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Non-Euclidean Analysis of Joint Variations in Multi-Object Shapes
This paper considers joint analysis of multiple functionally related structures in classification tasks.
Rigidity Properties of the Blum Medial Axis
We use a form of the cross ratio from projective geometry to show that in the case of four smooth sheets of the medial axis meeting along a branching submanifold, the cross ratio defines a function on the branching sheet which must be preserved under any diffeomorphism of the medial axis with another.
Modeling Multi-Object Configurations via Medial/Skeletal Linking Structures
We introduce a method for modeling a configuration of objects in 2D or 3D images using a mathematical "skeletal linking structure" which will simultaneously capture the individual shape features of the objects and their positional information relative to one another.
Shape and Positional Geometry of Multi-Object Configurations
In previous work, we introduced a method for modeling a configuration of objects in 2D and 3D images using a mathematical "medial/skeletal linking structure."
