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Blum's medial axes have great strengths, in principle, in intuitively describing object shape in terms of a quasi-hierarchy of figures. But it is well known that, derived from a boundary, they are damagingly sensitive to detail in that boundary. The development of notions of spatial scale has led to some definitions of multiscale medial axes different from(More)
We consider a region in R 2 or R 3 with generic smooth boundary B and Blum medial axis M, on which is defined a multivalued " radial vector field " U from points x on M to the points of tangency of the sphere at x with B. We introduce a " radial shape operator " S rad and an " edge shape operator " S E which measure how U bends along M. These are not(More)
The discrete m-rep, a medial representation of anatomical objects made from one or more meshes of medial atoms, has many attractive properties for biomedical image analysis. The nonlinear nature of the m-rep parameters captures nonlinear deformations in anatomical objects such as twisting and bending. Most uses of m-reps require extending them to one or(More)
We seek a form of object model that exactly and completely captures the interior of most non-branching anatomic objects and simultaneously is well suited for probabilistic analysis on populations of such objects. We show that certain nearly medial, skeletal models satisfy these requirements. These models are first mathematically defined in continuous(More)
In deformable model segmentation, the geometric training process plays a crucial role in providing shape statistical priors and appearance statistics that are used as likelihoods. Also, the geometric training process plays a crucial role in providing shape probability distributions in methods finding significant differences between classes. The quality of(More)
In non-Euclidean data spaces represented by manifolds (or more generally stratified spaces), analogs of principal component analysis can be more easily developed using a backwards approach. There has been a gradual evolution in the application of this idea from using increasing geodesic subspaces of submanifolds in analogy with PCA to using a “backward(More)
Ridges are characteristic curves of a surface that mark salient intrinsic features of its shape and are therefore valuable for shape matching, surface quality control, visualization and various other applications. Ridges are loci of points on a surface where one of the principal curvatures attain a critical value in its respective principal direction. We(More)