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- James N. Damon
- International Journal of Computer Vision
- 2005

We consider a region Ω in R2 or R3 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” Srad and an “edge shape operator” S E which measure how U bends along M. These are not traditional… (More)

- Stephen M. Pizer, Kaleem Siddiqi, Gábor Székely, James N. Damon, Steven W. Zucker
- International Journal of Computer Vision
- 2003

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)

- Pavel Dimitrov, James N. Damon, Kaleem Siddiqi
- CVPR
- 2003

We consider the average outward flux through a Jordan curve of the gradient vector field of the Euclidean distance function to the boundary of a 2D shape. Using an alternate form of the divergence theorem, we show that in the limit as the area of the region enclosed by such a curve shrinks to zero, this measure has very different behaviours at medial points… (More)

- James N. Damon
- Journal of Mathematical Imaging and Vision
- 1999

Pizer and Eberly introduced the “core” as the analogue of the medial axis for greyscale images. For two-dimensional images, it is obtained as the “ridge” of a “medial function” defined on 2 + 1-dimensional scale space. The medial function is defined using Gaussian blurring and measures the extent to which a point is in the center of the object measured at a… (More)

- Qiong Han, Derek Merck, +4 authors Stephen M. Pizer
- IPMI
- 2007

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)

- Suraj Musuvathy, Elaine Cohen, Joon-Kyung Seong, James N. Damon
- Symposium on Solid and Physical Modeling
- 2009

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 either of the principal curvatures attain a critical value in its respective principal direction.… (More)

- James N. Damon
- International Journal of Computer Vision
- 2006

For contractible regions ωin ℝ3 with generic smooth boundary, we determine the global structure of the Blum medial axis M. We give an algorithm for decomposing M into “irreducible components” which are attached to each other along “fin curves”. The attaching cannot be described by a tree structure as in the 2D case. However, a simplified but topologically… (More)

- James N. Damon, J. S. Marron
- Journal of Mathematical Imaging and Vision
- 2013

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)

- Suraj Musuvathy, Elaine Cohen, James N. Damon
- Computer-Aided Design
- 2011

A new approach is presented for computing the interior medial axes of generic regions in R bounded by C-smooth parametric B-spline surfaces. The generic structure of the 3D medial axis is a set of smooth surfaces along with a singular set consisting of edge curves, branch curves, fin points and six junction points. In this work, the medial axis singular set… (More)

- James N. Damon
- Theor. Comput. Sci.
- 2008

We consider “swept regions”Ω and “swept hypersurfaces”B in R n+1 (and especially R) which are a disjoint union of subspaces Ωt = Ω∩Πt or Bt = B∩Πt obtained from a varying family of affine subspaces {Πt : t ∈ Γ}. We concentrate on the case where Ω and B are obtained from a skeletal structure (M, U). This generalizes the Blum medial axis M of a region Ω,… (More)