A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
Journal of Mathematical Imaging and Vision
Generic evolutions of edges on families of diffused greyvalue surfaces
Journal of Mathematical Imaging and Vision
Zoom-invariant vision of figural shape: the mathematics of cores
Computer Vision and Image Understanding
Zoom-invariant vision of figural shape: effects on cores of image disturbances
Computer Vision and Image Understanding
Generic structure of two-dimensional dimages under Gaussian blurring
SIAM Journal on Applied Mathematics
Relative critical sets in RR(N) and applications to image analysis
Relative critical sets in RR(N) and applications to image analysis
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Image Loci are Ridges in Geometric Spaces
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
The multiresolution intensity axis of symmetry and its application to image segmentation
The multiresolution intensity axis of symmetry and its application to image segmentation
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
Uniform approximation of near-singular surfaces
Theoretical Computer Science
Tree edit distances from singularity theory
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Extraction of Dominant Extremal Structures in Volumetric Data Using Separatrix Persistence
Computer Graphics Forum
Ridge-Based automatic vascular centerline tracking in x-ray angiographic images
IScIDE'12 Proceedings of the third Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
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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 scale. Numerical calculations indicate the core has properties quite different from the medial axis. In this paper we give the generic properties of ridges and cores for two-dimensional images and explain the discrepancy between core and medial axis properties. We place cores in a larger “relative critical set structure”, which coherently relates disjoint pieces of core. We also give the generic transitions which occur for sequences of images varying with a parameter such as time. The genericity implies the stability of the full structure in any compact viewing area of scale space under sufficiently small L2 perturbations of the image intensity function. We indicate consequences for finding cores and also for adding “markings” tocompletely determine the structure of the medial function.