Abstract
Properties of points in images are often measured using con- volution 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 pa- rameter 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.
This work was supported by NSF Grant BIR-951-0228.
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Kerckhove, M. (1999). Computation of Ridges via Pullback Metrics from Scale Space. In: Nielsen, M., Johansen, P., Olsen, O.F., Weickert, J. (eds) Scale-Space Theories in Computer Vision. Scale-Space 1999. Lecture Notes in Computer Science, vol 1682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48236-9_8
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DOI: https://doi.org/10.1007/3-540-48236-9_8
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