Artificial Intelligence
Toward a computational theory of shape: an overview
ECCV 90 Proceedings of the first european conference on Computer vision
Ridges, crests and sub-parabolic lines of evolving surfaces
International Journal of Computer Vision
Symmetry Sets and Medial Axes in Two and Three Dimensions
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Multiscale Medial Loci and Their Properties
International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
Determining the Geometry of Boundaries of Objects from Medial Data
International Journal of Computer Vision
Interpolation in Discrete Single Figure Medial Objects
CVPRW '06 Proceedings of the 2006 Conference on Computer Vision and Pattern Recognition Workshop
Tree Structure for Contractible Regions in R3
International Journal of Computer Vision
Medial Representations: Mathematics, Algorithms and Applications
Medial Representations: Mathematics, Algorithms and Applications
Population-based fitting of medial shape models with correspondence optimization
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Geometrically proper models in statistical training
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Generalized Swept Mid-structure for Polygonal Models
Computer Graphics Forum
| Hi-index | 5.23 |
We consider ''swept regions'' @W and ''swept hypersurfaces'' B in R^n^+^1 (and especially R^3) which are a disjoint union of subspaces @W"t=@W@?@P"t or B"t=B@?@P"t obtained from a varying family of affine subspaces {@P"t:t@?@C}. We concentrate on the case where @W and B are obtained from a skeletal structure (M,U). This generalizes the Blum medial axis M of a region @W, which consists of the centers of interior spheres tangent to the boundary B at two or more points, with U denoting the vectors from the centers of the spheres to the points of tangency. We extend methods developed for skeletal structures so that they can be deduced from the properties of the individual intersections @W"t or B"t and a relative shape operator S"r"e"l, which we introduce to capture changes relative to the varying family {@P"t}. We use these results to deduce modeling properties of the global B in terms of the individual B"t, and determine volumetric properties of regions @W expressed as global integrals of functions g on @W in terms of iterated integrals over the skeletal structure of @W"t which is then integrated over the parameter space @C.