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
Marching Optimal-Parameter Ridges: An Algorithm to Extract Shape Loci in 3D Images
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
Image Loci are Ridges in Geometric Spaces
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
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Properties of points in images are often measured using convolution integrals with each convolution kernel associated to a particular scale and perhaps to other parameters, such as an orientation, as well. Assigning to each point the parameter values that yield the maximum value of the convolution integral gives a map from points in the image to the space of parameters by which the given property is measured. The range of this map is the optimal parameter surface. In this paper, we argue that ridge points for the measured quantity are best computed via the pullback metric from the optimal parameter surface. A relatively simple kernel used to measure the property of medialness is explored in detail. For this example, we discuss connectivity of the optimal parameter surface and the possibility of more than one critical scale for medialness at a given point. We demonstrate that medial loci computed as ridges of medialness are in general agreement with the Blum medial axis.