Abstract
3D partial surface matching approach is universal to 3D object recognition. In this paper, a new solution utilizing Gaussian curvature and mean curvature to represent the inherent structure of surface is proposed, Point-Pair Set is constructed by means of filtrating points with similar inherent characteristic in partial surface, then Triangle-Pair Set is demonstrated after locating 3D surface by asymmetry triangle skeleton and searching similar triangles in Point-Pair Set, finally, optimal transformation is illustrated by scoring function to transformations in Triangle-Pair Set and optimal matching is determined. Experiments show that the algorithm is suitable for 3D partial surface matching, and an encouraging matching efficiency, speed and running time complexity to irregular surfaces is introduced.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ritter, L., Reiz, S.D., Rothamel, D., Dreiseidler, T., Karapetian, V., Scheer, M., Zöller, J.E.: Registration accuracy of three-dimensional surface and cone beam computed tomography data for virtual implant planning. Clinical Oral Implants Research 23(4), 447–452 (2012)
Buntea, K., Biehla, M., Jonkmanb, M.F., Petkova, N.: Learning effective color features for content based image retrieval in dermatology. Pattern Recognition 44(9), 1892–1902 (2011)
Tarte, S.M., Talib, H., Ballester, M., Langlotz, F.: Evaluating partial surface matching for fracture reduction assessment. In: 3rd IEEE International Symposium on Biomedical Imaging: Macro to Nano, vol. 4, pp. 514–517 (2006)
Shibberu, Y., Holder, A.: A spectral approach to protein structure alignment. ACM Transactions on Computational Biology and Bioinformatics 8(4), 867–875 (2011)
Barequet, G., Sharir, M.: Partial surface and volume matching in three dimensions. IEEE Transactions on Pattern Analysis and Machine Intelligence 19(9), 29–948 (1997)
Barequet, G., Sharir, M.: Partial surface matching by using directed footprints. Computational Geometry: Theory and Applications 12(122), 45–62 (1999)
Alt, H., Bras, P., Godau, M.: Computing the Hausdorff distance of geometric at terns and shapes. In: Discrete and Computational Geometry, Special Issue-The Goodman-Pollack-Festschrift 2003, pp. 65–76 (1999)
Mitra, N.J., Guibas, L.J., Pauly, M.: Partial and approximate symmetry detection for 3D geometry. ACM Transactions on Graphics 25(3), 560–568 (2006)
Gal, R., Cohen-Or, D.: Salient geometric features for partial shape matching and similarity. ACM Transactions on Graphics 25(1), 130–150 (2006)
Wang, S., Wang, Y., Jin, M., Gu, X.D., Samaras, D.: Confromal geometry and its applications on 3D matching, recognition, and stitching. IEEE Transactions on Pattern Analysis and Machine Intelligence 29(7), 1209–1220 (2007)
Tierny, J., Vandeborre, J.P., Daoudi, M.: Partial 3D shape retrieval by Reeb pattern unfolding. Computer Graphics Forum 28, 41–55 (2009)
Castellani, U., Cristani, M., Fantoni, S., Murino, V.: Sparse points matching by combining 3D mesh saliency with statistical descriptors. Computer Graphics Forum 27(2), 643–652 (2008)
Itskovich, A., Tal, A.: Surface partial matching and application to archaeology. Computers & Graphics 35(2), 334–341 (2011)
Tabia, H., Daoudi, M., Vandeborre, J.P., Colot, O.: A new 3D-matching method of nonrigid and partially similar models using curve analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence 33(4), 852–858 (2011)
Guo, K.H., Liu, C.C., Yang, J.Y.: Differential geometry approach to 3D partially similar object matching. Pattern Recognition and Artificial Intelligence 21(5), 586–591 (2008)
Dubrovin, B.A., Fomenko, A.T., Novikov, S.P.: Modern geometry-methods and applications (I). In: GTM, 2nd edn., pp. 61–80. Springer (1999)
Mian, A.S., Bennamoun, M., Owens, R.: Three-dimensional model-based object recognition and segmentation in Cluttered scenes. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(10), 1584–1601 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Guo, K., Duan, G. (2013). 3D Partial Surface Matching Using Differential Geometry and Statistical Approaches. In: Yang, J., Fang, F., Sun, C. (eds) Intelligent Science and Intelligent Data Engineering. IScIDE 2012. Lecture Notes in Computer Science, vol 7751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36669-7_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-36669-7_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36668-0
Online ISBN: 978-3-642-36669-7
eBook Packages: Computer ScienceComputer Science (R0)