Affine Invariant Geometry for Non-rigid Shapes

Affine invariant non-rigid shape analysis

Shape recognition deals with the study geometric structures. Modern surface processing methods can cope with non-rigidity by measuring the lack of isometry, deal with similarity by multiplying the Euclidean arc-length by the Gaussian curvature, and manage equi-affine transformations by resorting to the special affine arc-length definition in classical affine geometry. Here, we propose a computa...

Numerical Geometry of Non-Rigid Shapes

Affine-invariant geodesic geometry of deformable 3D shapes

Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine-invariant arclength for surfaces in R in order to extend the set of existing non-rigid shape analysis tools. We show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated...

Scale Invariant Geometry for Nonrigid Shapes

Local scale variations within the same species are common in nature. The shape matching puzzle poses fascinating questions, like how should we measure the discrepancy between a small dog with large ears and a large one with small ears? are there similar geometric structures that are common to an elephant and a giraffe? what is the morphometric similarity between a blue whale and a dolphin? Exis...

Affine-Invariant Skeleton of 3D Shapes

In the recent past, different application fields have showed an increasing interest in shape description oriented to recognition and similarity issues. Beyond the application aims, the capability of handling details separating them from building elements, the invariance to a set of geometric transformations, the uniqueness and stability to noise represent fundamental properties of each proposed...