Error per Vertex and Error per Arc Length for Bias Computation

Using the polyline distance formulaes, we can compute the error per vertex from one polygon (ground truth) to another polygon (computer estimated). This is defined as the mean error for a vertex v over all the patients and all the slices. The error per vertex for a fixed vertex v when computed between ground truth and computer-estimated boundary is defined by eGC _ 1X1 I^n=1 db(v, Gnt) ,Q 9 ..

Similary we can compute the error per vertex between computer estimated and ground truth using Eq.(9. 20) Error per arc length is computed in the following way: For the values eGC where v = 1, 2, 3,..., Pi, we construct a curve fGC defined on the interval [0,1] which takes the value eGC at point x which is the normalized arc length to vertex v and whose in between values are defined by linear interpolation. We compute the curve fCG between computer estimated boundary and ground truth boundary in a similar way. We then add algebraically fGC1 fCG

these two curves to yield the final error per arc length, given as f = -—+—.

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