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for each table entry for @ do for each S and @ xX. = x +r(b)Scos la(p) + 6] Ye = y+r(p)Ssin la(b) + 0] Finally, step 2.2b is now A (Xe Yor S, 9) = A (Xes Yer S, 0) +1 4.4 EDGE FOLLOWING AS GRAPH SEARCHING A graph is a general object that consists of a set of nodes {n,} and arcs between nodes . In this section we consider graphs whose arcs may have numeri- cal weights or costs associated with them. The search for the boundary of an object is cast as a search for the lowest-cost path between two nodes of a weighted graph. Assume that a gradient operator is applied to the gray-level image, creating the magnitude image s(x) and direction image ¢ (x). Now interpret the elements of the direction image (x) as nodes in a graph, each with a weighting factor s(x). Nodes x;, x; have arcs between them if the contour directions ¢(x;), ¢(x iy) are ap- propriately aligned with the arc directed in the same sense as the contour direction. Figure 4.10 shows the interpretation. To generate Fig. 4.10b impose the following restrictions. For an arc to connect from x; to x;, x; must be one of the three possi- ble eight-neighbors in front of the contour direction ¢(x;) and, furthermore, g (x,) ' 4 41 |AI-|4% t \ ' ' x \ i ' \ ' ' \ | ° Fig. 4.10 Interpreting a gradient image as a graph (see text). Sec. 4.4 Edge Following as Graph Searching 131 
