Abstract
We gradually develop a novel functional for joint variational object segmentation and shape matching. The formulation, based on the Wasserstein distance, allows modelling of local object appearance, statistical shape variations and geometric invariance in a uniform way. For learning of class typical shape variations we adopt a recently presented approach and extend it to support inference of deformations during segmentation of new query images. The resulting way of describing and fitting trained shape variations is in style reminiscent of contour-based variational shape priors, but does not require an intricate conversion between the contour and the region representation of shapes. A well-founded hierarchical branch-and-bound scheme, based on local adaptive convex relaxation, is presented, that provably finds the global minimum of the functional.
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References
Charpiat, G., Faugeras, O., Keriven, R.: Shape statistics for image segmentation with prior. In: Computer Vision and Pattern Recognition (CVPR 2007), pp. 1–6 (2007)
Cremers, D., Kohlberger, T., Schnörr, C.: Shape statistics in kernel space for variational image segmentation. Patt. Recognition 36(9), 1929–1943 (2003)
Haker, S., Zhu, L., Tannenbaum, A., Angenent, S.: Optimal mass transport for registration and warping. Int. J. Comput. Vision 60, 225–240 (2004)
Klodt, M., Cremers, D.: A convex framework for image segmentation with moment constraints. In: ICCV (2011)
Michor, P., Mumford, D.: Riemannian geometries on spaces of plane curves. Journal of the European Mathematical Society 8(1), 1–48 (2006)
Schmitzer, B., Schnörr, C.: Weakly convex coupling continuous cuts and shape priors. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds.) SSVM 2011. LNCS, vol. 6667, pp. 423–434. Springer, Heidelberg (2012)
Schmitzer, B., Schnörr, C.: Modelling convex shape priors and matching based on the Gromov-Wasserstein distance. Journal of Mathematical Imaging and Vision 46(1), 143–159 (2013)
Sundaramoorthi, G., Mennucci, A., Soatto, S., Yezzi, A.: A new geometric metric in the space of curves, and applications to tracking deforming objects by prediction and filtering. SIAM Journal on Imaging Sciences 4(1), 109–145 (2011)
Villani, C.: Optimal Transport: Old and New. Springer (2009)
Wang, W., Slepčev, D., Basu, S., Ozolek, J.A., Rohde, G.K.: A linear optimal transportation framework for quantifying and visualizing variations in sets of images. International Journal of Computer Vision 101, 254–269 (2012)
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Schmitzer, B., Schnörr, C. (2013). Object Segmentation by Shape Matching with Wasserstein Modes. In: Heyden, A., Kahl, F., Olsson, C., Oskarsson, M., Tai, XC. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2013. Lecture Notes in Computer Science, vol 8081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40395-8_10
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DOI: https://doi.org/10.1007/978-3-642-40395-8_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40394-1
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