Method for recognizing concavities in an image subject to character recognition
This is a continuation of Application Ser. No. 07/334,322, filed on Apr. 7, 1989, now abandoned. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to an image processing method for calculating characteristics parameters of a concavity. 
     BACKGROUND OF THE INVENTION 
     For recognizing a handwritten character such as &#34;R&#34; in FIG. 1, concavities 1 and 2 and a hole are important characteristics. Therefore, convexity and concavity are important characteristics of a configuration. The smallest convex configuration including a configuration to be processed (original configuration hereinafter) is called convex hull. By subtracting the original configuration from the convex hull, concavities and holes are extracted, for characterizing the original configuration. However, the convex hull cannot easily generated in the strict meaning, in the conventional method. In the conventional method, top points of convex hull are successively connected by straight lines. In a digital image, a straight line is different from a line in the mathematical meaning, because a digital image consists of dispersed pixels and mathematical continuous line cannot always be drawn. The digital line may be an approximation and pixels outside of the convex hull may be took as pixels on the line. When a pixels outside of the convex hull is took, the configurations generated by the above subtraction represent other characteristics than the characteristics to be extracted. Usually a graphic processor is used for drawing lines, so lines are drawn according to the algorithm of the processor. It is not guaranteed that a suitable convex hull for recognition is always generated. 
     For evaluating a concavity, several characteristic parameters are proposed; chord length of a concavity, inner peripheral length of a concavity, concavity ratio etc. Unless concavities are exactly extracted, calculation of these parameters become in vain. 
     SUMMARY OF THE INVENTION 
     The present invention has an object to provide an image processing method for extracting exact concavities. 
     According to the present invention, between adjacent two top points of a convex hull, border pixels between the top points are successively evaluated from the chain code each border pixel has or from the distance between each pixels and a line connecting the top points so as to found the boundary pixels defines concavity or not. 
    
    
     BRIEF DESCRIPTION OF DRAWINGS 
     FIG. 1 shows a configuration having concavities; 
     FIG. 2 shows a table of data of boundary pixels of a configuration to be processed; 
     FIGS. 3A-D show a rule of chain code; 
     FIG. 4 shows a portion including boundary pixels of a configuration; 
     FIG. 5 shows another configuration including concavities; 
     FIGS. 6A-C show an inclined line connecting adjacent two top points on convex hull; 
     FIG. 7 shows steps of generating convex hull. 
    
    
     PREFERRED EMBODIMENT OF THE PRESENT INVENTION 
     Exemplary preferred embodiments of the image processing method according to the present invention will be described in detail hereinafter. 
     FIG. 1 shows a configuration including concavities A, B, C, D and E, hatched. A horizontal rectangle R circumscribed about the configuration is shown, as well. The configuration is divided into quadrants from first to fourth by the rectangle R. On tracing boundary pixels of the configuration, boundary pixels from upper side left contact point to left side lower contact point belong to the first quadrant, boundary pixels from left side lower contact point to lower side right contact point belong to the second quadrant, boundary pixels from lower side right contact point to right side upper contact point belong to the third quadrant, and boundary pixels from right side upper contact point to upper side left contact point belong to the fourth quadrant. The number of first to fourth may be changed as far as they are defined according to predetermined rule. Anyway, the information concerning quadrant is important for the processing below. 
     A table in FIG. 2 is generated, which includes informations of boundary pixels arranged in chain code order; whether they are top points on convex hull; x- and y-coordinates thereof; to which quadrant the points belong. In FIG. 2, top points on convex hull are indicated by Y or N, Y means top points and N means not. 
     FIGS. from 3(a) to 3(d) show the relationship between the quadrant and the chain code. FIG. 3(a) shows chain codes of boundary pixels in the first quadrant but not in a concavity. FIG. 3(b) shows chain codes of boundary pixels in the second quadrant but not in a concavity. FIG. 3(c) shows chain codes of boundary pixels in the third quadrant but not in a concavity. FIG. 3(d) shows chain codes of boundary pixels in the fourth quadrant but not in a concavity. It will be understood from FIGS. 3(a) to 3(d) that chain code other than from 4 to 6 in the first quadrant indicates a concavity, chain code other than from 6 to 0 in the second quadrant indicates a concavity, chain code other than from 0 to 2 in the third quadrant indicates a concavity, and chain code other than from 2 to 4 in the fourth quadrant indicates a concavity. 
     In the case that no chain code indicating concavity can be found, the following processing is necessary. 
     In FIG. 4, top points P1 and P2 on the convex hull are found. The inclination of the line 1 connecting P1 and P2 is calculated. The inclination is 5/7=0.714 and the inclination angle θ is 35.5 deg. Then boundary pixels are traced from P1 to P2. The distances between the line 1 and the boundary pixels are evaluated. For calculating the distance, a relationship between the chain code and distance increment Δd is calculated in advance. The distance increment Δd of boundary pixels traced are integrated so as to calculate a distance between the line 1 and the boundary pixel just traced. 
     As for the configuration in FIG. 4, the relationship is shown in the following Table 1. 
     
                       TABLE 1                                                     
______________________________________                                    
Chain code        Δ.sup.d                                           
______________________________________                                    
4                 -sinθ = -0.581                                    
5                 cosθ - sinθ = 0.233                         
6                 cosθ = 0.814                                      
______________________________________                                    
 
    
     In Table 1, Δd is defined as positive when it has inward direction from the line 1. 
     The boundary pixels from Pb1 to Pb7 between P1 and P2 have distances from the line 1, as shown in Table 2. The distances are calculated by the integration of d as described above. 
     
                       TABLE 2                                                     
______________________________________                                    
Boundary pixel  Distance                                                  
______________________________________                                    
Pb1             0.233                                                     
Pb2             0.466                                                     
Pb3             -0.115                                                    
Pb4             0.699                                                     
Pb5             0.902                                                     
Pb6             1.135                                                     
Pb7             0.554                                                     
______________________________________                                    
 
    
     Here, a rule is applied that boundary pixels between adjacent top points defines a concavity when one or more boundary pixels have distance not less than &#34;1&#34; from the line connecting the top points. 
     In Table 2, the pixel Pb6 has distance of &#34;1.135&#34;. On tracing boundary pixels from Pb1 toward Pb7, it is found first on the point Pb6 that the boundary pixels define concavity. 
     By counting number of boundary pixels from Pb1 to Pb7 on tracing them, the inner peripheral length of a concavity is calculated. If it is found that the boundary pixels do not define a concavity, the counted value is canceled. 
     The chord length of a concavity is calculated by calculating distance between top points P1 and P2. The distance is calculated by the x- and y-coordinates of P1 and P2. 
     Concavity ratio is calculated from the inner peripheral length, chord length of a concavity and peripheral length of the configuration, as follows. 
     
         Concavity ratio=(inner peripheral length)/ {(peripheral length)×(chord length)} 
    
     FIG. 5 shows another configuration to be processed. The configuration has boundary pixels from Pb1 to Pb9 between top points P1 and P2. The distances of each boundary pixel from the line 1 connecting P1 and P2 are shown in Table 3. The inclination of line 1 is 6/5=1.20, and the inclination angle θ is 50.2 deg. 
     
                       TABLE 3                                                     
______________________________________                                    
Boundary pixel  Distance                                                  
______________________________________                                    
Pb1             0.640                                                     
Pb2             1.280                                                     
Pb3             0.512                                                     
Pb4             1.152                                                     
Pb5             1.792                                                     
Pb6             2.432                                                     
Pb7             1.664                                                     
Pb8             0.896                                                     
Pb9             0.128                                                     
______________________________________                                    
 
    
     In Table 3, Pb2 has a distance more than &#34;1&#34;, Pb3 has a distance less than &#34;1&#34;, and Pb4 has a distance more than &#34;1&#34; again. In this case, concavity may be defined in two manners. In the first manner, one concavity is defined by the boundary pixels from Pb1 to Pb9. In the second manner, two concavities are defined, that is, one concavity is defined by the boundary pixels from Pb1 to Pb3 and the other concavity is defined by the boundary pixels from Pb4 to Pb9. 
     Table 1 shows distance increment in the first quadrant. The following Table 4 shows distance increment in the quadrants from the second to the fourth. The inclination angle θ is defined for each quadrant as shown in FIG. 6. 
     
                       TABLE 4                                                     
______________________________________                                    
Quadrant  Chain code      Δ.sup.d                                   
______________________________________                                    
II        6               cosθ                                      
          7               sinθ + cosθ                         
          0               sinθ                                      
III       0               -sinθ                                     
          1               cosθ - sinθ                         
          2               cosθ                                      
IV        2               cosθ                                      
          3               -sinθ - cosθ                        
          4               sinθ                                      
______________________________________                                    
 
    
     In the above rule, a concavity is defined when one or more boundary pixels has distance not less than &#34;1&#34;. Such distance may be another value, for example &#34;2&#34; considering noises. 
     In a practical processing of concavities, data in Table 2 is successively read out, distances are calculated with integrating distance increment, simultaneously the chain codes are evaluated according to the rule shown in FIG. 3. When the integrated value reaches predetermined value or the chain code becomes a value other than the value shown in FIG. 3, a concavity is found. By counting boundary pixels on tracing, inner peripheral length is simultaneously calculated. The chord length is obtained by calculating distance between top points. 
     As for generating an exact convex hull, the inventor invented the following image processing method, which is filed in the United States with application number of Ser. No. 07/301,350. 
     FIG. 7 shows two adjacent top points a and b on convex hull as well as boundary pixels C1 to C9 therebetween. Top points a and b are connected with a line 1 for defining an inclination from a to b. For generating convex hull, continuous pixel train is generated from a to b. Each pixel of the train is inside of the line as well as the nearest pixel among pixels continuous to the previous pixel on the train. In this case, the pixel train is generated anticlockwisely. Clockwise pixel train may also be applied. 
     The chain code of each pixel of the chain code train is limited to be &#34;4&#34; or &#34;5&#34;. The pixel d&#39; of chain code &#34;4&#34; next to a is nearer than the pixel d1 of chain code &#34;5&#34;. However the pixel of chain code &#34;4&#34; is outside of the line 1. Then the pixel d1 is selected. Thereafter, pixels inside of the line 1 as well as nearest to the line 1 among the pixels continuous to the previous pixel on the pixel train. The pixels from d2 to d8 are to be selected. The convex hull is exactly generated by the method above. 
     When each pixel of the pixel train generated are indexed by a specified density or any other index, the chord length is defined by the number of indexed pixels. In the configurations generated by subtraction of the original image from the convex hull, the number of boundary pixels without index defines the inner peripheral length of concavity. 
     Although only a few exemplary embodiments of this invention have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel teachings and advantages of this invention. 
     Accordingly, all such modification are intended to be included within the scope of this invention as defined in the following claims.