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Issue No.10 - Oct. (2012 vol.34)
pp: 1952-1965
Vivek Kaul , Georgia Institute of Technology, Atlanta
Anthony Yezzi , Georgia Institute of Technology, Atlanta
Yichang Tsai , Georgia Institute of Technology, Savannah
Existing state-of-the-art minimal path techniques work well to extract simple open curves in images when both endpoints of the curve are given as user input or when one input is given and the total length of the curve is known in advance. Curves which branch require even further prior input from the user, namely, each branch endpoint. In this work, we present a novel minimal path-based algorithm which works on much more general curve topologies with far fewer demands on the user for initial input compared to prior minimal path-based algorithms. The two key novelties and benefits of this new approach are that 1) it may be used to detect both open and closed curves, including more complex topologies containing both multiple branch points and multiple closed cycles without requiring a priori knowledge about which of these types is to be extracted, and 2) it requires only a single input point which, in contrast to existing methods, is no longer constrained to be an endpoint of the desired curve but may in fact be ANY point along the desired curve (even an internal point). We perform quantitative evaluation of the algorithm on 48 images (44 pavement crack images, 1 catheter tube image, and 3 retinal images) against human supplied ground truth. The results demonstrate that the algorithm is indeed able to extract curve-like objects accurately from images with far less prior knowledge and less user interaction compared to existing state-of-the-art minimal path-based image processing algorithms. In the future, the algorithm can be applied to other 2D curve-like objects and it can be extended to detect 3D curves.
Euclidean distance, Mathematical model, Three dimensional displays, Topology, Minimization, cracks., Minimal paths, keypoints, multiple branches, closed cycles, arbitrary topology, curve detection
Vivek Kaul, Anthony Yezzi, Yichang Tsai, "Detecting Curves with Unknown Endpoints and Arbitrary Topology Using Minimal Paths", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.34, no. 10, pp. 1952-1965, Oct. 2012, doi:10.1109/TPAMI.2011.267
[1] D. Adalsteinsson and J.A. Sethian, "A Fast Level Set Method for Propagating Interfaces," J. Computational Physics, vol. 118, no. 2, pp. 269-269, 1995.
[2] R. Ardon, L.D. Cohen, and A. Yezzi, "Fast Surface Segmentation Guided by User Input Using Implicit Extension of Minimal Paths," J. Math. Imaging and Vision, vol. 25, no. 3, pp. 289-305, 2006.
[3] F. Benmansour and L.D. Cohen, "Fast Object Segmentation by Growing Minimal Paths from a Single Point on 2D or 3D Images," J. Math. Imaging and Vision, vol. 33, no. 2, pp. 209-221, 2009.
[4] S. Bonneau, M. Dahan, and L.D. Cohen, "Single Quantum Dot Tracking Based on Perceptual Grouping Using Minimal Paths in a Spatiotemporal Volume," IEEE Trans. Image Processing, vol. 14, no. 9, pp. 1384-95, Sept. 2005.
[5] V. Caselles, R. Kimmel, and G. Sapiro, "Geodesic Active Contours," Proc. IEEE Int'l Conf. Computer Vision, 1995.
[6] L.D. Cohen, "Multiple Contour Finding and Perceptual Grouping Using Minimal Paths," J. Math. Imaging and Vision, vol. 14, no. 3, pp. 225-236, 2001.
[7] L.D. Cohen and R. Kimmel, "Global Minimum for Active Contour Models: A Minimal Path Approach," Int'l J. Computer Vision, vol. 24, no. 1, pp. 57-78, 1997.
[8] N. Cornea, D. Silver, X. Yuan, and R. Balasubramanian, "Computing Hierarchical Curve-Skeletons of 3D Objects," The Visual Computer, vol. 21, pp. 945-955, 2005.
[9] P.-E. Danielsson and Q. Lin, "A Modified Fast Marching Method," Image Analysis, pp. 631-644, Springer, 2003.
[10] T. Deschamps, J.M. Letang, B. Verdonck, and L.D. Cohen, "Automatic Construction of Minimal Paths in 3D Images: An Application to Virtual Endoscopy," Proc. Computer Assisted Radiology and Surgery, pp. 151-155, 1999.
[11] M.S. Hassouna and A.A. Farag, "Multistencils Fast Marching Methods: A Highly Accurate Solution to the Eikonal Equation on Cartesian Domains," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 9, pp. 1563-1574, Sept. 2007.
[12] M. Hassouna and A. Farag, "On the Extraction of Curve Skeletons Using Gradient Vector Flow," Proc. IEEE Int'l Conf. Computer Vision, 2007.
[13] L. Hua and A. Yezzi, "Vessels as 4-D Curves: Global Minimal 4-D Paths to Extract 3-D Tubular Surfaces and Centerlines," IEEE Trans. Medical Imaging, vol. 26, no. 9, pp. 1213-1223, Sept. 2007.
[14] M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active Contour Models," Int'l J. Computer Vision, vol. 1, no. 4, pp. 321-331, 1987.
[15] V. Kaul, Y. Tsai, and R. Mersereau, "A Quantitative Performance Evaluation of Pavement Distress Segmentation Algorithms," Transportation Research Record: J. Transportation Research Board, vol. 2153, pp. 106-113, 2010.
[16] S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, and A. Yezzi, "Gradient Flows and Geometric Active Contour Models," Proc. IEEE Int'l Conf. Computer Vision, 1995.
[17] J.A. Sethian, "Fast Marching Methods," SIAM Rev., vol. 41, no. 2, pp. 199-235, 1999.
[18] Y. Tsai, V. Kaul, and R. Mersereau, "Critical Assessment of Pavement Distress Segmentation Methods," ASCE J. Transportation Eng., vol. 136, pp. 11-19, 2010.
[19] J.N. Tsitsiklis, "Efficient Algorithms for Globally Optimal Trajectories," IEEE Trans. Automatic Control, vol. 40, no. 9, pp. 1528-1538, Sept. 1995.
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