Morphological exploration of shape spaces

Abstract : The aim of this paper is to propose efficient tools for analysing shape families using morphological operators. The developments include the definition of shape statistics (mean and variance of shapes, modes of shape variation) and the interpolation/extrapolation in shape geodesic paths. The main required ingredients for the operators and the algorithms here introduced are well known in mathematical morphology such as the median set, the watershed on distance functions or the interpolation function. In addition, the projection of shapes in spaces with reduced dimensions using PCA or ISOMAP techniques permits to apply morphological interpolation techniques in shape manifolds.
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Michael H. F. Wilkinson and Jos B. T. M. Roerdink. 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing, ISMM 2009, Aug 2009, Groningen, Netherlands. Springer, 5720, pp.226-237, 2009, Lecture Notes in Computer Science. 〈10.1007/978-3-642-03613-2_21〉
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Jesus Angulo, Fernand Meyer. Morphological exploration of shape spaces. Michael H. F. Wilkinson and Jos B. T. M. Roerdink. 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing, ISMM 2009, Aug 2009, Groningen, Netherlands. Springer, 5720, pp.226-237, 2009, Lecture Notes in Computer Science. 〈10.1007/978-3-642-03613-2_21〉. 〈hal-00834033〉

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