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JMIV
2010

An SL(2) Invariant Shape Median

8 years 9 months ago
An SL(2) Invariant Shape Median
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 takes into account the area of the symmetric difference of shapes, where shapes are considered to be invariant with respect to different classes of affine transformations. To obtain a well–posed problem the perimeter is introduced as a geometric prior. Based on this model, an existence result can be established in the class of sets of finite perimeter. As alternative invariance classes other classical transformation groups such as pure translation, rotation, scaling, and shear are investigated. The numerical approximation of median shapes uses a level set approach to describe 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 controll...
Benjamin Berkels, Gina Linkmann, Martin Rumpf
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where JMIV
Authors Benjamin Berkels, Gina Linkmann, Martin Rumpf
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