Abstract
Matching occluded and noisy shapes is a problem frequently encountered in medical image analysis and more generally in computer vision. To keep track of changes inside the breast, for example, it is important for a computer aided detection system to establish correspondences between regions of interest. Shape transformations, computed both with integral invariants (II) and with geodesic distance, yield signatures that are invariant to isometric deformations, such as bending and articulations. Integral invariants describe the boundaries of planar shapes. However, they provide no information about where a particular feature lies on the boundary with regard to the overall shape structure. Conversely, eccentricity transforms (Ecc) can match shapes by signatures of geodesic distance histograms based on information from inside the shape; but they ignore the boundary information. We describe a method that combines the boundary signature of a shape obtained from II and structural information from the Ecc to yield results that improve on them separately.
Similar content being viewed by others
References
Alferez, R., & Wang, Y.-F. (1999). Geometric and illumination invariants for object recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21, 505–536.
Amanatiadis, A., Kaburlasos, V. G., Gasteratos, A., & Papadakis, S. E. (2011). Evaluation of shape descriptors for shape-based image retrieval. Image Process IET, 5, 493–499.
Arrebola, F., & Sandoval, F. (2005). Corner detection and curve segmentation by multiresolution chain-code linking. Pattern Recognition, 38, 1596–1614.
Arun, K. S., & Sarath, K. S. (2011). Evaluation of SUSAN filter for the identification of micro calcification. International Journal of Computational and Applied, 15, 41–44.
Bauer, M., Fidler, T., & Grasmair, M. (2011). Local uniqueness of the circular integral invariant. arXiv Prepr. arXiv:1107.4257.
Belongie, S., Malik, J., & Puzicha, J. (2002). Shape matching and object recognition using shape contexts. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24, 509–522.
Belongie, S., Malik, J., & Puzicha, J. (2001). Matching shapes. In: Proceedings of the 8th IEEE International Conference on Computer Vision ICCV. ICCV 2001 (pp. 454–461).
Bengtsson, A., & Eklundh, J.-O. (1991). Shape representation by multiscale contour approximation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13, 85–93.
Bertsekas, D. P. (1995). Dynamic programming and optimal control. Belmont, MA: Athena Scientific.
Und Bildverarbeitung, A.M. & Ion, D.-IA. (2009). The Eccentricity Transform of n-Dimensional Shapes with and without Boundary.
Boué, M., & Dupuis, P. (1999). Markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the control. SIAM Journal on Numerical Analysis, 36, 667–695.
Brandt, R. D., & Lin, F. (1996). Representations that uniquely characterize images modulo translation, rotation, and scaling. Pattern Recognition Letters, 17, 1001–1015.
Bronstein, A. M., Bronstein, M. M., Bruckstein, A. M., & Kimmel, R. (2008). Analysis of two-dimensional non-rigid shapes. International Journal of Computer Vision, 78, 67–88.
Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2006). Generalized multidimensional scaling: A framework for isometry-invariant partial surface matching. Proceedings of the National Academy of Sciences United States of America, 103, 1168–1172.
Bruckstein, A. M., Rivlin, E., & Weiss, I. (1997). Scale space semi-local invariants. Image and Vision Computing, 15, 335–344.
Calabi, E., Olver, P. J., Shakiban, C., et al. (1998). Differential and numerically invariant signature curves applied to object recognition. International Journal of Computer Vision, 26, 107–135.
Cao, W., Hu, P., Liu, Y., et al. (2011). Gaussian-curvature-derived invariants for isometry. Science China Information Sciences, 56(9), 1–12.
Chen, Y. W., & Xu, C. L. (2009). Rolling penetrate descriptor for shape-based image retrieval and object recognition. Pattern Recognition Letters, 30, 799–804.
Chetverikov, D., & Khenokh, Y. (1999). Matching for shape defect detection. Computer Analysis Images Patterns. pp. 367–374.
Cohen, F. S., & Wang, J.-Y. (1994). Part I: Modeling image curves using invariant 3-D object curve models-a path to 3-D recognition and shape estimation from image contours. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16, 1–12.
Cohen, L. D., & Kimmel, R. (1997). Global minimum for active contour models: A minimal path approach. International Journal of Computer Vision, 24, 57–78.
Cohignac, T., Lopez, C., & Morel, J. M. (1994). Integral and local affine invariant parameter and application to shape recognition. Pattern Recognition, 1994. Vol. 1-Conference A: Comput. Vis. & Image Process. In: Proceedings of 12th IAPR International Conference (pp. 164–168).
Cole, J. B., Murase, H., & Naito, S. (1991). A Lie group theoretic approach to the invariance problem in feature extraction and object recognition. Pattern Recognition Letters, 12, 519–523.
Davidovic, T., Ramljak, D., Selmic, M., & Teodorovic, D. (2010). Parallel bee colony optimization for scheduling independent tasks on identical machines. Proceedings of International Symposium on Operational Research (pp. 389–392).
Davies, E. R. (2004). Machine vision: Theory, algorithms, practicalities. Boston: Elsevier.
Davis, L. S. (1977). Understanding shape: Angles and sides. IEEE Transactions on Computers, 100, 236–242.
Dijkstra, E. W. (1968). Co-operating sequential processes. New York: F. Program. Lang. Acad. Press.
Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerical Mathematics, 1, 269–271.
Dijkstra, E. W. (1976). A discipline of programming. Englewood Cliffs, NJ: Prentice-Hall.
Duchenne, O., Bach, F., Kweon, I.-S., & Ponce, J. (2011). A tensor-based algorithm for high-order graph matching. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33, 2383–2395.
Duci, A., Yezzi, A. J., Mitter, S. K., & Soatto, S. (2003). Shape representation via harmonic embedding. Proceedings 9th IEEE International Conference on Computer Vision, 2003 (pp. 656–662).
Elad, A., & Kimmel, R. (2003). On bending invariant signatures for surfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25, 1285–1295.
Fidler, T., Grasmair, M., Pottmann, H., & Scherzer, O. (2007). Inverse problems of integral invariants and shape signatures.
Forsyth, D., Mundy, J. L., Zisserman, A., et al. (1991). Invariant descriptors for 3 d object recognition and pose. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13, 971–991.
Forsyth, D., Mundy, J. L., Zisserman, A., & Brown, C. M. (1990). Projectively invariant representations using implicit algebraic curves. Berlin: Springer.
Frenkel, M., & Basri, R. (2003). Curve matching using the fast marching method. Energy Minimization Methods in Computer Vision and Pattern Recognition, 2683, 35–51.
Gdalyahu, Y., & Weinshall, D. (1999). Flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21, 1312–1328.
Van Gool, L., Moons, T., & Ungureanu, D. (1996). Affine/photometric invariants for planar intensity patterns. Computer Vision–ECCV’96. Berlin: Springer.
Gorelick, L., Galun, M., Sharon, E., et al. (2006). Shape representation and classification using the poisson equation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28, 1991–2005.
Gu, Y.-H., & Tjahjadi, T. (2000). Coarse-to-fine planar object identification using invariant curve features and B-spline modeling. Pattern Recognition, 33, 1411–1422.
Hadley, G. (1964). Nonlinear and Dynamic Programming. Berlin: Addison-Wesley.
Hamza, A. B., & Krim, H. (2006). Geodesic matching of triangulated surfaces. IEEE Transactions on Image Processing, 15, 2249–2258.
Hann, C., & Hickman, M. S. (2002). Projective curvature and integral invariants. Acta Applied Mathematics, 74, 177–193.
Helgason, S. (1984). Groups & geometric analysis: Radon transforms, invariant differential operators and spherical functions. Burlington, ON: Elsevier.
Helmsen, J., Puckett, E., Colella, P., & Dorr, M. (1996). Two new methods for simulating photolithography development in 3D. In: Proceedings of SPIE (pp. 253–261).
Highnam, R., Brady, M., Yaffe, M. J., et al. (2010). Robust breast composition measurement-volparaTM. Digital mammography (pp. 342–349). Berlin: Springer.
Hong, B. W. (2004). Image segmentation, shape, and registration: Application to mammography. Oxford: University of Oxford.
Hong, B-W., & Brady, M. (2003). Segmentation of mammograms in topographic approach. In VIE 2003. International Conference on Visual Information Engineering (pp. 157–160).
Huang, C.-L., & Huang, D.-H. (1998). A content-based image retrieval system. Image and Vision Computing, 16, 149–163.
Huang, Q. X., Flöry, S., Gelfand, N., et al. (2006). Reassembling fractured objects by geometric matching. ACM Transactions on Graphics, 25(3), 569–578.
Huang, Z., & Cohen, F. S. (1996). Affine-invariant B-spline moments for curve matching. IEEE Transactions on Image Processing, 5, 1473–1480.
Ion, A., Artner, N. M., Peyré, G., et al. (2011). Matching 2D and 3D articulated shapes using the eccentricity transform. Computer Vision and Image Understanding, 115, 817–834.
Ion, A., Artner, N. M., & Peyré, G., et al. (2008). 3D shape matching by geodesic eccentricity. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition Work 2008. CVPRW’08 (pp. 1–8).
Ion, A., Peyré, G., & Haxhimusa, Y., et al. (2007). Shape matching using the geodesic eccentricity transform-a study. In: Proceedings of 31st Annual Workshop Austrian Association Pattern (pp. 97–104).
Janan, F., & Brady, M. (2012). Region matching in the temporal study of mammograms using integral invariant scale-space. Breast imaging (pp. 173–180). Berlin: Springer.
Jeffreys, M., Harvey, J., & Highnam, R. (2010). Comparing a new volumetric breast density method (VolparaTM) to cumulus. Digital mammography. Berlin: Springer.
Van Kaick, O., Hamarneh, G., Zhang, H., & Wighton, P. (2007). Contour correspondence via ant colony optimization. In:Proceedings of the 15th Pacific Conference on Computer Graphics and Applications (pp. 271–280).
Van Kaick, O., Zhang, H., Hamarneh, G., & Cohen-Or, D. (2011). A survey on shape correspondence. Computer Graphics Forum, 30, 1681–1707.
Kanatani, K. (1990). Group-theoretical methods in image understanding. Berlin: Springer.
Kendall, D. G. (1984). Shape manifolds, procrustean metrics, and complex projective spaces. Bulletin of the London Mathematical Society, 16, 81–121.
Kimmel, R. (2004). Fast marching methods. Numerical geometry of images. New York: Springer.
Kimmel, R., & Sethian, J. A. (1996). Fast marching methods for robotic navigation with constraints. Berkeley, CA: Center for Pure and Applied Mathematics Report, University of California.
Kimmel, R., & Sethian, J. A. (2001). Optimal algorithm for shape from shading and path planning. Journal of Mathematical Imaging and Vision, 14, 237–244.
Kliot, M., & Rivlin, E. (1998). Invariant-based shape retrieval in pictorial databases. Computer vision–ECCV’98. Berlin: Springer.
Lasenby, J., Bayro-Corrochano, E., Lasenby, A. N., & Sommer, G. (1996). A new framework for the formation of invariants and multiple-view constraints in computer vision. In: Proceedings of International Conference on Image Processing 1996 (pp. 313–316).
Latecki, L. J., Lakamper, R., & Eckhardt, T. (2000). Shape descriptors for non-rigid shapes with a single closed contour. In: Proceedings of IEEE Conference of Computer Vision Pattern Recognition 2000 (pp. 424–429).
Lenz, R. (1990). Group theoretical methods in image processing. New York: Springer.
Leordeanu, M., & Hebert, M. (2005). A spectral technique for correspondence problems using pairwise constraints. In: Proceedings of 10th IEEE Intrernational Conference on Computer Vision, 2005. ICCV 2005 (pp. 1482–1489).
Ling, H., & Jacobs, D. W. (2007). Shape classification using the inner-distance. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29, 286–299.
Li, S. Z. (1992). Matching: Invariant to translations, rotations and scale changes. Pattern Recognition, 25, 583–594.
Li, S. Z. (1999). Shape matching basedon invariants. In O. M. Omidvar (Ed.), Progress in neural networks: Shape recognition (Vol. 6, pp. 203–228). Intellect.
Maciel, J., & Costeira, J. P. (2003). A global solution to sparse correspondence problems. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25, 187–199.
Manay, S., Cremers, D., Hong, B.-W., et al. (2006). Integral invariants for shape matching. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28, 1602–1618.
Manay, S., Hong, B.-W., Yezzi, A. J., & Soatto, S. (2004). Integral invariant signatures. Berlin: Springer.
Mansoory, M. S., Ashtiyani, M., & Sarabadani, H. (2011). Automatic Crack Detection in Eggshell Based on SUSAN Edge Detector Using Fuzzy Thresholding. Modern Applied Science 5
Mardia, K. V., & Dryden, I. L. (1989). Shape distributions for landmark data. Advances in Applied Probability, 21, 742–755.
Mateus, D., Horaud, R., & Knossow, D., et al. (2008). Articulated shape matching using Laplacian eigenfunctions and unsupervised point registration. In: IEEE Conference on Computer Vision Pattern Recognition, 2008. CVPR 2008 (pp. 1–8).
Mikolajczyk, K., & Schmid, C. (2005). A performance evaluation of local descriptors. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, 1615–1630.
Mokhtarian, F., Abbasi, S., & Kittler, J. (1997). Efficient and robust retrieval by shape content through curvature scale space. Software Engineering and Knowledge Engineering, 8, 51–58.
Mokhtarian, F., & Mackworth, A. (1986). Scale-based description and recognition of planar curves and two-dimensional shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(1), 34–43.
Mokhtarian, F., & Mackworth, A. K. (1992). A theory of multiscale, curvature-based shape representation for planar curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14, 789–805.
Mumford, D. (1991). Mathematical theories of shape: Do they model perception? San Diego’,91. San Diego, CA: Academic Press.
Mumford, D., Latto, A., & Shah, J. (1984) The representation of shape. In: Proceedings of IEEE Workshop Computer Vision (pp. 183–191).
Nasreddine, K., Benzinou, A., & Fablet, R. (2009). Shape geodesics for boundary-based object recognition and retrieval. Image Process, pp. 405–408.
Nielsen, L., & Sparr, G. (1991). Projective area-invariants as an extension of the cross-ratio. CVGIP: Image Understanding, 54, 145–159.
Olver, P. J. (1995). Equivalence, invariants and symmetry. Cambridge: Cambridge University Press.
Osada, R., Funkhouser, T., Chazelle, B., & Dobkin, D. (2002). Shape distributions. ACM Transactions on Graphics, 21, 807–832.
Ozcan, E., & Mohan, C. K. (1997). Partial shape matching using genetic algorithms. Pattern Recognition Letters, 18, 987–992.
Petrakis, E. G. M., Diplaros, A., & Milios, E. (2002). Matching and retrieval of distorted and occluded shapes using dynamic programming. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24, 1501–1516.
Peyré, G. (2011). The numerical tours of signal processing part 2: Multiscale processings. Computing in Science & Engineering, 13(5), 68–71.
Peyré, G., Péchaud, M., Keriven, R., & Cohen, L. D. (2010). Geodesic methods in computer vision and graphics. Foundations and Trends in Computer Graphics and Vision, 5, 197–397.
Pottmann, H., Wallner, J., Huang, Q.-X., & Yang, Y.-L. (2009). Integral invariants for robust geometry processing. Computer Aided Geometric Design, 26, 37–60.
Qu, Z.-G., Wang, P., Gao, Y.-H., & Wang, P. (2011). Randomized SUSAN edge detector. Optical Engineering, 50, 110502–110502.
Rafajlowicz, E. (2007). SUSAN edge detector reinterpreted, simplified and modified. Multidimensional, pp. 69–74.
Reiss, T. H. (1993). Recognizing planar objects using invariant image features. New York: Springer.
Reuter, M., Wolter, F-E., & Peinecke, N. (2005). Laplace-spectra as fingerprints for shape matching. In: Proceedings of 2005 ACM Symposium on Solid Physical Modelling (pp. 101–106).
Rezai-Rad, G., & Aghababaie, M. (2006). Comparison of SUSAN and sobel edge detection in MRI images for feature extraction. In: Information and Communication Technologies 2006. ICTTA’06. 2nd (pp. 1103–1107).
Rosin, P. L. (2011). Shape description by bending invariant moments. Computer Analysis of Images and Patterns (pp. 253–260). Berlin: Springer.
Rothwell, C. A., Zisserman, A., Forsyth, D. A., & Mundy, J. L. (1995). Planar object recognition using projective shape representation. International Journal of Computer Vision, 16, 57–99.
Rothwell, C. A., Zisserman, A., Forsyth, D. A., & Mundy, J. L. (1992). Canonical frames for planar object recognition. Computer vision–ECCV’92 (pp. 757–772). Berlin: Springer.
Ruggeri, M. R., Patanè, G., Spagnuolo, M., & Saupe, D. (2010). Spectral-driven isometry-invariant matching of 3D shapes. International Journal of Computer Vision, 89, 248–265.
Rusinol, M., Dosch, P., & Lladós, J. (2007). Boundary shape recognition using accumulated length and angle information. Pattern Recognition and Image Analysis. Berlin: Springer.
Sampat, M. P., Markey, M. K., & Bovik, A. C. (2005). Computer-aided detection and diagnosis in mammography. Handbook of Image and Video Processing, 2, 1195–1217.
Sato, J., & Cipolla, R. (1997). Affine integral invariants for extracting symmetry axes. Image and Vision Computing, 15, 627–635.
Sato, J., & Cipolla, R. (1996). Affine integral invariants and matching of curves. In: Proceedings of 13th International Conference on Pattern Recognition, 1996 (pp. 915–919).
Sebastian, T. B., Klein, P. N., & Kimia, B. B. (2003). On aligning curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25, 116–125.
Sebastian, T. B., Klein, P. N., & Kimia, B. B. (2001). Alignment-based recognition of shape outlines. Visual Form 2001. Berlin: Springer.
Sethian, J. A. (1999). Level set methods and fast marching methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science. Cambridge: Cambridge University Press.
Sharma, A., & Horaud, R. (2010). Shape matching based on diffusion embedding and on mutual isometric consistency. In: Computer Vision and Pattern Recognition Workshops (pp. 29–36).
Sharon, E., & Mumford, D. (2006). 2d-shape analysis using conformal mapping. International Journal of Computer Vision, 70, 55–75.
Shashua, A., & Navab, N. (1996). Relative affine structure: Canonical model for 3D from 2D geometry and applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18, 873–883.
Shi, J., Chen, F., Lu, J., & Chen, G. (2013). An evolutionary image matching approach. Applied Soft Computing, 13, 3060–3065.
Siddiqi, K., Shokoufandeh, A., Dickinson, S. J., & Zucker, S. W. (1999). Shock graphs and shape matching. International Journal of Computer Vision, 35, 13–32.
Si-ming, H., Bing-han, L., & Wei-zhi, W. (2011). Moving shadow detection based on Susan algorithm. In: IEEE International Conference on Computer Science and Automation Engineering (pp. 16–20).
Smith, S. M., & Brady, J. M. (1997). SUSAN: A new approach to low level image processing. International Journal of Computer Vision, 23, 45–78.
Sniedovich, M. (2010). Dynamic programming: Foundations and principles. Boca Raton, FL: CRC Press.
Sonka, M., Hlavac, V., & Boyle, R. (1999). Image processing, analysis, and machine vision. London: Chapman and Hall Publishers.
Squire, D. M., & Caelli, T. M. (2000). Invariance signatures: Characterizing contours by their departures from invariance. Computer Vision and Image Understanding, 77, 284–316.
Sundar, H., Silver, D., Gagvani, N., & Dickinson, S. (2003). Skeleton based shape matching and retrieval. Shape Modeling International, 2003, 130–139.
Taubin, G., & Cooper, D. B. (1991). Object recognition based on moment (or algebraic) invariants. IBM TJ Watson Research Center.
Teodorovic, D., Davidovic, T., & Selmic, M. (2011). Bee colony optimization: The applications survey. ACM Transactions on Computational Logic, 1529, 3785.
Thomas, T. Y. (1934). The differential invariants of generalized spaces. Cambridge: Cambridge University Press.
Tian, J., Ma, L., & Yu, W. (2011a). Ant colony optimization for wavelet-based image interpolation using a three-component exponential mixture model. Expert Systems With Applications, 38, 12514–12520.
Tian, J., Yu, W., Chen, L., & Ma, L. (2011b). Image edge detection using variation-adaptive ant colony optimization. Transactions on Computational Collective Intelligence V. Berlin: Springer.
Torresani, L., Kolmogorov, V., & Rother, C. (2008). Feature correspondence via graph matching: Models and global optimization. Computer Vision-ECCV 2008. Berlin: Springer.
Trucco, E. (1995). Geometric invariance in computer vision. AI Communications, 8, 193–194.
Tsai, Y.-H. R., Cheng, L.-T., Osher, S., & Zhao, H.-K. (2003). Fast sweeping algorithms for a class of Hamilton–Jacobi equations. SIAM Journal on Numerical Analysis, 41, 673–694.
Tsitsiklis, J. N. (1995). Efficient algorithms for globally optimal trajectories. IEEE Transactions on Automatic Control, 40, 1528–1538.
Veltkamp, R. C. (2001). Shape matching: Similarity measures and algorithms. In: SMI 2001 International Conference on Shape Modeling and Applications (pp. 188–197).
Veltkamp, R. C., & Hagedoorn, M. (2001). State of the art in shape matching. London: Springer.
Wang, S., Wang, Y., Jin, M., et al. (2007). Conformal geometry and its applications on 3d shape matching, recognition, and stitching. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29, 1209–1220.
Wang, Y., & Teoh, E. K. (2004). A novel 2D shape matching algorithm based on B-spline modeling. In: 2004 International Conference on Image Processing, ICIP 2004 (pp. 409–412).
Wang, Y., Teoh, E. K., & Shen, D. (2004). Lane detection and tracking using B-Snake. Image and Vision Computing, 22, 269–280.
Wang, Y., Teoh, E. K., & Shen, D. (2001). Structure-adaptive B-snake for segmenting complex objects. In: Proceedings 2001 International Conference On Image Processing (pp. 769–772).
Weiss, I. (1993). Noise-resistant invariants of curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15, 943–948.
White, R., Kamath, C., & Newsam, S. (2004). Matching Shapes Using Local Descriptors. United States. Department of Energy.
Xingfang, Y., Yumei, H., & Yan, L. (2010). An improved SUSAN corner detection algorithm based on adaptive threshold. In IEEE - 2010 2nd International Conference on Signal Processing Systems (ICSPS, Vol. 2).
Xu, C., & Duan, H. (2010). Artificial bee colony (ABC) optimized edge potential function (EPF) approach to target recognition for low-altitude aircraft. Pattern Recognition Letters, 31, 1759–1772.
Xu, C., Liu, J., & Tang, X. (2009). 2D shape matching by contour flexibility. IEEE Transactions on Pattern Analysis and Machine Intelligence, 31, 180–186.
Xu, J. (2008). Shape matching using morphological structural shape components. In: 15th IEEE International Conference on Image Processing, 2008. ICIP 2008 (pp. 2596–2599).
Xu, S., Han, L., & Zhang, L. (2006). An algorithm to edge detection based on SUSAN filter and embedded confidence. In: 6th International Conference on Intelligent Systems Design and Applications 2006 (ISDA’06) (pp. 720–723).
Xu, Y., Wang, B., Liu, W., & Bai, X. (2010). Skeleton graph matching based on critical points using path similarity. Computer Vision-ACCV 2009. Berlin: Springer.
Yang, Y-L., Lai, Y-K., Hu, S-M., & Pottmann, H. (2006). Robust principal curvatures on multiple scales. In: Symposium on Geometry Processing (pp. 223–226).
Yu, B., Guo, L., Zhao, T., & Qian, X. (2010). A curve matching algorithm based on Freeman Chain Code. In: Intell. Comput. Intell. Syst. (pp. 669–672).
Zahn, C. T., & Roskies, R. Z. (1972). Fourier descriptors for plane closed curves. IEEE Transactions on Computers, 100, 269–281.
Zeng, J., & Li, D. (2011). SUSAN edge detection method for color image. Jisuanji Gongcheng yu Yingyong, 47, 194–196.
Zhang, D., & Lu, G. (2004). Review of shape representation and description techniques. Pattern Recognition, 37, 1–19.
Zhang, S., & Ma, K-K. (2000). A novel shape matching method using biological sequence dynamic alignment. In: 2000 IEEE International Conference on Multimedia and Expo (ICME) (pp. 343–346).
Zhao, H. (2005). A fast sweeping method for eikonal equations. Mathematics of Computation, 74, 603–627.
Zhou, D., et al. (2011). Hybrid corner detection algorithm for brain magnetic resonance image registration. In: IEEE - 2011 4th International Conference on Biomedical Engineering and Informatics (BMEI, Vol. 1).
Zisserman, A., Forsyth, D., Mundy, J., et al. (1995). 3D object recognition using invariance. Artificial Intelligence, 78, 238–239.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Gerard Medioni.
Rights and permissions
About this article
Cite this article
Janan, F., Brady, M. Shape Description and Matching Using Integral Invariants on Eccentricity Transformed Images. Int J Comput Vis 113, 92–112 (2015). https://doi.org/10.1007/s11263-014-0773-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11263-014-0773-x