Shape Median Based on Symmetric Area Differences

Median averaging is a powerful averaging concept on sets of vector data in finite dimensions. A generalization of the median for shapes in the plane is introduced. The underlying distance measure for shapes is based on the area of the symmetric difference of shapes and takes into account different invariance classes. These classes are generated by classical transformation groups such as translation, rotation, anisotropic scaling, and shear. As in the finite dimensional case, non-uniqueness of the median is observed. The numerical approximation of shape medians is based on a level set approach for the description of the shape contour. The level set function and the parameter sets of the group action on every given shape are incorporated in a joint variational functional, which is minimized based on step size controlled, regularized gradient descent. Various applications show in detail the qualitative behavior of the method.

• Type: Conference
• Year: 2008
• Where: VMV
• Authors: Benjamin Berkels, Gina Linkmann, Martin Rumpf
• Keywords: Level Set, Median Averaging, Powerful Averaging Concept, Visualization, VMV 2008