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IEEE Transactions on Pattern Analysis and Machine Intelligence
Uniqueness of the Gaussian Kernel for Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Based Description and Recognition of Planar Curves and Two-Dimensional Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Cellular automata machines: a new environment for modeling
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IEEE Transactions on Pattern Analysis and Machine Intelligence
CVGIP: Image Understanding
Area and Length Preserving Geometric Invariant Scale-Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Local Reproducible Smoothing Without Shrinkage
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Curve and surface smoothing without shrinkage
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
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In this paper the general concept of a migration process (MP) isintroduced; it involves iterative displacement of each point in a set asfunction of a neighborhood of the point, and is applicable to arbitrary setswith arbitrary topologies. After a brief analysis of this relatively generalclass of iterative processes and of constraints on such processes, werestrict our attention to processes in which each point in a set isiteratively displaced to the average (centroid) of its equigeodesicneighborhood. We show that MPs of this special class can be approximated by “reaction-diffusion”-type PDEs, which have received extensiveattention recently in the contour evolution literature. Although we showthat MPs constitute a special class of these evolution models, our analysisof migrating sets does not require the machinery of differential geometry.In Part I of the paper we characterize the migration of closed curves andextend our analysis to arbitrary connected sets in the continuous domain (R^m) using the frequency analysis of closed polygons,which has been rediscovered recently in the literature. We show thatmigrating sets shrink, and also derive other geometric properties of MPs. InPart II we will reformulate the concept of migration in a discreterepresentation (Z^m).