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Learning Robust Similarity Measures for 3D Partial Shape Retrieval

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Abstract

In this paper, we propose a novel approach to learning robust ground distance functions of the Earth Mover’s distance to make it appropriate for quantifying the partial similarity between two feature-sets. First, we define the ground distance as a monotonic transformation of commonly used feature-to-feature base distance (or similarity) measures, so that in computing the Earth Mover’s distance, the algorithm could better turn its focus on the feature pairs that are correctly matched, while being less affected by irrelevant ones. As a result, the proposed method is especially suited for 3D partial shape retrieval where occlusion and clutter are serious problems. We prove that when the transformation satisfies certain conditions, the metric property of the base distance is sufficient to guarantee the ground distance is a metric (and so is the Earth Mover’s distance), which makes fast shape retrieval on large databases technically possible. Second, we propose a discriminative learning framework to optimize the transformation function based on the real Adaboost algorithm. The optimization is performed in the space of the piecewise constant approximations of the transformation without making any parametric assumption. Finally, extensive experiments on 3D partial shape retrieval convincingly demonstrate the effectiveness of the proposed techniques.

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References

  • Athitsos, V., Alon, J., Sclaroff, S., & Kollios, G. (2004). BoostMap: a method for efficient approximate similarity rankings. In Proceedings of IEEE conference on computer vision and pattern recognition (Vol. 2, pp. 268–275), June 2004.

  • Athitsos, V., Hadjieleftheriou, M., Kollios, G., & Sclaroff, S. (2005). Query-sensitive embeddings. In Proceeding of ACM SIGMOD conference (pp. 706–717), June 2005.

  • Belongie, S., Malik, J., & Puzicha, J. (2002). Shape matching and object recognition using shape context. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(4), 509–522.

    Article  Google Scholar 

  • Berretti, S., Del Bimbo, A., & Pala, P. (2000). Retrieval by shape similarity with perceptual distance and effective indexing. IEEE Transactions on Multimedia, 2(4), 225–239.

    Article  Google Scholar 

  • Bespalov, D., Shokoufandeh, A., Regli, W. C., & Sun, W. (2003). Scale space representation of 3D models and topological matching. In Proceedings of symposium on solid modeling and applications (pp. 208–215).

  • Biasotti, S., Marini, S., Spagnuolo, M., & Falcidieno, B. (2006). Sub-part correspondence by structural descriptors of 3D shapes. Computer Aided Design, 38(9), 1002–1019.

    Article  Google Scholar 

  • Bourgain, J. (1985). On Lipschitz embedding of finite metric spares in Hilbert space. Israel Journal of Mathematics, 52(1–2), 46–52.

    Article  MATH  MathSciNet  Google Scholar 

  • Bustos, B., Keim, D. A., Saupe, D., Schreck, T., & Vranic, D. V. (2006). An experimental effectiveness comparison of methods for 3D similarity search. International Journal on Digital Libraries, 6(1), 39–54.

    Article  Google Scholar 

  • Cornea, N. D., Demirci, M. F., Silver, D., Shokoufandeh, A., Dickinson, S. J., & Kantor, P. B. (2005). 3D object retrieval using many-to-many matching of curve skeletons. In Proceedings of international conference on shape modeling and applications (pp. 368–373).

  • Datar, K. M., Immorlica, N., Indyk, P., & Mirrokni, V. S. (2004). Locality-sensitive hashing scheme based on p-stable distributions. In Proceedings of ACM symposium on computational geometry (pp. 253–262).

  • Davis, J. V., Kulis, B., Jain, P., Sra, S., & Dhillon, I. S. (2007). Information-theoretic metric learning. In Proceedings of the 24th international conference on machine learning.

  • Funkhouser, T., & Shilane, P. (2006). Partial matching of 3D shapes with priority-driven search. In Proceedings of symposium on geometry processing (pp. 131–142).

  • Funkhouser, T., Min, P., Kazhdan, M., Chen, J., Halderman, A., Dobkin, D., & Jacobs, D. (2003). A search engine for 3D models. ACM Transactions on Graphics, 22(1), 83–105.

    Article  Google Scholar 

  • Gal, R., & Cohen-Or, D. (2006). Salient geometric features for partial shape matching and similarity. ACM Transactions on Graph, 25(1), 130–150.

    Article  Google Scholar 

  • Grauman, K., & Darrell, T. (2005a). Efficient image matching with distributions of local invariant features. In Proceedings of IEEE conference on computer vision and pattern recognition (vol. 2, pp. 627–634).

  • Grauman, K., & Darrell, T. (2005b). The pyramid match kernel: discriminative classification with sets of image features. In Proceedings of international conference on computer vision (pp. 1458–1465).

  • Grauman, K., & Darrell, T. (2007a). Approximate correspondences in high dimensions. In Proceedings of advances in neural information processing systems 19 (NIPS) (pp. 505–512).

  • Grauman, K., & Darrell, T. (2007b). The pyramid match kernel: efficient learning with sets of features. Journal of Machine Learning Research, 8, 725–760.

    Google Scholar 

  • Hastie, T., Tibshirani, R., & Friedman, J. (2001). The elements of statistical learning. New York: Springer.

    MATH  Google Scholar 

  • Huttenlocher, D., & Felzenszwalb, P. (2005). Pictorial structures for object recognition. International Journal of Computer Vision, 61(1), 55–79.

    Article  Google Scholar 

  • Indyk, P., & Thaper, N. (2003). Fast image retrieval via embeddings. In 3rd international workshop on statistical and computational theories of vision, Nice, France, October 2003.

  • Järvelin, K., & Kekäläinen, J. (2002). Cumulated gain-based evaluation of IR techniques. ACM Transactions on Information Systems, 20(4), 422–446.

    Article  Google Scholar 

  • Johnson, A. E., & Hebert, M. (1999). Using spin-images for efficient multiple model recognition in cluttered 3-D scenes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(5), 443–449.

    Article  Google Scholar 

  • Kim, H.-K., & Kim, J.-D. (2000). Region-based shape descriptor invariant to rotation, scale and translation. Signal Processing: Image Communications, 16(1–2), 87–93.

    Article  Google Scholar 

  • Ling, H., & Okada, K. (2006). Diffusion distance for histogram comparison. In Proceedings of IEEE conference on computer vision and pattern recognition (Vol. 1, pp. 246–253), June 2006.

  • Ling, H., & Okada, K. (2007). An efficient earth mover’s distance algorithm for robust histogram comparison. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(5), 840–853.

    Article  Google Scholar 

  • Liu, Y., Zha, H., & Qin, H. (2006a). Shape topics: a compact representation and algorithms for 3D partial shape retrieval. In Proceedings of IEEE international conference on computer vision and pattern recognition (Vol. 2, pp. 2025–2032).

  • Liu, Y., Zha, H., & Qin, H. (2006b). The generalized shape distributions for shape matching and analysis. In Proceedings of international conference on shape modeling and applications (Vol. 16).

  • Liu, Y., Wang, X.-L., & Zha, H. (2008). Dimension amnesic pyramid match kernel. In Proceedings of the twenty third AAAI conference on artificial intelligence (pp. 652–658).

  • Lowe, D. (2004). Distinctive image features from scale-invariant keypoints. International Journal on Computer Vision, 60(2), 91110.

    Article  Google Scholar 

  • Marini, S., Paraboschi, L., & Biasotti, S. (2007). SHape REtrieval Contest 2007 (SHREC07): partial matching track: In R. C. Veltkamp, F. B. ter Haar (Eds.), SHREC2007: 3D shape retrieval contest (Technical report UU-CS-2007-015).

  • Mikolajczyk, K., & Schmid, C. (2001). Indexing based on scale invariant interest points. In Proceedings of international conference on computer vision (pp. 525–531).

  • Nister, D., & Stewenius, H. (2006). Scalable recognition with a vocabulary tree. In Proceedings of IEEE conference on computer vision and pattern recognition (Vol. 2, pp. 2161–2168), June 2006.

  • Osada, R., Funkhouser, T., Chazelle, B., & Dobkin, D. (2002). Shape distributions. ACM Transactions on Graphics, 21(4), 807–832.

    Article  Google Scholar 

  • Rote, G. (1991). Computing the minimum Hausdorff distance between two point sets on a line under translation. Information Processing Letters, 38, 123–127.

    Article  MATH  MathSciNet  Google Scholar 

  • Rubner, Y., Tomasi, C., & Guibas, L. J. (2000). The earth mover’s distance as a metric for image retrieval. International Journal of Computer Vision, 40(2), 99–121.

    Article  MATH  Google Scholar 

  • Schapire, R. E., & Singer, Y. (1999). Improved boosting algorithms using confidence-rated predictions. Machine Learning, 37(3), 297–336.

    Article  MATH  Google Scholar 

  • Shan, Y., Sawhney, H. S., Matei, B., & Kumar, R. (2006). Shapeme histogram projection and matching for partial object recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28(4), 568–577.

    Article  Google Scholar 

  • Shilane, P., & Funkhouser, T. A. (2007). Distinctive regions of 3D surfaces. ACM Transactions on Graph, 26(2).

  • Shilane, P., Min, P., Kazhdan, M., & Funkhouser, T. (2004). The Princeton shape benchmark. In Proceedings of international conference on shape modeling and applications (pp. 167–178).

  • Sivic, J., & Zisserman, A. (2003). Video google: a text retrieval approach to object matching in videos. In Proceedings of international conference on computer vision (pp. 1470–1477).

  • Tangelder, J. W. H., & Veltkamp, R. C. (2003). Polyhedral model retrieval using weighted point sets. International Journal of Image and Graphics, 3(1), 209–229.

    Article  Google Scholar 

  • Tangelder, J. W. H., & Veltkamp, R. C. (2008). A survey of content based 3D shape retrieval methods. Multimedia Tools and Applications, 39(3), 441–471.

    Article  Google Scholar 

  • Vranic, D. V. (2003). An improvement of rotation invariant 3D-shape based on functions on concentric spheres. In Proceedings of international conference on image processing (Vol. 3, pp. 757–760.

  • Wang, X.-L., Liu, Y., & Zha, H. (2009). Learning robust cross-bin similarities for the bag-of-features model. Technical report, available at http://www.cis.pku.edu.cn/vision/Visual&Robot/people/wang/pubs/tr2009_draft.pdf.

  • Weston, J., Scholkopf, B., Eskin, E., Leslie, C., & Noble, W. (2003). Dealing with large diagonals in kernel matrices. Annals of the Institute of Statistical Mathematics, 55(2), 391–408.

    MATH  MathSciNet  Google Scholar 

  • Winn, J., Criminisi, A., & Minka, T. (2005). Object categorization by learned universal visual dictionary. In Proceedings of international conference on computer vision (pp. 1800–1807).

  • Zhang, J., Marszalek, M., Lazebnik, S., & Schmid, C. (2007). Local features and kernels for classification of texture and object categories: a comprehensive study. International Journal on Computer Vision, 73(2), 213–238.

    Article  Google Scholar 

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Authors and Affiliations

  1. Key Laboratory of Machine Perception (Ministry of Education), Peking University, Beijing, China

    Yi Liu, Xu-Lei Wang & Hongbin Zha

  2. Chinese Academy of Sciences Key Laboratory of Molecular Developmental Biology, Center for Molecular Systems Biology, Institute of Genetics and Developmental Biology, Chinese Academy of Sciences, Beijing, China

    Yi Liu

  3. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Hong Kong, China

    Hua-Yan Wang

  4. Department of Computer Science, State University of New York at Stony Brook, Stony Brook, NY, 11794-4400, USA

    Hong Qin

Authors
  1. Yi Liu
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  2. Xu-Lei Wang
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  3. Hua-Yan Wang
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  4. Hongbin Zha
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  5. Hong Qin
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Correspondence to Yi Liu.

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Liu, Y., Wang, XL., Wang, HY. et al. Learning Robust Similarity Measures for 3D Partial Shape Retrieval. Int J Comput Vis 89, 408–431 (2010). https://doi.org/10.1007/s11263-009-0298-x

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