Abstract
We present two new algorithms for correspondence and classification of planar curves in a non-rigid sense. In the first algorithm we define deforming energy based on aligning curves using certain of their properties, namely Multi-Step-Size Local Similarity (MSSLS) and the difference between the angle changes of beginning and ending tangent lines of two corresponding curve segments, as well as local scale of stretching. MSSLS overcomes the noise of local shape information of curves to be aligned. In the second algorithm, we improve the computation of shape context so that it catches the local information of ordered sets representing planar curves better. The optimal correspondence is found by a modified dynamic-programming method. Based on deforming energy, we can do pattern recognition among curves, which is very important in many areas such as recognition of hand-written characters and cardiac curves where rigid transformations and scaling do not work well. Finally, the effect of correspondence and classification is shown in application to hand-written characters and cardiac curves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Sebastian, T.B., Klein, P.N., Kimia, B.B.: On Aligning Curves. IEEE Trans. on Pattern Analysis and Machine Intelligence 25(1), 116–124 (2003)
Cohen, I., Ayache, N., Sulger, P.: Tracking Points on Deformable Objects Using Curvature Information. In: Proc. European Conf. Computer Vision, pp. 458–466 (1992)
Tagare, H.D.: Shape-Based Non-Rigid Correspondence with Application to Heart Motion Analysis. IEEE Trans. Medical Imaging 18(7), 570–578 (1999)
Basri, R., Costa, L., Geiger, D., Jacobs, D.: Determining the Similarity of Deformable Shapes. Vision Research 38, 2365–2385 (1998)
Younes, L.: Computable Elastic Distance between Shapes. SIAM J. Applied Math. 58, 565–586 (1998)
Tagare, H.D., O’Shea, D., Groisser, D.: Non-Rigid Shape Comparison of Plane Curves in Images. J. Mathematical Imaging and Vision 16(1), 57–68 (2002)
Belongie, S., Malik, J., Puzicha, J.: Shape Contexts: A New Descriptor for Shape Matching and Object Recognition. NIPS 13, 831–837 (2001)
Belongie, S., Malik, J., Puzicha, J.: Shape Matching and Object Recognition Using Shape Contexts. IEEE Trans. on Pattern Analysis and Machine Intelligence 24(24), 509–522 (2002)
Frenkel, M., Basri, R.: Curve Matching Using the Fast Marching Method. LNCS, vol. 2683, pp. 35–51. Springer, Heidelberg (2003)
Sethian, J.: A Fast Marching Level Set Method for Monotonically Advancing Fronts. Proc. Nat. Acad. Sci. 93(4), 1591–1595 (1996)
Rangarajan, A., Chui, H., Mjolsness, E.: A relationship between spline-based deformable models and weighted graphs in non-rigid matching. In: IEEE Computer Vision and Pattern Recognition (CVPR), vol. 1, pp. 897–904 (2001)
Chui, H., Rangarajan, A.: A new point matching algorithm for non-rigid registration. In: Computer Vision and Image Understanding (CVIU), vol. 89, pp. 114–141 (2003)
Marzal, A., Vidal, E.: Computation of Normalized Edit Distances and Applications. IEEE Trans. Pattern Analysis and Machine Intelligence 15, 926–932 (1993)
Sermesant, M., Forest, C., Pennec, X., Delingette, H., Ayache, N.: Deformable biomechanical models: Application to 4D cardiac image analysis. Medical Image Analysis 7(4), 475–488 (2003)
Liu, H.C., Srinath, M.D.: Partial Shape Classification Using Contour Matching in Distance Transformation. IEEE Trans. Pattern Analysis and Machine Intelligence 12(11), 1072–1079 (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zheng, X., Chen, Y., Groisser, D., Wilson, D. (2005). Some New Results on Non-rigid Correspondence and Classification of Curves. In: Rangarajan, A., Vemuri, B., Yuille, A.L. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2005. Lecture Notes in Computer Science, vol 3757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11585978_31
Download citation
DOI: https://doi.org/10.1007/11585978_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30287-2
Online ISBN: 978-3-540-32098-2
eBook Packages: Computer ScienceComputer Science (R0)