Abstract:
A process for thinning an image, comprising the steps of defining an image in terms of a plurality of discrete picture elements (pixels), convolving each horizontal string of pixels of the image with itself shifted a predetermined number of pixels, weighting each shifted position of each horizontal string, selecting certain of the pixels of the weighted horizontally convolved pixel strings which correspond to predetermined descriptors, convolving each vertical string of pixels of the image with itself shifted a predetermined number of pixels, weighting each shifted position of each vertical string, selecting certain of the pexels of the weighted vertically convolved pixel strings which correspond to predetermined descriptors, adding thee selected pixels from the weighted vertical and horizontal convolutions and the pixels of the original image, retaining those pixels which are common to the original image and the selected pixels of both the horizontal and vertical weighted convolutions, discarding those pixels which are absent from the original image, filtering those pixels which are common to the original image and the original image and only one of the selected pixels of the horizontal and vertical weighted convolutions, further retaining certain of the filtered pixels and discarding others in accordance with a predetermined filter matrix, and providing an output signal of the retained pixels which represents a thinned image.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation-in-part of copending application Ser. No. 532,255, filed on Sept. 15, 1983, now abandoned, in the name of Dr. Jose Pastor, entitled, IMAGE THINNING PROCESS. 
    
    
     PROGRAM APPENDIX 
     Attached to the last page of the Specification are program listings in CHIPS Language for implementing the process of the present invention with an image processor, such as available from Gould DeAnza. A conventional pre-processing feature designated PRELUT is used in the listings to smooth out the rough edges of the binary image. 
     BACKGROUND OF THE INVENTION 
     The present invention relates to image preprocessing, and more specifically to an image thinning process. 
     Typically, after a character is scanned and the features to be analyzed are detected, the detected image (characters for an OCR machine) is compared with a mask stored in memory for recognition. If there is sufficient correspondence between the detected image and the mask, the character is recognized. However, it has long been recognized as desirable to find the skeleton of an image during image preprocessing to facilitate computer interpretation of images in optical character recognition and robotic systems. Present thinning techniques first require detection and isolation of the entire character prior to thinning. See, for example, U.S. Pat. No. 3,846,754, issued to Oka et al. on Nov. 5, 1974; U.S. Pat. No. 3,940,737, issued to Beun on Feb. 24, 1976; U.S. Pat. No. 3,975,709, issued to Beun et al. on Aug. 17, 1976; U.S. Pat. No. 4,034,344, issued to Savaga et al. on July 5, 1977; U.S. Pat. No. 4,115,760 issued to Ito on Sept. 19, 1978; and U.S. Pat. No. 4,162,482, issued to Su on July 24, 1979. Thereafter, complicated computations are performed on the detected image including finding edge gradients, chordal distances, etc. to find the skeleton of the image. With such techniques, one of the advantages of thinning, i.e., helping with line finding and the segmentation of lines into characters, is not used. 
     U.S. Pat. No. 3,339,179 issued to Shelton, Jr., et al. on Aug. 29, 1967 discloses an image thinning technique based on eliminating all the pixels not necessary for connectivity. Specifically, a pattern is obtained by iteratively operating on the pattern to be identified with an incidence matrix. The result of operating on the input pattern by the incidence matrix is to generate an output pattern having a ridge of relatively high values along the center and lower values on either side of the ridge. Intersection points and end points are also determinable by the relative amplitudes of the values along the ridges. Such a thinning technique is not deterministic or universally applicable, but requires adjustments in the preservation values for different characters, e.g., by adjusting a potentiometer. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide an improved image thinning process. 
     It is a further object of the present invention to provide an image thinning process which results in a thinned image which is more easily recognized. 
     It is a further object of the present invention to provide an image thinning process which facilitates line finding and segmentation of the images in optical character recognition machines. 
     It is a still further object of the present invention to provide an image thinning process which facilitates definition of the resulting thinned image in vector space. 
     It is still a further object of the present invention to provide an improved image thinning process which facilitate character recognition and therefore facsimile transmission. 
     It is a still further object of the present invention to provide an improved image thinning process which overcomes the disadvantages of prior image thinning processes. 
     Briefly, in accordance with the present invention, a process is disclosed for thinning an image, comprising the steps of defining an image in terms of a plurality of discrete picture elements (pixels), convolving each horizontal string of pixels of the image with itself shifted a predetermined number of pixels, weighting each shifted position of each horizontal string, selecting certain of the pixels of the weighted horizontally convolved pixel strings which correspond to predetermined descriptors, convolving each vertical string of pixels of the image with itself shifted a predetermined number of pixels, weighting each shifted position of each vertical string, selecting certain of the pixels of the weighted vertically convolved pixel strings which correspond to predetermined descriptors, adding the selected pixels from the weighted vertical and horizontal convolutions and the pixels of the original image, retaining those pixels which are common to the original image and the selected pixels of both the horizontal and vertical weighted convolutions, discarding those pixels which are absent from the original image, filtering those pixels which are common to the original image and the original image and only one of the selected pixels of the horizontal and vertical weighted convolutions, further retaining certain of the filtered pixels and discarding others in accordance with a predetermined filter matrix, and providing an output signal of the retained pixels which represent a thinned image. 
    
    
     Other objects, aspects and advantages of the present invention will be apparent from the detailed description considered in conjunction with the drawings, as follows: 
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic view of a generalized system for performing the image thinning process of the present invention; 
     FIG. 2A is a schematic representation of the horizontal convolution of a pixel string of seven (7) pixels; 
     FIG. 2B is a schematic representation of the horizontal convolution of a pixel string of five (5) pixels; 
     FIG. 3 is a plan view of a typical image, shown as the alphanumeric character six (6); 
     FIG. 4 is a plan view of a weighted horizontal convolution for the horizontal pixel strings of the image of FIG. 3 with the retained pixels shaded for clarity; 
     FIG. 5 is a plan view of a weighted vertical convolution for the vertical pixel strings of the image of FIG. 3 with the retained pixels shaded for clarity; 
     FIG. 6 is a composite image formed by summing pixel elements from the images of FIGS. 3, 4 and 5; 
     FIG. 7 illustrates a matrix neighborhood for forming a binary filter about each contingent pixel for determining whether the pixel is to be preserved or discarded; 
     FIG. 8 illustrates the matrix neighborhood with reassigned binary values; 
     FIG. 9 illustrates how the matrix filter is prepared from the matrix neighborhoods of FIGS. 7 and 8; 
     FIG. 10 illustrates a completed matrix filter with assigned values for the matrix neighborhoods; 
     FIG. 11 shows an original image, illustrated as the alphanumeric characters zero (0), six (6) and eight (8); 
     FIG. 12 shows the thinned image which results when the image of FIG. 11 is convolved and filtered with the matrix filter of FIG. 10; 
     FIG. 13 shows a still thinner image which results when the thinned image of FIG. 12 is further filtered with an anorexic matrix filter; 
     FIG. 14 is an anorexic matrix filter for eliminating overlapping pixels of portions of the thinned image shown in FIG. 12; 
     FIG. 15a-c, is a flowchart for implementing the process of the present invention on a digital computer with a matrix filter of the type illustrated in FIG. 10; 
     FIG. 16 illustrates another filter matrix for application to pixels of value 1; 
     FIG. 17 illustrates another filter matrix for application to pixels of value 2 if there are pixels of value 3 present in its 3×3 neighborhood; 
     FIG. 18 illustrates another filter matrix for application to pixels of value 2 if there are pixels of value 3 present in its 3×3 neighborhood; 
     FIG. 19 illustrates another filter matrix for application to pixels of value 2 if there are no pixels of value 3 or 2 present in the neighborhood; 
     FIG. 20 is a flowchart for implementing the process of the present invention with different matrix filters, where pixels of value 1 and 2 are filtered in one sequence; and 
     FIG. 21 is a flowchart for implementing the process of the present invention with different filter matrices, where pixels of value 1 and 2 are filtered in one sequence with the filter matrix of FIG. 16 being utilized. 
    
    
     DETAILED DESCRIPTION 
     Referring to FIG. 1, a system for employing the process of the present invention, e.g., on a digital computer, is generally illustrated as 20. Binary image pulses 22 are supplied to a digital computer which is programmed to accomplish the thinning process 24, e.g., in accordance with the Program in the Appendix and flowcharts illustrated in FIGS. 15, 20, or 21, as desired. The output in the form of the binary thinned image 26 may be displayed on a CRT display, as desired. 
     Referring to FIG. 2A, a seven (7) element horizontal pixel string of an image is illustrated at 30. The convolution ##EQU1## is performed to find the center of the pixel string 30 by shifting the axis of the horizontal pixel string 30 with itself by three (3) pixels and adding the results. That is, the horizontal pixel string is convolved with a Dirac comb. The function f(x-3) is designated 32, the functions f (x-2) is designated 34, the function f(x-1) is designated 36, the function f(x) is designated 30, the function f (x+1) is designated 38, the function f (x+2) is designated 40, and the function f (x+3) is designated 42. Additionally, f (x+3), f (x+2), f (x+1), f (x), f (x-1), f (x-2) and (x-3) are multiplied by the weighting factors a, b, c, d, e, f and g, respectively. The convolution which results from adding the functions f (x±i) is designated 44 in FIG. 2A. 
     Advantageously, each horizontal pixel position of the resulting convolution 44 has a value which results from adding the weights for each function. In this way a weighted horizontal map 46 is provided for each horizontal pixel position resulting from the horizontal convolution 44. Moreover, significantly, by utilizing the weighting factors the horizontal pixel position of the convolution 44 is readily weighted. For example, reading the horizontal map 46 from right to left in FIG. 2A, the first position is assigned the number 1 (representing 1 pixel) and the weighting factor a, the second position the number 2 (representing 2 pixels) and the weighting factor a+b, the third position the number 3 (representing 3 pixels) and the weighting factor a+b+c, the fourth position the number 4 (representing 4 pixels) and the weighting factor a+b+c+d, the fifth position the number 5 (representing 5 pixels) and the weighting factor a+b+c+d+e, the sixth position the number 6 (representing 6 pixels) and the weighting factor a+b+c+d+e+f, the seventh position the number 7 (representing 7  pixels) and the weighting factor a+b+c+d+e+f+g, the eighth position the number 6 (representing 6 pixels) and the weighting factor b+c+d+e+f+g, the ninth position the number 5 (representing 5 pixels) and the weighting factor c+d+e+f+g, the tenth position the number 4 (representing 4 pixels) and the weighting factor d+e+f+g, the eleventh position the number 3 (representing 3 pixels) and the weighting factor e+f+g, the twelveth position the number 2 (representing 2 pixels) and the weighting factor f+g, and thirteenth position the number 1 (representing 1 pixel) and the weighting factor g. 
     Referring to FIG. 2B, a five (5) element horizontal pixel string of an image is illustrated at 47. As with FIG. 2A the convolution ##EQU2## is performed to find the center of the pixel string 47 by shifting the axis of the horizontal pixel string 47 with itself by three (3) pixels and adding the results. The resulting convolution is designated 48 and its associated weighted horizontal map is designated 49. As with each horizontal pixel position in FIG. 2A, each horizontal pixel position of the convolution in FIG. 2B has a value which results from adding the weights for each function as seen at 49. 
     In assigning values to the pixels, the centers of the strings can be readily determined if the weighting factors are such that they produce for each weighted pixel a different value. Advantageously, this is achieved by defining the weights as powers of a number R, i.e., R 1 , R 2 , R 3 , R 0 , R 4 , R 5 , R 6 , as shown in FIGS. 2A and 2B for the example of a ±3 convolution. As a result, the values of the pixels are all different numbers in base R. Very advantageously, the base 2 may be used to facilitate implementation with digital electronics. Therefore, preferably R becomes a 2 as illustrated in FIGS. 2A and 2B and the resulting values of the horizontal pixel positions are designated as 43 and 45, respectively. 
     Thus, in the binary system moving from right to left the values for the pixels are indicated in FIGS. 2A and 2B. The values that correspond to the centers are the descriptors indicated by the arrows whose formulation is discussed in detail below. The pixels having a value equal to these descriptors are preserved and all the other pixels eliminated. Thus, the centers of all the horizontal pixel strings, and similarly the centers of all the vertical pixel strings are determined. Thus, each center pixel of odd pixel strings and both center pixels of even pixel strings are uniquely described in binary digits. Moreover, it is apparent that each center pixel will always be described by an odd number or descriptor in decimal numbers. 
     It should be understood that although horizontal pixel strings of 7 and 5 pixels are illustrated in FIGS. 2A and 2B, respectively, the horizontal and vertical pixel strings of an image can, and normally will, include varying numbers of pixels. Further, it should also be apparent from FIGS. 2A and 2B that the maximum number of pixels eliminated from a pixel string undergoing a 3×3 convolution is equal to 5 pixels. Therefore, for long pixel strings additional convolutions may be applied to the resulting pixel strings, as desired. 
     In addition to preserving the descriptors for the center pixels of the pixel string, it is desired to preserve already short strings of pixels, e.g., those having only one or two pixels, to preserve voids in a pixel string, i.e., separations between characters, and prevent any artificial breaks in the resulting thinned image. To generalize from the illustration and description of FIGS. 2A and 2B, this is accomplished by a Weighted Convolution defined as ##EQU3## where the selection of the 2k+1 pixels coefficients a i  finds the center for images up to 2k+1pixels in length, the central plateau for strings longer than 2k+1 pixels, and preserves the already thin lines and the voids (character separations) in the strings of pixels. 
     Assume k=2 and that there are six pixel strings having lengths of 1, 2, 3, 4, 5 and 6 pixels. If a -2  =a, a -1  =b, a 0  =c, a 1  =d and a 2  =e, the coefficients are selected to satisfy the following conditions: 
     For the string of one pixel c≠other C 5   1 , C 5   2 , C 5   3 , C 5   4 , C 5   5   
     For the string of two pixels a+b≠C 5   1 , other C 5   2 , C 5   3 , C 5   4 , C 5   5   
     For the string of three pixels b+c+d≠C 5   1 , C 5   2 , other C 5   3 , C 5   4 , C 5   5   
     For the string of four pixels a+b+c+d≠C 5   1 , C 5   2 , C 5   3 , other C 5   4 , C 5   5   
     For the string of five or more pixels a+b+c+d+e≠C 5   1 , C 5   2 , C 5   3 , C 5   4 , other C 5   5   
     c 5   i  represents the addition of the numbers a i  in the combinations of order i with 5 elements (a, b, c, d, and e). The solution to this set of conditions locates the centers of pixel strings up to 2k+1 pixels in length and the center plateau for pixel strings having a length greater than 2k+1. 
     For any k, this approach can be generalized. As previously described with reference to FIGS. 2A and 2B, the coefficients are a 0  =1 and the other power of a particular base in ascending order. Advantageously, when powers of 2 are utilized the coefficients are as follows: 
     
         ______________________________________For k = 2: a.sub.-2 = 2.sup.1                 For k = 4: a.sub.-4 = 2.sup.1      a.sub.-1 = 2.sup.2    a.sub.-3 = 2.sup.2      a.sub.0 = 1           a.sub.-2 = 2.sup.3      a.sub.1 = 2.sup.3     a.sub.-1 = 2.sup.4      a.sub.2 = 2.sup.4     a.sub.0 = 1                            a.sub.1 = 2.sup.5For k = 3: a.sub.-3 = 2.sup.1    a.sub.2 = 2.sup.6      a.sub.-2 = 2.sup.2    a.sub.3 = 2.sup.7      a.sub.-1 = 2.sup.3    a.sub.4 = 2.sup.8      a.sub.0 = 1      a.sub.1 = 2.sup.4                 etc. for larger ks.      a.sub.2 =  2.sup.5      a.sub.3 = 2.sup.6______________________________________ 
    
     Further, by defining the coefficients in this manner, it is apparent that what results are 5 bit, 7 bit, 9 bit, etc. binary numbers. 
     The weighted convolution (WC) is then compared with a one-dimensional matrix of preservation values or descriptors D i  as described above. Pixels of value D i  are assigned the value 1 and all others the value 0. 
     For k=3, the center descriptors to preserve for strings of 1, 2, 3, 4, 5, 6 and 7 pixels are 1, 3, 5, 7, 9, 11, 25, 27, 29, 33, 35, 37, 39, 41, 43, 59, 61, 63, 65, 67, 69, 71, 73, 89, 91, 93, 95, 97, 99, 101, 105, 107, and 127. The descriptors 1, 9, 25, 29, 61, 63 and 127 define the center pixel for the seven isolated strings of pixels. The other descriptors preserve the center pixels for the same strings when they are adjacent to other strings and separated by only one (1) or two (2) pixels. For an N×N convolution, adjacent strings separated by N or more pixels do not intrude to change the center descriptors. 
     Referring to FIG. 3, a two dimensional image in the form of alphanumeric character six (6) is designated 50. Thinning of the image 50 in accordance with the present invention is accomplished by digitizing the same and performing a weighted horizontal convolution ##EQU4## The resulting convolution is then compared with the matrix D i  to determine the horizontal pixels to be preserved. The pixels to be preserved result in the shaded binary image 52 illustrated in dotted outline in FIG. 4. The specific horizontal pixels 54 to be preserved are shaded for clarity and superimposed over the original image 50. Next, the weighted vertical convolution ##EQU5## is performed and compared with the matrix D i  to determine the vertical pixels to be preserved. The result is the shaded binary image 56 illustrated in dotted outline in FIG. 5. The specific vertical pixels 58 to be preserved are shaded for clarity and superimposed over the original image 50. 
     A composite image can now be formed, as illustrated in FIG. 6, by overlaying the original image 50 of FIG. 3 with the selected pixels from the weighted horizontal convolution 52 of FIG. 4 and the weighted vertical convolution 56 of FIG. 5. The resulting image 60 is composed of pixels which are assigned four distinct value or levels: 0, 1, 2 and 3. Pixels assigned a value of 0 are not part of the original image and remain 0. Pixels assigned a value of 3 are common to the original image of FIG. 3, and both the preserved pixels of the weighted horizontal convolution of FIG. 4 and the preserved pixels of the weighted vertical convolution of FIG. 5. Therefore, pixels of value 3 definitely belong to the thinned image or skeleton. Pixels of value 2 are common to the original image and only one of the selected pixels of the weighted horizontal or vertical convolutions, i.e., FIG. 4 or 5. Pixels of value 1 are only common to the original image, see FIG. 3. 
     The composite image 60 is now filtered. The pixels of value 3 are preserved, the pixels of value 0 are discarded. The skeleton of the image 50 is then rebuilt with pixels of value 3 and predetermined pixels of value 1 and 2. That is, some of the pixels of value 1 and 2 are preserved, while others are eliminated. To accomplish this, a 3×3 neighborhood is applied to each pixel of value 1 or 2. In accordance with a selection rule, that pixel is discarded or made either a 3 (preserved) or a 2 (contingent). It is made a 3 if it is to be part of the skeleton and a 2 if the decision is conditional. Once the filter is applied, all the remaining pixels will have a value of 2 or 3. The filter is applied again to the pixels of value 2 and either all the pixels of value 2 are eliminated, converted to 3s, or a very few 2s remain. The filter is then applied to the pixels of value 2 again. For a 3×3 convolution, preferably the filter is applied 3 consecutive times. 
     Referring to the pixel designated A in FIG. 6, a 3×3 neighborhood is applied thereto as shown in FIG. 7 as 70. The pixels of this neighborhood are binarized resulting in the neighborhood 80 illustrated in FIG. 8. That is, pixels of value 0 are assigned the value zero. Pixels of value 1, 2 or 3 are assigned the value 1. 
     Referring to FIG. 9, advantageously, the pixels of the neighborhood 90 are formed into all combinations of two (2) four bit numbers or nibbles as shown in the double entry table or filter matrix 92 of FIG. 9. Each neighborhood 90, as illustrated in FIG. 9, has pixels 1-4 assigned to a specific nibble along the horizontal axis of the double entry table 92 and pixels 5-8 assigned to a specific nibble along the vertical axis of the double entry table 92 to form a filter matrix for each pixel of the convolved composite image 60 of FIG. 6. The nibbles and specific values corresponding to the nibbles are set forth in the filter matrix illustrated as 100 in FIG. 10. For example, with regard to the pixel A in FIG. 6, the value assigned to this pixel in the filter matrix of FIG. 10, for the horizontal nibble 1110 and the vertical nibble of 0001, is 0. That is, pixel A is discarded. 
     In deriving the filter matrix 100 of FIG. 10, all pixels of value 1 are eliminated except: a. Those that will produce a break in the image; they are made 3, and b. Those pixels that are immersed in a full 3×3 neighborhood are made 2. From the pixels of value 2, those pixels are preserved which would produce a break if eliminated. Instead of defining a mathematical algorithm in terms of 4 and 8 connectivities, all 256 cases (2 8 ) have been analyzed one by one to define the filter matrix 100. However, as seen in the first program listing in th Program Appendix two different filter matrices have been utilized in the Image Thinning Process. The second filter matrix is actually the filter matrix 100. However, preferably, these two filter matrices are combined to form the single filter matrix 100. 
     FIG. 11 illustrates an original image 110 in the form of the alphanumeric characters 068. The result obtained by subjecting the image 110 of FIG. 11 to the thinning process in accordance with the present invention is the thinned alphanumeric characters 068, illustrated in FIG. 12 as 120. 
     The foregoing discussion has focused on 2×2 and 3×3 convolutions by way of example. However, it should be understood that the convolution N×N may be any integer. Instead of a horizontal convolution of 3 right and 3 left, and a vertical convolution of 3 up and 3 down for individual pixel strings, the convolution may be generalized to N right and N left, and N up and N down. The total numbers to preserve as descriptors of the centers of the pixel strings are as follows: TD=2 2N-1  +1. 
     
         ______________________________________N × N             2N + 1 Total Numbers toconvolution   Total Numbers = 2                   Preserve = TD______________________________________2 × 2    32              93 × 3   128              334 × 4   512             1295 × 5   2048            513______________________________________ 
    
     Moreover, it is desirable to differentiate between right and left center pixels for strings of even numbers of pixels in which two center pixels are present. The descriptors to preserve are defined as follows: 
     For strings of odd numbers of pixels L=2j+1 j=0 . . . (N-1) Preserve descriptors D 1 , . . . D 2j+1  ##EQU6## For even strings L=2k k=1,2 . . . N ##EQU7## 
     Thus, the total numbers to be preserved are: ##EQU8## 
     If both D k  Right and D k  Left are preserved, the centers of even strings of pixels will be defined by two pixels. However, by preserving only D k  Right or D k  Left, advantageously the center of each even string of pixels is defined by only one pixel. Further, if only the right side pixels or the left side pixels are preserved, certain thinned images, specifically, those that are originally very thick and require the successive application of the convolution more than once may be biased to one side. Therefore, as desired, the weighted convolutions performed on an image may alternate between D k  Right and D k  Left. Moreover, to prevent holes or breaks in the thinned image, pixel strings having a length of two pixels are preserved without thinning. To accomplish this for a 3×3 convolution, the center descriptors for Left side thinning D k  Left for two pixel strings are added to the center descriptors for the Right side thinning D k  Right. 
     For a 3×3 weighted convolution, the descriptors to be preserved are: 
     1, 3, 5, 7, 9, 11,  17, 19, 21, 23   25, 27, 29, 33, 35, 37, 39, 41, 43, 57, 59 , 61, 63, 65, 67, 69, 71, 73, 75, 81, 83, 85, 87, 89, 91, 93, 97, 99, 101, 103, 105, 107,  125 , 127. 
     The numbers inside the brackets represent the additional descriptors from Left side thinning D k  Left. 
     Further, although the prior discussions have focused on N×N convolutions, i.e., a square for the convolution kernel, it may be advantageous to convolve with a rectangle M×N where M≠N. This may be advantageous for increasing speed or where an image is already thinner in one direction, e.g., the vertical direction. For M=3 and N=2, the horizontal center descriptors are as previously indicated and the vertical center descriptors are reduced to 1, 3, 5, 9, 11, 13, 15, 17, 19, 21, 29 and 31. 
     To provide further image thinning for maximum data compression and recognition algorithms, it is desirable to eliminate any line connections having more than one pixel, i.e., the overlapping of lines. This overlapping is due to the fact that strings of two pixels are retained as already thin because for such strings there is no center pixel. As seen in FIG. 12, a portion of the resulting thinned image may include overlapping connecting lines such as 130. It is advantageous for the reasons mentioned to eliminate such overlapping or double connecting lines 130 resulting in single connecting lines 140 as illustrated in the further thinned image 150 of FIG. 13. 
     To accomplish this further thinning, double connections of the resulting thinned image, such as seen in FIG. 12, are eliminated to produce the lines such as 140 illustrated in FIG. 13. Resulting lines at an angle of 45°, greater than 45°, or less than 45° are all thinned as seen in FIG. 13. 
     Referring to FIG. 14, this further thinning is accomplished with a non-symmetric anorexic matrix filter or double entry table 190 which may be advantageously applied to each pixel of the thinned image of FIG. 12. The anorexic matrix filter 190 is constructed from pixel neighborhoods in a manner similar to the construction of the matrix filter 100 of FIG. 10, with the precaution that breaks must be avoided. This means that either left and up pixels are eliminated and right and down pixels are preserved, or vice versa, but not both. Therefore, FIG. 14 is only illustrative of one possible anorexic filter. 
     Referring to FIG. 15, a flowchart designated 200 is illustrated for carrying out the process of the present invention with a digital computer. The image is digitized. Thereafter, the desired number of vertical and horizontal convolutions is determined. If the number of convolutions performed is odd, both vertical and horizontal convolutions are applied to the table of right sided center descriptors. If the number of convolutions performed is even, both vertical and horizontal convolutions are applied to the table of left sided center descriptors. That is, in accordance with whether the number of convolutions performed thus far is odd or even, the center descriptors to be applied alternate between left and right sided descriptors. The results of the convolutions are summed with the working binary image and the resulting pixels are assigned the values 0, 1, 2 or 3. 
     The filter matrix is then applied. If only partial thinning is required, the thinning is terminated after the filter matrix is applied once (EXIT). If the thinning is to proceed, the computer determines if any pixels of value 2 remain. If they do, the decision filter is applied N times. If no pixels of value 2 remain, it is determined whether the desired number of convolutions has been accomplished. When this occurs, it is determined whether anorexic thinning is desired. If not, thinning is complete. If anorexic thinning is desired, the anorexic filter is applied to the thinned image and thinning is complete. If the desired number of convolutions has not been accomplished, the partially thin image becomes the new working image and further convolutions and filtering is applied as desired. 
     The filter matrix 100 of FIG. 10 is applied sequentially until all or most of the pixels having a value 2 are eliminated. However, with the filter matrix 100 the information provided by the pixels having a value or weight of 3 is used only passively. Advantageously, the pixels having a value 3 may be used actively and a plurality of filter matrices constructed to immediately filter each pixel once in accordance with its value and the values of the pixels in its 3×3 neighborhood, thereby increasing the speed of the thinning process. 
     Specifically, if the pixel value is 1, the 1s, 2s and 3s present in the 3×3 neighborhood are made 1s and the 0s are made 0, and the filter matrix illustrated in FIG. 16 as 210 is applied in the same manner as the filter matrix 100 of FIG. 10. However, if the pixel value is 2, the values in its 3×3 neighborhood are analyzed and one of three (3) filter matrices is applied as follows: If there are pixels of value 3 present in the 3×3 neighborhood, the 3s are made 1s and the 2s, 1s and 0s are made 0s. The filter matrix illustrated in FIG. 17 as 220 is then applied. If there are no pixels of value 3 present in the 3×3 neighborhood, but pixels of value 2 are present, the 2s and 1s are made 1s and the 0s are made 0. The filter matrix illustrated in FIG. 18 as 230 is then applied. If there are no pixels of value 3 or 2 in the 3×3 neighborhood, but only 1s and 0s, the filter matrix illustrated in FIG. 19 as 240 is applied. It is apparent, that the filter matrix 210 illustrated in FIG. 16 also includes the filter matrix 240 illustrated in FIG. 19. 
     Referring to FIG. 20, a flowchart designated 260 is illustrated for using the matrices 210, 220, 230 and 240 of FIGS. 16, 17, 18 and 19 in the process of the present invention. Initially, this process utilizes the same sequence of operations as described with reference to the flowchart 200 of FIG. 15, with the exception of the decision filters to be applied and the two decision blocks thereafter regarding remaining 2s and the number of filters to be applied (the loop). Thereafter, the flowchart illustrated in FIG. 20 as 260 is utilized. If the pixel value is 1 the filter matrix 210 of FIG. 16 is applied. If the pixel value is 2, the 3×3 neighborhood is checked to determine the absence or presence of 3 or 2s therein. If 3s are present, the filter matrix 220 of FIG. 17 is applied. If 2s are present but no 3s, the filter matrix 230 of FIG. 18 is applied. If no 3s or 2s are present in the neighborhood, the filter matrix 240 of FIG. 19 is applied. 
     However, if it is desired to utilize the filter matrix 210 of FIG. 16 for both pixels of value 1, and pixels of value 2 without pixels of value 2 or 3 in the 3×3 neighborhood, the flowchart illustrated in FIG. 21 as 270 is utilized in place of the sequence of operations specified in flowchart 260 of FIG. 20. 
     Specifically, if the pixel has a value of 1 or a value of 2 and no 2s or 3s are present in its 3×3 neighborhood the filter matrix 210 of FIG. 16 is applied. With regard to other pixels of value 2 the filter matrix 220 of FIG. 17 is applied if 3s are present in the 3×3 neighborhood and the filter matrix 230 of FIG. 18 is applied if there are no 3s in the 3×3 neighborhood, but 2s are present in the neighborhood. 
     Thus, as apparent from the foregoing description, the thinning process of the present invention can employ a weighted convolution, followed by one or more filter matrices, as well as the anorexic filter matrix, as desired. Further, additional weighted convolutions and filtering may be utilized in various combinations as desired. However, if a new convolution is to be applied after filtering, all the non-zero pixels are first made 1 to effectively represent the new working image. 
     It should be apparent to those skilled in the art that various modifications may be made in the process of the present invention without departing from the spirit and scope thereof, as described in the specification and defined in the appended claims. 
     PROGRAM APPENDIX 
     © Pitney Bowes Inc. ##SPC1## ##SPC2##