Abstract
In this paper we develop partial differential equations (PDEs) that model the generation of a large class of morphological filters, the levelings and the openings/closings by reconstruction. These types of filters are very useful in numerous image analysis and vision tasks rang- ing from enhancement, to geometric feature detection, to segmentation. The developed PDEs are nonlinear functions of the first spatial deriva- tives and model these nonlinear filters as the limit of a controlled growth starting from an initial seed signal. This growth is of the multiscale di- lation or erosion type and the controlling mechanism is a switch that reverses the growth when the difference between the current evolution and a reference signal switches signs. We discuss theoretical aspects of these PDEs, propose discrete algorithms for their numerical solution and corresponding filter implementation, and provide insights via several ex- periments. Finally, we outline the use of these PDEs for improving the Gaussian scale-space by using the latter as initial seed to generate mul- tiscale levelings that have a superior preservation of image edges and boundaries.
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Maragos, P., Meyer, F. (1999). Nonlinear PDEs and Numerical Algorithms for Modeling Levelings and Reconstruction Filters. 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_32
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DOI: https://doi.org/10.1007/3-540-48236-9_32
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