Performance Evaluation System Rulers and Error Curves

The polyline distance Ds(B1 : B2) between two polygons representing boundary B1 and B2 is symmetrically defined as the average distance between a vertex of one polygon and the boundary of the other polygon. To define this measure precisely, we first need to define a distance d(v, s) between a point v and a line segment s. The distance d(v, s) between a point v having coordinates (xo, y0), and a line segment having end points (x\, yi) and (x2, y2) is

|dx| if < 0,k < 1, where d1 = V(X0 - X1)2 + (y0 - y02 d = V(X0 - X2)2 + (y0 - V2)2

d± _ (y2 - y1)(x1 - xq) + (X2 - X1)(yo - yQ - X1)2 + (y2 - y1)2

The distance db(v, .62) measuring the polyline distance from vertex v to the boundary B2 is defined by db(v, B2) = min d(v, s) (9.20)

s g sidesB2

The distance dvb(B1, B2) between the vertices of polygon B1 and the sides of polygon B2 is defined as the sum of the distances from the vertices of the polygon B1 to the closest side of B2.

v g vertices B1

Reversing the computation from B2 to B1, we can similarly compute dvb (B2, B1). Using Eq. (9.20), the polyline distance between polygons, Ds(B1 : B2) is defined by

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