Geodesic Shape Retrieval via Optimal Mass Transport
Conference paper
Abstract
This paper presents a new method for 2-D and 3-D shape retrieval based on geodesic signatures. These signatures are high dimensional statistical distributions computed by extracting several features from the set of geodesic distance maps to each point. The resulting high dimensional distributions are matched to perform retrieval using a fast approximate Wasserstein metric. This allows to propose a unifying framework for the compact description of planar shapes and 3-D surfaces.
Keywords
Point Cloud Geodesic Distance Local Descriptor Global Descriptor Shape Retrieval
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Download
to read the full conference paper text
References
- 1.Veltkamp, R.C., Latecki, L.: Properties and performance of shape similarity measures. In: Proc. of Conference on Data Science and Classification (2006)Google Scholar
- 2.Zhang, D.S., Lu, G.J.: Review of shape representation and description techniques. Pattern Recognition 37, 1–19 (2004)zbMATHCrossRefGoogle Scholar
- 3.Bustos, B., Keim, D.A., Saupe, D., Schreck, T., Vranić, D.V.: Feature-based similarity search in 3D object databases. ACM Comput. Surv. 37, 345–387 (2005)CrossRefGoogle Scholar
- 4.Tangelder, J.W.H., Veltkamp, R.C.: A survey of content based 3D shape retrieval methods. Multimedia Tools Appl. 39, 441–471 (2008)CrossRefGoogle Scholar
- 5.Teague, M.: Image analysis via the general theory of moments. Journal of the Optical Society of America 70, 920–930 (1980)CrossRefMathSciNetGoogle Scholar
- 6.Teh, C.H., Chin, R.T.: On image analysis by the methods of moments. IEEE Trans. Patt. Anal. and Mach. Intell. 10, 496–513 (1988)zbMATHCrossRefGoogle Scholar
- 7.Liao, S., Pawlak, M.: On image analysis by moments. IEEE Trans. Patt. Anal. and Mach. Intell. 18, 254–266 (1996)CrossRefGoogle Scholar
- 8.Zahn, C.T., Roskies, R.Z.: Fourier descriptors for plane closed curves. IEEE Transactions on Computer 21, 269–281 (1972)zbMATHCrossRefMathSciNetGoogle Scholar
- 9.Prokop, R.J., Reeves, A.P.: A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP 54, 438–460 (1992)Google Scholar
- 10.Reuter, M., Wolter, F.E., Peinecke, N.: Laplace-spectra as fingerprints for shape matching. In: Symposium on Solid and Physical Modeling, pp. 101–106 (2005)Google Scholar
- 11.Osada, R., Funkhouser, T., Chazelle, B., Dobkin, D.: Shape distributions. ACM Transactions on Graphics 21, 807–832 (2002)CrossRefGoogle Scholar
- 12.Ben Hamza, A., Krim, H.: Geodesic matching of triangulated surfaces. IEEE Trans. Image Proc. 15, 2249–2258 (2006)CrossRefGoogle Scholar
- 13.Ion, A., Peyré, G., Haxhimusa, Y., Peltier, S., Kropatsch, W., Cohen, L.: Shape matching using the geodesic eccentricity transform - a study. In: Proc. Workshop of the Austrian Association for Pattern Recognition, OCG, pp. 97–104 (2007)Google Scholar
- 14.Ion, A., Artner, N., Peyré, G., López Mármol, S., Kropatsch, W., Cohen, L.: 3D shape matching by geodesic eccentricity. In: Proc. Workshop on Search in 3D. IEEE, Los Alamitos (2008)Google Scholar
- 15.Gorelick, L., Galun, M., Sharon, E., Basri, R., Brandt, A.: Shape representation and classification using the Poisson equation. IEEE TPAMI 28, 1991–2005 (2006)Google Scholar
- 16.Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE Trans. Patt. Anal. and Mach. Intell. 24, 509–522 (2002)CrossRefGoogle Scholar
- 17.Ling, H., Jacobs, D.W.: Shape classification using the inner-distance. IEEE Trans. Patt. Anal. and Mach. Intell. 29, 286–299 (2007)CrossRefGoogle Scholar
- 18.Johnson, A., Hebert, M.: Using spin images for efficient object recognition in cluttered 3D scenes. IEEE Trans. Patt. Anal. and Mach. Intell. 21, 433–449 (1999)CrossRefGoogle Scholar
- 19.Villani, C.: Topics in Optimal Transportation. American Mathematical Society, Providence (2003)zbMATHGoogle Scholar
- 20.Rubner, Y., Tomasi, C., Guibas, L.J.: The Earth Mover’s Distance as a Metric for Image Retrieval. International Journal of Computer Vision 40, 99–121 (2000)zbMATHCrossRefGoogle Scholar
- 21.Grauman, K., Darrell, T.: Fast contour matching using approximate earth mover’s distance. In: Proc. of IEEE CVPR 2004, pp. I: 220–227 (2004)Google Scholar
- 22.Ling, H., Okada, K.: An Efficient Earth Mover’s Distance Algorithm for Robust Histogram Comparison. IEEE Trans. PAMI 29, 840–853 (2007)Google Scholar
- 23.Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. of the National Academy of Sciences 93, 1591–1595 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
- 24.Tsitsiklis, J.: Efficient Algorithms for Globally Optimal Trajectories. IEEE Trans. on Automatic Control 40, 1528–1538 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
- 25.Kimmel, R., Sethian, J.: Computing Geodesic Paths on Manifolds. Proc. of the National Academy of Sciences 95, 8431–8435 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
- 26.Bornemann, F., Rasch, C.: Finite-element discretization of static Hamilton-Jacobi equations based on a local variational principle. Comput. Visual Sci. 9 (2006)Google Scholar
- 27.Gonzalez, T.F.: Clustering to minimize the maximum intercluster distance. Theoretical Computer Science 38, 293–306 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
- 28.Peyré, G., Cohen, L.D.: Geodesic remeshing using front propagation. International Journal of Computer Vision 69, 145–156 (2006)CrossRefGoogle Scholar
- 29.Veltkamp, R.C., Hagedoorn, M.: State of the art in shape matching, pp. 87–119 (2001)Google Scholar
- 30.Burkard, R., Dell’Amico, M., Martello, S.: Assignment Problems. SIAM, Philadelphia (2009)zbMATHGoogle Scholar
- 31.Rabin, J., Peyré, G., Delon, J., Bernot, M.: Wasserstein Barycenter and its Application to Texture Mixing, http://hal.archives-ouvertes.fr/hal-00476064/en/
- 32.Bottou, L.: Online algorithms and stochastic approximations. In: Saad, D. (ed.) Online Learning and Neural Networks. Cambridge University Press, Cambridge (1998)Google Scholar
- 33.Pitié, F., Kokaram, A., Dahyot, R.: Automated colour grading using colour distribution transfer. In: Computer Vision and Image Understanding (2007)Google Scholar
- 34.Shirdhonkar, S., Jacobs, D.: Approximate Earth Mover’s Distance in linear time. In: Proc. CVPR 2008, pp. 1–8 (2008)Google Scholar
- 35.McGill 3-D shapes dataset, http://www.cim.mcgill.ca/~shape/benchMark/
- 36.Siddiqi, K., Zhang, J., Macrini, D., Shokoufandeh, A., Bouix, S., Dickinson, S.: Retrieving articulated 3-D models using medial surfaces. Mach. Vision Appl. 19, 261–275 (2008)CrossRefGoogle Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2010