Edge Curve Estimation by the Nonparametric Parzen Kernel Method

The article concerns the problem of finding the spatial curve which is the line of the abrupt or jump change in the 3d-shape, namely: the edge curve. There are many real applications where such a problems play a significant role. For instance, in computer vision in detection of edges in monochromatic pictures used in e.g. medicine diagnostics, biology and physics; in geology in analysis of satellite photographs of the earth surface for maps and/or determination of borders of forest areas, water resources, rivers, rock cliffs etc. In architecture the curves arising as a result of intersecting surfaces often are also objects of interest. The main focus of this paper is detection of abrupt changes in patterns defined by multidimensional functions. Our approach is based on the nonparametric Parzen kernel estimation of functions and their derivatives. An appropriate use of nonparametric methodology allows to establish the shape of an interesting edge curve.

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