original image is greater than or equal to the threshold value θ_2 for all θ_1 and θ_2.
two-dimensional cumulative histogram calculation means (18); and first, second and third cumulative histogram calculation means (9).
, (10), (16) and the results of the first and second two-dimensional cumulative histograms, the image after the density gradient calculation process is binarized using the threshold value θ_1, and the edge and original image obtained by binarizing the image are converted to the threshold value θ.
The matching degree of the boundary of the figure obtained by binarizing with _2 is θ_1
The threshold value θ_
A binarization threshold determination method characterized by determining 1 and θ at the same time. 2) The binarization threshold determination method according to claim 1, wherein the order filter means (3) has a predetermined rank of the last one (that is, outputs the minimum value). 3) The order filter means (3) has a predetermined order of 1.
2. The binarization threshold determination method according to claim 1, wherein the binarization threshold value determination method is characterized in that the binarization threshold value determination method outputs the maximum value. 4) The order filter means (3) selects both the one whose predetermined rank is the first (that is, outputs the maximum value) and the one whose predetermined rank is the last (that is, outputs the minimum value). 2. The binarization threshold determination method according to claim 1, further comprising: 5) The binarization threshold determination method according to claim 1, wherein the order filter means (3) has a variable order to be determined. 6) The coincidence calculation means (19) calculates a cumulative histogram H(θ_2) of the original image and a cumulative histogram M(θ_2) of the image after the sequential filter processing with the determined rank being the last.
2) Cumulative histogram E of the image after differential filter processing
(θ_1), two-dimensional cumulative histogram EH (θ_1, θ_2) of the image after differential filter processing and the original image, two-dimensional image after differential filter processing and the image after sequential filter processing with the determined rank being the last. Cumulative histogram EM (
θ_1, θ_2), the matching degree is {EH(θ_1, θ_2)EM(θ_1, θ_2)}/
{E(θ_1)+H(θ_2)-M(θ_2)-[EH
2. The binarization threshold determination method according to claim 1, wherein: (θ_1, θ_2)−EM(θ_1, θ_2)]}. 7) The coincidence calculation means (19) calculates a cumulative histogram H(θ_2) of the original image and a cumulative histogram X(θ_2) of the image after order filter processing with a predetermined first rank.
), the cumulative histogram E(
θ_1), two-dimensional cumulative histogram EH (θ_1, θ_2) of the image after differential filter processing and the original image, two-dimensional cumulative histogram of the image after differential filter processing and the image after sequential filter processing with the determined rank of 1st Histogram EX(θ_
1, θ_2), the matching degree is {EX(θ_1, θ_2)−EH(θ_1, θ_2)}
/{E(θ_1)+X(θ_2)-H(θ_2)-(E
2. The binarization threshold determination method according to claim 1, wherein: X(θ_1, θ_2)−EH(θ_1, θ_2)]}. 8) The coincidence degree calculation means (19) calculates a cumulative histogram X(θ_2) of the image after the ordinal filter processing in which the predetermined rank is the first, and an image after the ordinal filter processing in which the predetermined rank is the last one. Cumulative histogram M(θ_2) of
Cumulative histogram E(θ_
1), the determined rank of the image after differential filter processing is 1
The two-dimensional cumulative histogram EX(θ_1, θ_2) of the image after the ordered filter processing is the lowest, and the two-dimensional cumulative histogram EM(θ_1) of the image after the differential filter processing is the last. ,θ_2
), the degree of matching is {EX(θ_1, θ_2)−EM(θ_1, θ_2)}
/{E(θ_1)×2+X(θ_2)−M(θ_2)−
[EX (θ_1, θ_2) - EM (θ_1, θ_2)]
} The binarization threshold determination method according to claim 1, wherein: } is calculated. 9) The first and second two-dimensional cumulative histogram calculation means (17) and (18) receive the pixel values of one image and the pixel values of the other image as addresses, and calculate the set of input pixel values ( A histogram memory having addresses corresponding to θ_1, θ_2) and a set of input pixel values (
a first control means that increments the content of the histogram memory at the address corresponding to θ_1, θ_2);
A second control means for accumulating the contents of the histogram of pixel values stored in the histogram memory for all input pixel value sets (θ_1, θ_2) at the end of the increment operation. Threshold value determination method for binarization described in Section 1.