Abstract
This paper introduces mathematical morphology for real-valued images whose support space is a Riemannian manifold. The starting point consists in replacing the Euclidean distance in the canonic quadratic structuring function by the Riemannian distance. Besides the definition of Riemannian dilation/erosion and Riemannian opening/closing, their properties are explored. We generalize also some theoretical results on Lasry–Lions regularization for Cartan–Hadamard manifolds. Theoretical connections with previous works on adaptive morphology and on manifold shape are considered. Various useful image manifolds are formalized, with an example using real-valued 3D surfaces.
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Angulo, J., Velasco-Forero, S. (2013). Mathematical Morphology for Real-Valued Images on Riemannian Manifolds. In: Hendriks, C.L.L., Borgefors, G., Strand, R. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2013. Lecture Notes in Computer Science, vol 7883. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38294-9_24
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DOI: https://doi.org/10.1007/978-3-642-38294-9_24
Publisher Name: Springer, Berlin, Heidelberg
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