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Partial Similarity of Objects, or How to Compare a Centaur to a Horse

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Abstract

Similarity is one of the most important abstract concepts in human perception of the world. In computer vision, numerous applications deal with comparing objects observed in a scene with some a priori known patterns. Often, it happens that while two objects are not similar, they have large similar parts, that is, they are partially similar. Here, we present a novel approach to quantify partial similarity using the notion of Pareto optimality. We exemplify our approach on the problems of recognizing non-rigid geometric objects, images, and analyzing text sequences.

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References

  • Berchtold, S., Keim, D. A., & Kriegel, H. P. (1997). Using extended feature objects for partial similarity retrieval. International Journal on Very Large Data Bases, 6(4), 333–348.

    Article  Google Scholar 

  • Besl, P. J., & McKay, N. D. (1992). A method for registration of 3D shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(2), 239–256.

    Article  Google Scholar 

  • Boiman, O., & Irani, M. (2006). Similarity by composition. In Proc. NIPS.

  • Bonhoeffer, S., Chappey, C., Parkin, N. T., Whitcomb, J. M., & Petropoulos, C. J. (2004). Evidence for positive epistasis in HIV-1. Science, 306, 1547–1550.

    Article  Google Scholar 

  • Borg, I., & Groenen, P. (1997). Modern multidimensional scaling—theory and applications. Berlin: Springer.

    MATH  Google Scholar 

  • Bronstein, A. M., & Bronstein, M. M. (2008). Partial matching of rigid shapes. (Technical Report CIS-2008-02). Dept. of Computer Science, Technion, Israel.

  • Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2003). Expression-invariant 3D face recognition. In Lecture notes on computer science : Vol. 2688. Proc. audio and video-based biometric person authentication (pp. 62–69). Berlin: Springer.

    Chapter  Google Scholar 

  • Bronstein, A. M., Bronstein, M. M., Gordon, E., & Kimmel, R. (2004). Fusion of 3D and 2D information in face recognition. In Proc. ICIP (pp. 87–90).

  • Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2005). Three-dimensional face recognition. IJCV, 64(1), 5–30.

    Article  Google Scholar 

  • Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2006a). Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. PNAS, 103(5), 1168–1172.

    Article  MATH  MathSciNet  Google Scholar 

  • Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2006b). Face2face: an isometric model for facial animation. In Proc. AMDO (pp. 38–47).

  • Bronstein, A. M., Bronstein, A. M., & Kimmel, R. (2006c). Robust expression-invariant face recognition from partially missing data. In Proc. ECCV (pp. 396–408).

  • Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2006d). Efficient computation of isometry-invariant distances between surfaces. SIAM Journal on Scientific Computing, 28(5), 1812–1836.

    Article  MATH  MathSciNet  Google Scholar 

  • Bronstein, A. M., Bronstein, M. M., Bruckstein, A. M., & Kimmel, R. (2006e). Matching two-dimensional articulated shapes using generalized multidimensional scaling. In Proc. AMDO (pp. 48–57).

  • Bronstein, M. M., Bronstein, A. M., Kimmel, R., & Yavneh, I. (2006f). Multigrid multidimensional scaling. Numerical Linear Algebra with Applications (NLAA), 13, 149–171.

    Article  MATH  MathSciNet  Google Scholar 

  • Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2007a). Calculus of non-rigid surfaces for geometry and texture manipulation. IEEE Transactions on Visualization and Computer Graphics, 13(5), 902–913.

    Google Scholar 

  • Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2007b). Rock, paper, and scissors: extrinsic vs. intrinsic similarity of non-rigid shapes. In Proc. ICCV.

  • Bronstein, M. M., Bronstein, A. M., Bruckstein, A. M., & Kimmel, R. (2007c). Paretian similarity for partial comparison of non-rigid objects. In F. Sgallari, A. Murli, & N. Paragios (Eds.), Proc. scale space and variational methods in computer vision (pp. 264–275). Berlin: Springer.

    Chapter  Google Scholar 

  • Bronstein, A. M., Bronstein, M. M., Bruckstein, A. M., & Kimmel, R. (2008a). Analysis of two-dimensional non-rigid shapes. IJCV, 78(1), 67–88.

    Article  Google Scholar 

  • Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2008b). Numerical geometry of nonrigid shapes. Berlin: Springer.

    Google Scholar 

  • Bruckstein, A. M., Katzir, N., Lindenbaum, M., & Porat, M. (1992). Similarity-invariant signatures for partially occluded planar shapes. IJCV, 7(3), 271–285.

    Article  Google Scholar 

  • Bruckstein, A. M., Holt, R. J., & Netravali, A. N. (1998). Holographic representations of images. IEEE Transactions on Image Processing, 7(11), 1583–1597.

    Article  Google Scholar 

  • Buades, A., Coll, B., & Morel, J. M. (2005). A non-local algorithm for image denoising. IEEE Conference on Computer Vision and Pattern Recognition, 2, 60–65.

    Google Scholar 

  • Burago, D., Burago, Y., & Ivanov, S. (2001). A course in metric geometry. Graduate studies in mathematics (Vol. 33). Providence: American Mathematical Society.

    Google Scholar 

  • Chen, Y., & Medioni, G. (1991). Object modeling by registration of multiple range images. In Proc. conf. robotics and automation.

  • Chen, Y., & Wong, E. K. (2003). Augmented image histogram for image and video similarity search. Proceedings of SPIE, 3656, 523.

    Article  Google Scholar 

  • Cheng, S. W., Edelsbrunner, H., Fu, P., & Lam, K. P. (2001). Design and analysis of planar shape deformation. Computational Geometry: Theory and Applications, 19(2-3), 205–218.

    MATH  MathSciNet  Google Scholar 

  • Connelly, R. (1978). A flexible sphere. The Mathematical Intelligencer, 1(3), 130–131.

    Article  MATH  MathSciNet  Google Scholar 

  • Damerau, F. J. (1964). A technique for computer detection and correction of spelling errors.

  • de Rooij, S., & Vitanyi, P. (2006). Approximating rate-distortion graphs of individual data: Experiments in lossy compression and denoising. IEEE Transactions on Information Theory, submitted.

  • Di Lucca, G. A., Di Penta, M., & Fasolino, A. R. (2002). An approach to identify duplicated web pages. In Proc. computer software and applications conference (pp. 481–486).

  • Dunn, E., Olague, G., Lutton, E., & Schoenauer, M. (2004). Pareto optimal sensing strategies for an active vision system. In Proc. congress on evolutionary computation (CEC).

  • Elad, A., & Kimmel, R. (2003). On bending invariant signatures for surfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(10), 1285–1295.

    Article  Google Scholar 

  • Everingham, M., Muller, H., & Thomas, B. (2002). Evaluating image segmentation algorithms using the Pareto front. In Proc. ECCV (pp. 34–48).

  • Everson, R. M., & Fieldsend, J. E. (2006). Multi-class ROC analysis from a multi-objective optimization perspective. Pattern Recognition Letters, 27(8), 918–927.

    Article  Google Scholar 

  • Felzenszwalb, P. F. (2005). Representation and detection of deformable shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(2), 208–220.

    Article  Google Scholar 

  • Foote, J. (1997). Content-based retrieval of music and audio. Proceedings of SPIE, 3229, 138.

    Article  Google Scholar 

  • Foote, J., Cooper, M., & Nam, U. (2002). Audio retrieval by rhythmic similarity. Proc. International Conf. Music Information Retrieval, 3, 265–266.

    Google Scholar 

  • Geiger, D., Basri, R., Costa, L., & Jacobs, D. (1998). Determining the similarity of deformable shapes. Vision Research, 38, 2365–2385.

    Article  Google Scholar 

  • Geiger, D., Liu, T. L., & Kohn, R. (2003). Representation and self-similarity of shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(1), 86–99.

    Article  Google Scholar 

  • Gelfand, N., Mitra, N. J., Guibas, L., & Pottmann, H. (2005). Robust global registration. In Proc. symp. geometry processing (SGP).

  • Gheorghiades, A. S., Belhumeur, P. N., & Kriegman, D. J. (2001). From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(6), 643–660.

    Article  Google Scholar 

  • Giles, C. L., Bollacker, K. D., & Lawrence, S. (1998). CiteSeer: an automatic citation indexing system. In Proc. 3rd ACM conference on digital libraries (pp. 89–98).

  • Gluck, H. (1974). Almost all simply connected closed surfaces are rigid. In Proc. conf. geometric topology.

  • Gooskens, C., & Heeringa, W. (2004). Perceptive evaluation of Levenshtein dialect distance measurements using Norwegian dialect data. Language Variation and Change, 16, 189–207.

    Article  Google Scholar 

  • Greene, B. (2000). The elegant universe. New York: Vintage Books.

    Google Scholar 

  • Gromov, M. (1981). Structures métriques pour les variétés riemanniennes. Number 1 in Textes Mathématiques.

  • Gudivada, V. N., & Raghavan, V. V. (1995). Content based image retrieval systems. Computer, 28(9), 18–22.

    Article  Google Scholar 

  • Hallinan, P. (1994). A low-dimensional representation of human faces for arbitrary lighting conditions. In Proc. CVPR (pp. 995–999).

  • Hatzivassiloglou, V., Klavans, J., & Eskin, E. (1999). Detecting text similarity over short passages: exploring linguistic feature combinations via machine learning. In Proceedings of the joint SIGDAT conference on empirical methods in natural language processing and very large corpora.

  • Hochbaum, D., & Shmoys, D.B. (1985). A best possible heuristic for the k-center problem. Mathematics of Operations Research, 10(2), 180–184.

    Article  MATH  MathSciNet  Google Scholar 

  • Jacobs, D., Ling, H. (2005). Deformation invariant image matching. Proc. ICCV, 2, 719–726.

    Google Scholar 

  • Jacobs, D., Weinshall, D., & Gdalyahu, Y. (2000). Class representation and image retrieval with non-metric distances. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(6), 583–600.

    Article  Google Scholar 

  • Kim, C. R., & Chung, C. W. (2006). XMage: An image retrieval method based on partial similarity. Information Processing and Management, 42, 484–502.

    Article  MATH  Google Scholar 

  • Kimmel, R., & Sethian, J. A. (1998). Computing geodesic on manifolds. PNAS, 95, 8431–8435.

    Article  MATH  MathSciNet  Google Scholar 

  • Kruskal, J. B. (1999). An overview of sequence comparison. Chapter: Time warps, string edits, and macromolecules: the theory and practice of sequence comparison. CSLI Publications.

  • Latecki, L. J., Lakaemper, R., & Wolter, D. (2005). Optimal partial shape similarity. Image and Vision Computing, 23, 227–236.

    Article  Google Scholar 

  • Latecki, L. J., & Lakamper, R. (2000). Shape similarity measure based on correspondence of visual parts. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(10), 1185–1190.

    Article  Google Scholar 

  • Levenshtein, V. I. (1965). Binary codes capable of correcting deletions, insertions, and reversals. Doklady Akademii Nauk SSSR, 163(4), 845–848.

    MathSciNet  Google Scholar 

  • Ling, H., & Jacobs, D. (2005). Using the inner-distance for classification of articulated shapes. In Proc. CVPR.

  • Mémoli, F., & Sapiro, G. (2005). A theoretical and computational framework for isometry invariant recognition of point cloud data. Foundations of Computational Mathematics, 5(3), 313–347.

    Article  MATH  MathSciNet  Google Scholar 

  • Mumford, D., & Shah, J. (1990). Boundary detection by minimizing functionals. In Image understanding.

  • Oliveira, L. S., Sabourin, R., Bortolozzi, F., & Suen, C. Y. (2002). Feature selection using multi-objective genetic algorithms for handwritten digit recognition. In Proc. int’l conf. pattern recognition (ICPR).

  • Pareto, V. (1906). Manuale di economia politica.

  • Platel, B., Balmachnova, E., Florack, L. M. J., Kanters, F. M. W., & ter Haar Romeny, B. M. (2005). Using top-points as interest points for image matching. In Lecture notes in computer science (Vol. 3753, p. 211). Springer: Berlin.

    Google Scholar 

  • Raviv, D., Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2007). Symmetries of non-rigid shapes. In Proc. workshop on non-rigid registration and tracking through learning (NRTL).

  • Reuter, M., Wolter, F.-E., & Peinecke, N. (2006). Laplace-Beltrami spectra as shape-DNA of surfaces and solids. Computer-Aided Design, 38, 342–366.

    Article  Google Scholar 

  • Salukwadze, M. E. (1979). Vector-valued optimization problems in control theory. San Diego: Academic Press.

    Google Scholar 

  • Sethian, J. A. (1996). A review of the theory, algorithms, and applications of level set method for propagating surfaces. Acta Numerica, 309–395.

  • Sochen, N., Kimmel, R., & Malladi, R. (1998). A general framework for low level vision. IEEE Transactions on Image Processing, 7(3), 310–318.

    Article  MATH  MathSciNet  Google Scholar 

  • Stricker, M., & Orengo, M. (1995). Similarity of color images. Proceedings of SPIE, 2420, 381–392.

    Article  Google Scholar 

  • Tal, A., Elad, M., & Ar, S. (2001). Content based retrieval of VRML objects—an iterative and interactive approach. In Proc. eurographics workshop on multimedia.

  • Tomasi, C., & Manduchi, R. (1998). Bilateral filtering for gray and color images. In Proc. ICCV.

  • Veltkamp, R. C. (2001). Shape matching: similarity measures and algorithms. In International conference on shape modeling and applications (pp. 188–197).

  • Wagner, R. A., & Fischer, M. J. (1974). The string-to-string correction problem. JACM, 21(1), 168–173.

    Article  MATH  MathSciNet  Google Scholar 

  • Wise, M. J. (1996). YAP3: improved detection of similarities in computer program and other texts. In Proc. 27th SIGCSE technical symposium on computer science education (pp. 130–134).

  • Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.

    Article  MATH  MathSciNet  Google Scholar 

  • Zhang, Z. Y. (1994). Iterative point matching for registration of free-form curves and surfaces. IJCV, 13(2), 119–152.

    Article  Google Scholar 

  • Zhang, J., Collins, R., & Liu, Y. (2004). Representation and matching of articulated shapes. In Proc. CVPR (Vol. 2, pp. 342–349).

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Bronstein, A.M., Bronstein, M.M., Bruckstein, A.M. et al. Partial Similarity of Objects, or How to Compare a Centaur to a Horse. Int J Comput Vis 84, 163–183 (2009). https://doi.org/10.1007/s11263-008-0147-3

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