Abstract:
Information on the shape of an object is extracted by generating an image of the object, encoding and ordering the boundary points of the image, selecting points on the outermost portions of the boundary, partitioning the boundary at the selected points into segments of either a first or second kind wherein the segments are distinguished according to a selected smoothness test, and segments of the first kind are smoother than segments of the second kind, partitioning each segment of the second kind into segments of the first or second kind according to the above test, and continuing the partitioning of each of the segments of the second kind into segments of the first or second kind until no further segments of the second kind are identified. An apparatus for performing the above steps is also disclosed.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to means and methods of processing an object image to extract information on the shape of the object. The invention employs successively finer levels of analysis of segments of the objects boundary by an iterative process. 
     2. Related Art 
     The problem of quantitatively describing the shape of an object is central to the field of image processing (IP). Although shape description techniques have been developed for such diverse purposes as character recognition, classification of tactical targets, and assembly line inspection, none of these systems meet current needs and the demand for improved performance at less cost. 
     Hu and Alt in 1962 described certain boundary moment approximtaions which exhibited rotationally invariant shape information. Using fourier boundary descriptions, Cosgriff and Brill in 1968 demonstrated that the shape of numerals could be quantified and reconstructed with varying degrees of resolution, depending on how many coefficients were used. Both the above techniques are computationally very expensive. The widely investigated Medial Axis Transformation (MAT) or skeletonization first reported by H. Blum in 1968 has also shown promise. However, it is generally conceded that MAT is very sensitive to boundary noise and generally requires presmoothing, which itself uses additional parameters that are difficult to automate. 
     Much research in character recognition has been founded on the premise that handwritten characters are composed of pen stroke primitives. One example of this approach is W. W. Stallings&#39; stroke based Chinese character recognizer, &#34;Chinese Character Recognition&#34;, Syntatic Pattern Recognition Applications, Springer-Verlag (1977) pp. 95-123. T. Pavlidis and H. Y. F. Feng in &#34;Shape Discrimination&#34;, Syntatic Pattern Recognition Applications, Springer-Verlag (1977), pp. 125-145, reported an approach which decomposes object shape into a series of convex polygons. Although the aforementioned represent significant achievements, techniques such as polygonal decomposition and skeletonization either are frauhht with algorithmic constraints such as presmoothing or are computationally too expensive to present a realistic option for real time IP systems today. Consequently, many IP systems are forced to rely on simple features such as length to width ratio and perimeter to supply gross shape information to an object classifier. There is a clear need for a computationally inexpensive technique for extracting detailed shape information from a scene. 
     SUMMARY OF THE INVENTION 
     The present invention includes a method for extracting information on the shape of an object by: 
     (a) generating an image of the object, 
     (b) encoding and ordering the boundary points of the object, 
     (c) selecting a set of n points, wherein each of the set of points lies on the outermost portions of the boundary, 
     (d) partitioning the boundary into segments of either a first or second kind, wherein the end points of either kind of segment are two points from the set of outermost boundary points and wherein segments of the first kind are smoother than segments of the second kind according to a selected smoothness test, 
     (e) partitioning each segment of the second kind into segments of either the first or second kind according to the above smoothness test, and 
     (f) continuing partitioning segments of the second kind according to step (e) until no segments of the second kind are further identified. 
     More particularly, in step (c) of the method of the present invention, the set of n points are, preferably, the &#34;convex hull&#34; points. The convex hull points are identified by selecting a reference point (lying outside the object age) and a reference line, and identifying the first convex hull point. The first convex hull point is that boundary point, which when connected by a line to a suceeding boundary point, forms the minimum angle with the reference line of all of the boundary points. The first convex hull point then becomes the reference point and the next convex hull point is identified in the same manner as the first convex hull point. The convex hull point selection process continues until the first convex hull point is again identified as a convex hull point. 
     In addition to the above basic method of the present invention, whenever a segment of the second kind is identified, any of a number of shape descriptors can be determined for each segment of the second kind to further characterize that segment and therefore the object. 
     Apparatus corresponding to the above method is also part of the present invention. 
     The basic method is further embellished by techniques to minimize the number of boundary points that are processed and for combining adjacent segments of the boundary when the curvature of the adjacent segments is relatively gradual. 
     The method of the present invention will be referred to as hierarchical boundary decomposition (HBD). 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1 is a hardware block diagram of a system suitable for HBD. 
     FIG. 2 is a high level flow chart of the general HBD method. 
     FIG. 3 is high level flow chart of the HBD method in &#34;breadth first&#34; mode. 
     FIGS. 4 through 6 show the HBD method of FIG. 3 applied through part of the first level of decomposition of an arbitary shape. 
     FIG. 7 shows the HBD method of FIG. 3 applied through part of the second level of decomposition of an arc identified as concave by the first level of decomposition. 
     FIG. 8 shows the &#34;shape tree&#34; generated by three levels of HBD applied to the shape in FIG. 4. 
     FIG. 9 shows a &#34;convex hull&#34; resulting from a scaled down application of HBD at its first level. The convex hull is superimposed over the shape from which the convex hull points were generated. 
     FIG. 10 shows a convex hull resulting from a full scale application of HBD to a shape, with the hull again superimposed as in FIG. 8. 
     FIGS. 11a and 11b show a flow chart of the HBD method, much expanded as compared to FIG. 3, with optional point minimization and low level smoothing included. 
     FIG. 12 shows an arc with a depth less than one. 
     FIG. 13 shows an arc with a depth greater than one. 
     FIG. 14 shows two adjacent arcs each with a depth less than one and the merging of the arcs by low level smoothing. 
     FIG. 15 shows the &#34;corner angles&#34; for each boundary point. 
     FIG. 16 is an example of a detailed flow chart for generating the convex hull. 
     FIG. 17 is an example of a detailed flow chart for ac decomposition. 
     FIG. 18 is a high level flow chart of HBD in a &#34;depth first&#34; mode. 
     FIGS. 19 is an expanded flow chart of the method of FIG. 18, which substitutes selected steps for certain steps of FIGS. 11a and 11b. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The invention presumes generation of a two-dimensional image representing the shape of an object. Preferably the image is a digital image. Many current systems are suitable for supplying such an image. The image will be processed by the present invention. HB system 20 in FIG. 1 includes conventional components which will generate the two-dimensional digital image. 
     That is, the system for generating the two-dimensional digital image (i.e. the blocks within dashed line 22 , includes a video digitizer 24, image buffer 26, timing logic 28, digital processing logic 30, address register 32 and resolution controller 34. All components within dashed line 22 are typically combined into a single device. For example, an International Imaging Systems (IIS) model 70 video digitizer (made by Stanford Research Institute) includes all of the above components within dashed line 22 and is suitable for many applications of the HBD process. Of course, as with any digitizer, its memory capacity may not be sufficient for a particular application, the resolution may be insufficient for a particular application or simply the speed with which a digital image is produced may be insufficient. Systems with increased capabilities in these areas can be used with the presen invention if desired. 
     The IIS model 70 video digitizer, as with most video digitizers, interfaces with a host computer (represented schematically by dashed line 36 and the blocks within) by inserting a card into a slot in the host computer, the card is designed and selected to make the data format and data busing of a particular video digitizer system 22 compatible with the particular host computer 26 selected. Again these are conventional techniques and hardware. A host computer 36 suitable for many applications of HBD and which can be used directly with an IIS model 70 video digitizer are the Honeywell Level 6/53 computer or a VAX 11/750 computer. 
     The output from video digitizer system 22 is transmitted on bus line 38. It is, in conventional fashion, a stream of digital signals representative, preferably, of a pixel matrix of a×b dimension with an individual pixel i being uniquely identified by coordinates (a i , b i ). The digital signals are often a word of several bits including gray scale information for a particular pixel. 
     Boundary encoding processor 40 identifies the boundary points or pixels, encodes the boundary points and, preferably, orders the boundary points. Encoding and ordering can be accomplished by programming the host computer 36 with a standard encoding technique such as the Freeman chain code. The output from boundary encoding processor 40 will identify all the edge or boundary points, and order them consecutively from some arbitary boundary starting point. Ordering the boundary points consecutively (either clockwise or counterclockwise) is preferred in the present invention since it reduces the number of pixels which are processed within the various levels, as discussed further below. 
     Boundary point minimizer 42, arc detection logic 44, arc feature extractor 46 and iteration decision logic 48 are, as shown, all included within host computer 36. Each of the blocks shown within host computer 36 can be provided by customized hard- wired data processors or, more typically, by programming a general purpose computer of the kinds described above. The invention will be further described in the form of a programmed general purpose computer. The memory, speed or other capabilities of the host computer 36 can, of course, be tailored to the particular task HBD is assigned. 
     The program used in the general purpose computer (e.g. host computer 36) will be described with reference to FIGS. 3 through 19. In artificial intelligence, the processing of a digital image of an object shape is often described by a &#34;tree&#34; structure (for example, see FIG. 8). In a tree structure, selected features are identified at a first broad level, and each level is broken down into successively finer levels with each successive level containing more detailed information regarding a portion of the level immediately above it. 
     Further, techniques for processing this tree structure include, but are not limited to, &#34;breadth first&#34; search (or mode) or &#34;depth first&#34; search (or mode). In breadth first mode, all features at the same level in the tree are processed first before any feature in the next level is processed. In depth first mode, all levels of a first feature or branch are processed before a second feature or branch is processed. 
     No particular order of detection of the individual nodes in the shape tree is required in the invention, however, breadth first search is preferred. Note that whatever the order of detection of nodes, the common result of the invention is a hierarchical description. 
     The program used in general purpose computer 36 to accomplish HBD will first be described in general. Thereafter the operation of HBD in breadth first and depth first mode will be described. 
     FIG. 2 shows a high level flow chart for HBD. The boundary points are ordered and encoded at 50, the output of step 50 is an ordered set of boundary verticies or points. At step 52, a subset of the boundary points is identified as the points which will be used to partition the boundary into segments. This subset of boundary points are n points lying on the outermost or extremities of the object shape, such that an n sided polygon with each side connecting two of the points of the subset, will roughly enclose most of the shape, and all large depressions or concave areas will be within the polygon. 
     More particularly, this subset of boundary points are the &#34;convex hull&#34; verticies. The convex hull is defined as the smallest area which can be enclosed by an n sided polygon circumscribing a given set of n points, wherein each side of the polygon includes two of the n points as end-points. The output of step 52 is the subset of n boundary points or, preferably the convex hull verticies or points. 
     During step 54, the boundary is segmented into segments of either a first or second kind. More specifically, the boundary is divided into a series of consecutive &#34;arcs&#34;, either concave or convex. A set of consecutive boundary points are either identified as a segment of a first or second kind (e.g. is either a concave or convex arc) according to selected criteria. The segments should be distingushed by utilizing the outermost points determined from step 52 to identify which segments follow the extremes of the object shape and which segments deviate substantially from the extremes. 
     In particular, the preferred method of segmenting the boundary employs a correspondence test. If there is a one to one correspondence between a consecutive set of boundary points and a consecutive set of points in the n points identified in step 52, then the set of boundary points satisfying the one to one correspondence test is defined as a &#34;convex arc&#34; (CV). If the correspondence test is not met, then the set of boundary points between (and including) the two points of the n point subset of outermost points where the correspondence failed, is defined as a &#34;concave arc&#34; (CC). Note that by definition a straight line segment is a convex arc. 
     The output of step 54 is a set of first and/ or second segments (e.g. convex and/or concave arcs) at a first level of the shape tree (i.e. level n). 
     The next step, step 56, is optional and involves calculations at level n of a variety of &#34;shape descriptors&#34;. These descriptors give detailed information on the arcs in level n. For example, the depth of a concave arc can now be calculated. Twenty shape descriptors are described below in detail but other descriptors useful in processing some or all of the set of points within a given arc or segment can also be used if desired. 
     In step 58, the &#34;hierarchical&#34; nature of the process is made explicit. In the most general case, the inquiry is simply &#34;Do subarcs exists? &#34; If the answer is yes, iteration occurs according to whatever mode is selected for constructing the shape tree. 
     FIG. 3 shows a high level flow chart for HBD in breadth first search or mode. Corresponding steps are like-numbered between FIGS. 2 and 3. In breadth first mode, the next level, i.e., level n+1, of the shape tree is examined for &#34;subarcs&#34;. Subarcs will appear only within concave arcs (and each decomposible concave arc will include at least two subarcs), but subarcs may be either convex or concave. A brief look at FIG. 8 may be helpful at this point in visualizing a shape tree of multilevels. In FIG. 8 one branch terminates at level 1 and a second branch includes subarcs and terminates at level 3. 
     If no subarcs exist at the current level, the HBD processes is terminated (step 60). If subarcs exist, HBD is applied again to each subarc identified at the current level (i.e. the breadth first approach). This completes the basic HBD breadth first method. 
     FIGS. 4 through 6 show HBD breadth first through part of its first level for an arbitary shape 62. A digital a×b matrix (not shown) of points depicting FIG. 62 is presumed displayed in FIG. 3. Two othogonal axes (e.g. x and y) are also presumed as the coordinate system used to label the various pixels in the matrix. The x coordinate is parallel to dashed lines 64 and 66, and and y coordinate is parallel to dashed lines 68 and 70. 
     The following procedure will be implemented by an HBD program in general purpose computer 38. A first reference point 0 1 , which lies outside the maximum x dimension of shape 62 and outside the maximum y dimension of shape 62 (i.e. outside of the rectangle form by line 64 and 66, and lines 68 and 70) is selected. Using either the x or y axis, a reference line is determined, which is formed by passing through point 0 1  and arbitrarily through one of the boundary points (e.g. point A) in FIG. 4. 
     Initially a series of direction lines are passed through point A and respectively through all the succeeding boundary points. Only nine boundary points (A, B, C, D, E, F, G, H and I) are shown for simplicity. Of course, typically hundreds of boundary points will be available. In the present example, however, nine direction lines will be determined--one for each of the nine boundary points. 
     The angle between each of the nine direction lines and the reference axis will be determined (i.e. calculated in a standard manner using the coordinates of 0 1 , the coordinates of the boundary points passing through which the relevant direction lines pass and the location of the reference axis), and the minimum angle of the nine angles selected. The boundary point lying on the direction line forming the minimum angle with the reference axis is selected as the first convex hull point. If more than one direction line has the same minimum angle, any of the boundary points laying on one of these direction lines can be selected, or for convenience, the first of these boundary points according to their ordering can be selected as the first convex hull point. 
     FIG. 4 shows shape 62 with boundary point A already selected by the above process as the first convex hull point. A first level reference line or direction, Ref 1  is selected by using the reference from above (i.e. the x axis) or by the direction defined by a line through 0 1  and the first convex hull point A. A new series of angle directions or direction lines are determined by connecting point A in turn individually to each of the other boundary points. FIG. 4 shows only three of the possible eight new angle directions or lines, i.e. the three lines connecting points B, G and E individually to point A. The angle measured from Ref 1  with each of the three lines are, respectively, α B , α G  and α E . The minimum angle, i.e. α B , is selected. Clearly, if the angle direction had also been determined for the remaining boundary points, i.e. points C, D, F, H and I, the angle from Ref 1  associated with each of these remaining directions would have exceeded α B . The boundary point associated with α B , i.e. B, is identified as the second convex hull point because it is the point forming the minimum direction angle with Ref 1  from the first convex hull point. 
     The third convex hull point is determined as shown in FIG. 5. The second identified convex hull point, point B, now becomes in effect (in the algorithm employed in the present invention), the first convex hull point. Angle directions are determined between point B and all boundary points subsequent thereto according to the order of the boundary points. That is, angle directions are determined between point B and each of points C, D, E, F, G, H and I. For simplicity only two of the angle directions in this step are shown in FIG. 5, that is the angle direction for points G and E. The angles between Ref 1  and each of these two lines (the lines between points B and G, and points B and E) are determined (i.e. angles α G  and α E1 ) and the minimum angle (α G ) selected. The point associated with the minimum angle, point G, is identified as the third convex hull point. Again clearly the angle formed between Ref 1  and each of the direction lines for points C, D, F, H and I, would exceed angle α G  so that point G is clearly the next convex hull point in FIG. 5. 
     The identification of convex hull points continues in the same fashion above. FIG. 6 shows the next step where G now becomes the convex hull point used to generate angle determination directions. Point H will be identified as the next convex hull point. 
     In a further step using point H as the first convex hull point, point I will also be identified as a convex hull point. The convex hull point identification process will end when the first convex hull point, point A, is again identified as a convex hull point. More generally, when any convex hull point is twice identified as a convex hull point, the identification of the convex hull points is complete and the &#34;generation of a convex hull&#34; is accomplished. In relation to the flow chart of FIG. 3, step 52 is now complete. 
     The arcs are now identified per step 54 in FIG. 3. More generally, the boundary will be partitioned into segments of either a first or second kind. Preferrably, the boundary will now be segmented into either concave or convex arcs. 
     Referring to the shape tree in FIG. 8, level 1, the process of FIGS. 4, 5 and 6 and the application of the correspondence test of step 54 will segment the boundary of shape 62 into two parts, a concave arc including points B, C, D, E, F and G, and a convex arc including points G, H, I, A and B. Note that the points between adjacent arcs are included in each arc. 
     If a convex arc is identified in level 1, that branch of the tree terminates. A convex arc is not decomposed into subarcs. The concave arc at level 1 will be further decomposed. With reference to FIG. 3, arc detection step 54 is now complete. 
     One can skip step 56 of FIG. 3, calculation of shape descriptor at levels n, if desired and move to step 58--subarc identification. Subarc identification is accomplished by taking each concave arc identified at the current level, reversing the order of processing the boundary points from the order used at the immediate preceding level, and applying steps 52 and 54 of FIG. 3 to each concave arc. The process has thus moved to the second level (or level n+1). In the example of shape 62, this means that convex hull points will now be identified on the concave arc shown in FIG. 7. 
     In FIG. 7 the order of processing boundary points is reversed from that of FIGS. 4 through 6. A new reference point O 2 , which lies outside the rectangle formed by dashed lines 72, 74, 76 and 78, is selected. A first convex hull point at level 2, point G, is identified by finding the minimum angle between a reference axis and the angles formed by a set of direction lines connecting point G 2  to each of the boundary points in FIG. 7. This process results in point G being identified as the first convex hull point at this level. The same process as in FIGS. 4 through 6 is repeated. FIG. 7 shows direction lines joining points G and F, and points G and E with angles α F  and α E2  as measured from Ref 2 . Angle α F  is smaller than α E2 , thus point F is identified as the second convex hull point at the second level. 
     The process continues at the second level, identifying points D, Δ (a boundary point added to FIG. 7) and B as other convex hull points at level 2. Concave and convex arcs are now identified for level 2. FIG. 8 shows the results of this identification as two concave and two convex arcs at level 2. 
     Since concave arcs remain at level 2, HBD is applied again (i.e. at level 3) to each of the concave arcs in level 2. The order of processing points in level 3 is the reverse of the order in which points were processed in level 2. In general, all even numbered levels will be processed in the same direction and all odd numbered levels will be processed in the direction opposite to the even numbered levels. 
     The results of applying HBD to level 3 are shown as the lowest level in FIG. 8. Note that all arcs are now convex and therefore this branch of the tree is terminated at level 3. 
     On the gross level with which shape 62 is described by only the nine points in FIG. 4, the convex hull would, if superimposed on shape 62, appears as a five sided polygon 80 shown in FIG. 9. The convex hull points are circled. 
     If many additional boundary points (e.g. hundreds) were included in FIG. 4, the convex hull would be a many sided polygon (see FIG. 10) very nearly tracing the large curve segment 82 of shape 62 between points S and T, and including a straight line segment 84 expanding the large cavity in shape 62 and joining points S and T. 
     FIGS. 11a and 11b are an expanded flow chart of the process depicted in FIG. 3 (and includes the process of FIGS. 4 through 8). Dashed lines 86, 88 and 90 show optional enhancements. Steps 50, 52, 54, 56 and 58 in FIG. 3 correspond, respectively, to steps b, c-m, n-o, 0 4 , p and q in FIG. 11. 
     Th routine consisting of steps b 1  to b 4  in FIG. 11 is called boundary point minimization. If the slope of a line between two adjacent boundary points is sufficiently close to the slope of a line between one of these first two boundary points and the next (a third) boundary point, all three points will be considered included in an arc which is smooth enough to require processing of only one of the points through the HBD algorithm. In FIG. 10, for example, all the points in curve 82, except endpoints S and T, could be skipped. Steps b 1  through b 4  in FIG. 11 show a convenient way of providing this point minimization function by using a threshold value to determine if the slope between adjacent boundary points warrants processing of the points. 
     Low level smoothing (LLS) is the routine depicted by line 88 and steps 0 1  to 0 3 . FIGS. 12, 13 and 14 show LLS in graphic form. LLS smooths out arcs generated solely by discretization resulting from from the digitization process of an edge (as opposed to arcs which depict a shape feature). In FIG. 12, the arc formed by points p 1 , p 2  and p 3  is the result of discretization of a shape&#39;s straight edge. The depth of arc p 1  -p 3  is defined in a meaningful way. One useful definition is given in local descriptor L 4 , below. 
     Using the above definition of depth, if the depth d is less than 1, then LLS would be involved. LLS will merge adjacent arcs, i.e. arcs with a boundary point as a common end point, with a depth less than the threshold depth into one arc. In FIG. 13, arcs q 1  to q 4  and q 4  to q 6  each have a depth less than 1,  and are merged into one arc, q 1  to q 6 . Only q 1  and q 6  would be examined as possible convex hull points (i.e. angle direction lines will be drawn to them) and points q 2  through q 5  would be excluded as potential convex hull points. 
     The arc r 1  to r 7  in FIG. 14 is an arc with (according to the above definition) a depth greater than 1. It would not be merged with adjacent arcs even if the adjacent arcs had a depth less than 1. 
     The optional subroutine of calculating shape descriptors is shown as inserted by line 90 in FIG. 11. It allows the determination of selected additional features for each arc. The twenty shape descriptors (global and local) listed below are useful for various artificial intelligent purposes, but one could use others or additional shape descriptors as desired. 
     A. Global Shape Descriptors 
     1. f 1  =object pixel area=number of non- zero (gray scale) pixels contained in the object. 
     2. f 2  =object perimeter= ##EQU1## n object vertices=V i  ; distance=(x i  -x i+1 ) 2  +(Y i  -Y i+1 )1/2. 
     3. f 3  =convex area=sum of areas of triangle substended by C 1  and C i , C i+1  ; 2≦i≦m-1; m convex hull vertices=C i . 
     4. f 4  =convex perimeter= ##EQU2## 
     5. f 5  =convex hull fill ratio=f1/f3 
     6. f 6  =perimeter ratio=f 2  /f 4   
     7. f 7  =relative subframe coordinates=coordinates of the minimum bounding rectangle (MBR) of the object relative to the coordinate system. 
     8. f 8  =object heights=maximum y-minimum y 
     9. f 9  =object width=maximum x-minimum x 
     10. f 10  =heighth/width=f 8  /f 9   
     11. f 11  =corner angles=a corner angle θ for each boundary vertex V i . K=a selected portion of the object length (i.e. number of boundary points) used to compute the vector sum of unit vectors V xi  and V yi  over K, i.e., ##EQU3## with V i  laying within K. 
     The angle θ i  is the angle subtended by V x  and V y  (see FIG. 14). 
     B. Local Descriptors 
     1. L 1  =convexity or concavity: 1 convex arc, 0 concave arc. 
     2. L 2  =Arc area. 
     3. L 3  =Arc length in pixels= ##EQU4## K=arc start point 1=arc endpoint 
     4. L 4  =normalized arc depth=arc depth/object depth 
     Definitions of arc depth and object depth are given in &#34;Measuring Concavity on a Rectangular Mosiac&#34;, J. Sklansky, IEEE Transactions on Computers, Vol. C-21, Dec. 1972, the same being incorporated herein by reference 
     5. L 5  =normalized arc length=L 3  /f 2   
     6. L 6  =Corner angles=f 11  =set of θ i   
     7. L 7  =Curvature= ##EQU5## 
     8. L 8  =Straightness=Standard Deviation of θ i , 1≦i≦n. 
     9. L 9  =Normalized arc area=L 2  /f 1 . 
     It is useful to relate FIG. 11 to FIG. 1. The boundary point minimizer 42 can be implemented by programming general purpose computer 36 with the routine including steps b 1  to b 4 . Arc detection logic 44 can similarly be a program including steps c through p (and steps o 1  to o 3  if desired). Arc feature extractor 46 corresponds to the step depicted as o 4 . Iteration decision logic 48 is depicted as step q in FIG. 11. Boundary recording processor 40 corresponds to step b in FIG. 11 and video digitizer system 22 corresponds to step a in FIG. 11. 
     FIG. 16 is a detailed flow chart useful in generating a source code program for performing steps c through m of FIG. 11 (i.e. generation of the convex hull points). The optional routines are not included in FIG. 16. The inputs to the flow chart of FIG. 16 are a list of boundary vertices or points, and the number of vertices in the list. The output is a list of the boundary vertices which lie on the convex hull (i.e. the &#34;pointers&#34; to the convex hull points). It is assumed in FIG. 16 that the boundary points are clockwise ordered and are bounded by the two-dimensional space addressable by the image buffer 26 (of course a different ordering could be used for a different flow chart). AIl calculations used in the convex hull procedure of FIG. 16 assume a raster scan display memory which possesses an inverted y axis relative to standard Cartesian coordinates. Further the input vertex list is assumed to lie in quadrant 1 of the Cartesian coordintae system. Definitions employed are: 
     outside x=Maximum X coordinate of the image buffer+1000. 
     outside y=Maximum Y coordinate of the image buffer+1000. 
     prevangle=0.0 
     remainder=v length 
     
         ______________________________________hull x = outside x      Defines the zeroth                   convex hull pointhull y = outside y      outside the domain of                   the inut vertex list.______________________________________ 
    
     origin=1, Pointer to the current origin. 
     c length=0, number of convex hull points detected. 
     In FIG. 16, step 92, minang=32000.0, selects a large initial angle value which is arbitrarily large so that the proper minimum angle can be determined by the procedure. Steps 94 through 98 adjust the angles between the direction lines and the reference line so that they are all between 0 and π/2. 
     FIG. 17 is a detailed flow chart useful in generating source code programs for performing steps n through q of FIG. 11 (including step o 4  if desired). 
     In FIG. 17, step 100 says that if the level is not equal to 1, then the next arc to be processed will be pulled from the shape tree. If the level is 1, than the order of points is inverted and the convex hull procedure (e.g. the FIG. 16 flow chart) is performed as step 102. Step 104 is the optional calculation of shape descriptors. Step 106 is the correspondence test (step 52 of FIG. 3). The inputs to step 106 are the current arc vertices and the convex hull pointers within the current arc. The result or output of the part of FIG. 16 beginning with step 106 is found, in part, at each of steps 108 and 110. The output is the number of subarcs detected, a list of the locations of each dttected subarc and a list of local features for each detected subrac. 
     LLS routine steps o 1  to o 3  is not shown in FIG. 17, but it is strongly recommended that it be used with HBD, particularly when the method of the invention is applied to a digital raster scan device. 
     Appendix A attached hereto and incorporated herein, is an assembly code listing for the Honeywell Level 6/53 minicomputer. The listing contains two subroutines which are separately described in Appendix A by comments in the listing. The CVHULL subroutine performs the algorithm of FIGS. 16A and 16B. The BLDTRE subroutine performs the algorithm of FIG. 17, excluding calculation of shape descriptors but including LLS. Together they perform steps (c) through (q) in FIGS. 11a and 11b (i.e. the listing is for breadth first mode), including steps 0 1  to 0 3 . 
     FIG. 18 corresponds to FIG. 3 but shows a &#34;depth first&#34; application of HBD. Corresponding steps in FIGS. 3 and 18 are like-numbered. 
     FIG. 19 corresponds to part of FIG. 11a and FIG. 11b, but is modified to show a depth first application of HBD. Steps (a) through (l) in FIG. 19 are the same as steps (a) through (l) in FIG. 11a. 
     The present invention has been described primarily in the digital domain, however, continuous line representations of the boundary can also be processed by the present invention The boundary must however be separated into a series of points. ##SPC1##