Polygonal Curve Evolutions for Planar Shape Modeling and Analysis

Two Handy Geometric Prediction Methods of Cancer Growth

“…. , n. Other methods to approximate the normal direction to a point P t 1 i , like the bisector direction or the median direction, can be found in [1]. Figure 3: Calculus of the predicted points P t 3 k with the normal method At each point P t 2 j we determine the normal vector N 2 (P t 2 j ) to the polygonal curve α 2 and, following that direction, at a distance f 1 (P t 1 i ), we plot the predicted points P t 3 (x j , y j ), j = 1, 2, .…”

“…Several examples of functions F (s, t) can be found in [1], for instance, when the function is the curvature of the initial curve, we have a curvaturedriven evolution of the initial curve α 0 .…”

Region segmentation via deformable model-guided split and merge

“…The assumption is that significant visual parts will become convex at higher stages of the evolution. In related work, Belyaev, et al [1] developed a polygonal curve evolution method that can be used for multi-scale shape analysis. A major drawback of contour evolution approaches is that it is unclear how to distinguish cuts between objects from cuts between parts inside the same object.…”

“…The neighborhood size Ð Ò will influence the accuracy and robustness of the result. 1 3. After smoothing the convexity of each point to eliminate noise influence, the whole segment × will be decomposed into concave and convex sub-segments.…”

“…To select a cut based on a set of candidates of cut endpoints, the direct strategy is: test all possible cuts. For 1 We choose ÐÒ in our experiments.…”