article published yes Alexander Bronstein author 58f3726e-7cba-11ef-ad8b-e6e8cb3904e60000-0001-9699-8730 Michael M. Bronstein author Ron Kimmel author This paper explores the problem of similarity criteria between nonrigid shapes. Broadly speaking, such criteria are divided into intrinsic and extrinsic, the first referring to the metric structure of the object and the latter to how it is laid out in the Euclidean space. Both criteria have their advantages and disadvantages: extrinsic similarity is sensitive to nonrigid deformations, while intrinsic similarity is sensitive to topological noise. In this paper, we approach the problem from the perspective of metric geometry. We show that by unifying the extrinsic and intrinsic similarity criteria, it is possible to obtain a stronger topology-invariant similarity, suitable for comparing deformed shapes with different topology. We construct this new joint criterion as a tradeoff between the extrinsic and intrinsic similarity and use it as a set-valued distance. Numerical results demonstrate the efficiency of our approach in cases where using either extrinsic or intrinsic criteria alone would fail. Springer Nature2009 eng 0920-5691 1573-140510.1007/s11263-008-0172-2 813281-301 yes Bronstein AM, Bronstein MM, Kimmel R. 2009. Topology-invariant similarity of nonrigid shapes. International Journal of Computer Vision. 81(3), 281–301. Bronstein AM, Bronstein MM, Kimmel R. Topology-invariant similarity of nonrigid shapes. <i>International Journal of Computer Vision</i>. 2009;81(3):281-301. doi:<a href="https://doi.org/10.1007/s11263-008-0172-2">10.1007/s11263-008-0172-2</a> Bronstein, Alex M., Michael M. Bronstein, and Ron Kimmel. “Topology-Invariant Similarity of Nonrigid Shapes.” <i>International Journal of Computer Vision</i>. Springer Nature, 2009. <a href="https://doi.org/10.1007/s11263-008-0172-2">https://doi.org/10.1007/s11263-008-0172-2</a>. Bronstein, Alex M., et al. “Topology-Invariant Similarity of Nonrigid Shapes.” <i>International Journal of Computer Vision</i>, vol. 81, no. 3, Springer Nature, 2009, pp. 281–301, doi:<a href="https://doi.org/10.1007/s11263-008-0172-2">10.1007/s11263-008-0172-2</a>. Bronstein, A. M., Bronstein, M. M., &#38; Kimmel, R. (2009). Topology-invariant similarity of nonrigid shapes. <i>International Journal of Computer Vision</i>. Springer Nature. <a href="https://doi.org/10.1007/s11263-008-0172-2">https://doi.org/10.1007/s11263-008-0172-2</a> A.M. Bronstein, M.M. Bronstein, R. Kimmel, International Journal of Computer Vision 81 (2009) 281–301. A. M. Bronstein, M. M. Bronstein, and R. Kimmel, “Topology-invariant similarity of nonrigid shapes,” <i>International Journal of Computer Vision</i>, vol. 81, no. 3. Springer Nature, pp. 281–301, 2009. 183572024-10-15T11:20:54Z2024-10-22T07:27:15Z