Selection of Seed Points

In this subsection, we will discuss the influence of seed point selection on the derived GC axis and cross-sections. Consider the rectangular hexahedron shown in Fig. A.5. The MAT skeleton of the hexahedron obtained by Potential Skeleton using eight convex corners as seed points is shown in Fig. A.5(a). As for the GC axis of the object, Fig. A.5(b) shows the axis obtained using two of the eight corner points as seeds whereas centroids of the front and back end surfaces of the object are selected for the axis shown in Fig. A.5(c). The corresponding cross-sections obtained by Cross Section Gen for Figs. A.5(b) and (c) are shown in Figs.

A.5(d) and (e), respectively.

(a)

(c)

(e) (d)

(b)

Figure A.5: The MAT skeleton and different GC representations of a rectangular hexahedron (see text).

Obviously, the cross-sections shown in Fig. A.5(d) are too complex due to the large curvature of the GC axis at two locations, as shown in Fig. A.5(b). On the other hand, the GC axis shown in Fig. A.5(c) goes straight from the front to the back end of the object while maintaining maximum distances from the other four sides of the object. Thus, the cross-sections derived for the GC axis shown in Fig. A.5(c) are much simpler (all of identical shape and size) and more appropriate as the representation of the rectangular solid.

According to the above discussion, one can see clearly that, the selection of seed points plays a crucial role in the GC algorithm proposed in this thesis. In general, seed points should be selected such that a GC axis with smaller curvature can be generated and the corresponding cross-sections will be simpler and neater for representing the object. This is especially the case for elongated object with cross-sections of identical size and shape.

However, a systematic way of identifying optimal seed points for an object of arbitrary shape is yet to be established.

Bibliography

[1] J.H. Chuang, “Potential-based modeling of three-dimensional workspace of the obstacle avoidance,” IEEE Trans. on Robotics and Automation, vol. 14, no. 5, pp. 778–785, 1998.

[2] C.H. Tsai, J.S. Lee, and J.H. Chuang, “Path planning of 3-D objects using a new workspace model,” IEEE Trans. on Sys., Man, Cybern., Part B: Cybernetics, vol. 31, no. 3, pp. 405–410, Aug. 2001.

[3] T. Lozano-Perez, “Spatial planning: a configuration space approach,” IEEE Trans. on Computers, vol. C-32, no. 2, pp. 108–120, Feb. 1983.

[4] R. Brooks and T. Lozano-Preez, “A subdivision algorithm in configuration space for findpath with rotation,” IEEE Trans. on System, Man and Cybernetics, vol. 15, no. 2, pp. 224–233, March-April 1985.

[5] J. Barraquand and J.C. Latombe, “Robot motion planning: A distributed representa-tion approach,” Internarepresenta-tional Journal of Robotics Research, vol. 10, no. 6, pp. 628–649, 1991.

[6] L. Kavraki and J.C. Latombe, “Randomized preprocessing of configuration space for fast path planning,” Proc. IEEE Intl. Conf. on Robotics and Automation, pp. 2138–

2139, 1994.

[7] J.C. Latombe L.E. Kavraki, P. Svestka and M.H. Overmars, “Probabilistic roadmaps for path planning in high-dimensional configuration spaces,” IEEE Trans. on Robotics and Automation, vol. 12, no. 4, pp. 566–580, Aug. 1996.

[8] O. Khatib, “Real-time obstacle avoidance for manipulators and mobile robots,” Inter-national Journal of Robotics Research, vol. 5, no. 1, pp. 90–98, Spring 1986.

[9] J.H. Chuang and N. Ahuja, “An analytically tractable potential field model of free space and its application in obstacle avoidance,” IEEE Trans. on Systems, Man, and Cybern., part B: Cybernetics, vol. 28, no. 5, pp. 729–736, 1998.

[10] A. Thanailakis, P.G. Tzionas, and P.G. Tsalides, “Collision-free path planning for a diamond-shaped robot using two-dimensional cellular automata,” IEEE Trans. on Robotics and Automation, vol. 13, pp. 237–250, 1997.

[11] Y.K. Hwang and N. Ahuja, “Gross motion planning a survey,” ACM Computation Survey, vol. 24, no. 3, pp. 219–291, 1992.

[12] P. Khosla and R. Volpe, “Superquadric artificial potentials for obstacle avoidance and approach,” Proc. IEEE Intl. Conf. on Robotics and Automation, pp. 1778–1784, 1988.

[13] J.H. Chuang, C.H. Tsai, W.H. Tsai, and C.Y. Yang, “Potential-based modeling of 2-d regions using nonuniform source distribution,” IEEE Trans. on Systems, Man, and Cybern., part A: Systems and Humans, vol. 3, no. 2, pp. 197–202, 2000.

[14] K.P. Valavanis, T. Herbert, and N.C. Tsourveloudis, “Mobile robot navigation in 2-D dynamic environments using electrostatic potential fields,” IEEE Trans. on Sys., Man, Cybern., Part A: Systems and Humans, vol. 30, no. 2, pp. 187–196, 2001.

[15] N.C. Tsourveloudis, K.P. Valavanis, and T. Herbert, “Autonomous vehicle navigation utilizing electrostatic potential fields and fuzzy logic,” IEEE Trans. on Robotics and Automation, vol. 17, no. 4, pp. 490–497, 2001.

[16] J.C. Latombe, Robot Motion Planning, MA: Kluwer, Boston, 1991.

[17] D.T. Kuan, J.C. Zamiska, and R.A. Brooks, “Natural decomposition of free space planning,” Proc. IEEE Intl. Conf. on Robotics and Automation, pp. 168–173, 1985.

[18] J.H. Chuang, C.H. Tsai, and M.C. Ko, “Skeletonization of three-dimensional object using generalized potential field,” IEEE Trans. Pattern Analysis and Machine Intelli-gence, vol. 22, no. 11, pp. 1241–1251, Nov. 2000.

[19] W.A. Perkins, “A model based vision system for industrial parts,” IEEE Trans. Com-put., vol. 21, pp. 126–143, 1978.

[20] P. Rummel and W. Beutel, “Workpiece recognition and inspection by a model-based scene analysis system,” Pattern Recognition, vol. 17, pp. 141–148, 1984.

[21] N. Ayache and O.D. Faugeras, “HYPER: A new approach for the recognition and positioning of two-dimensional objects,” IEEE Trans. Pattern Anal. Mach. Intell, vol.

8, pp. 44–54, 1986.

[22] C.T. Zahn and R.Z. Roskies, “Fourier descriptors for plane closed curves,” IEEE Trans.

Comput., vol. 21, pp. 269–281, 1972.

[23] E. Persoon and K.S. Fu, “Shape discrimination using Fourier descriptors,” IEEE Trans.

Syst. Man Cybern., vol. 7, pp. 170–179, 1977.

[24] M.K. Hu, “Visual pattern recognition by moment invariants,” IEEE Trans. Inf. Theory, vol. 8, pp. 179–187, 1962.

[25] S. Maitra, “Moment invariants,” Proc. IEEE, vol. 67, pp. 697–699, 1979.

[26] S.S. Reddi, “Radial and angular moment invariants for image identification,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 3, pp. 240–242, 1981.

[27] J.G. Leu, “Computing a shape’s moments from its boundary,” Pattern Recognition, vol. 24, pp. 949–957, 1991.

[28] S.R. Dubois and F.H. Glanz, “An autoregressive model approach to two-dimensional shape classification,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 8, pp. 55–66, 1977.

[29] R.L. Kashyap and R. Chellappa, “Stochastic models for close boundary analysis: rep-resentation and reconstruction,” IEEE Trans. Inf. Theory, vol. 27, pp. 627–637, 1981.

[30] M. Das, M.J. Paulik and N.K. Loh, “A bivariate autoregressive modeling technique for analysis and classification of planar shapes,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 12, pp. 97–103, 1990.

[31] H. Freeman and L.S. Davis, “A corner finding algorithm for chain coded curves,” IEEE Trans. Comput., vol. 26, pp. 297–303, 1977.

[32] W.H. Tsai, and S.S. Yu, “Attributed string matching with merging for shape recogni-tion,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 7, pp. 453–462, 1985.

[33] M. Maes, “Polygonal shape recognition using string-matching techniques,” Pattern Recognition, vol. 24, pp. 433–440, 1991.

[34] A. Blumenkrans, “2-dimensional object recognition using a 2-dimensional polar trans-form,” Pattern Recognition, vol. 24, pp. 879–890, 1991.

[35] C.C. Chang, S.M. Hwang and D.J. Buehrer, “A shape recognition scheme based on relative distances of feature points from the centroid,” Pattern Recognition, vol. 24, pp.

1053–1063, 1991.

[36] L.G. Shapiro and R.M. Haralic, “Structural descriptions and inexact matching,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 3, pp. 504–519, 1981.

[37] N. Ueda and S. Suzuki, “Learning visual models from shape contours using multiscale convex/concave structure matching,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 15, pp. 337–352, 1993.

[38] P.J. Flynn and A.K. Jain, “3-D object recognition using invariant feature indexing of interpretation tables,” Image Understanding, vol. 55, no. 2, pp. 119–129, March 1992.

[39] P.J. Flynn, “3-D object recognition with symmetric models: symmetry extraction and encoding,” IEEE Trans. Pattern Anal. Mach. Intell, vol. 16, no. 8, pp. 814–818, 1994.

[40] J. Mao, P.J. Flynn and A.K. Jain, “Integration of multiple feature groups and multiple views into a 3-D object recognition system,” Computer Vision and Image Understand-ing, vol. 62, no. 3, pp. 309–325, 1995.

[41] P.J. Flynn and A.K. Jain, “BONSAI: 3-D object recognition using constrained search,”

IEEE Trans. Pattern Anal. Mach. Intell, vol. 13, no. 10, pp. 1066–1075, 1991.

[42] K.C. Wong, Y. Cheng and J. Kittler, “Recognition of polyhedral using triangle pair features,” IEE Proceedings-I, vol. 140, no. 1, pp. 72–85, 1993.

[43] D.P. Huttenlocher and S. Ullman, “Recognition solid objects by alignment with an image,” Int. Journal of Computer Vision, vol. 5, pp. 195–212, 1990.

[44] R. Horaud and H. Sossa, “Polyhedral object recognition by indexing,” Pattern Recog-nition, vol. 28, no. 12, pp. 1855–1870, 1995.

[45] C.F. Olson, “Probabilistic indexing for object recognition,” IEEE Trans. Pattern Anal.

Mach. Intell, vol. 17, no. 5, pp. 518–522, 1995.

[46] K. Arbter, W.E. Snyder, H. Burkhardt and G. Hirzinger, “Application of affine-invariant fourier descriptors to recognition of 3-D objects,” IEEE Trans. Pattern Anal. Mach.

Intell, vol. 12, no. 7, pp. 640–647, 1990.

[47] A. Pentland and S. Sclaroff, “Closed-form solutions for physically based shape modeling and recognition,” IEEE Trans. Pattern Anal. Mach. Intell, vol. 13, no. 7, pp. 715–729, 1991.

[48] Y. Chen and G. Medioni, “Surface description of complex objects from multiple range images,” Proc. IEEE Conf. CVPR, pp. 153–158, 1994.

[49] K. Wu and M.D. Levine, “3-D parts segmentation using simulated electrical charge distributions,” IEEE Trans. Pattern Anal. Mach. Intell, vol. 19, no. 11, pp. 1223–1235, 1997.

[50] J.H. Chuang, “A potential-based approach for shape matching and recognition,” Pat-tern Recognition, vol. 29, no. 3, pp. 463–470, 1996.

[51] D.R. Wilton, S.M. Rao, A.W. Glisson, D.H. Schaubert, O.M. Al-Bundak, and C.M.

Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antennas and Propagation, vol. AP-32, no. 3, pp. 276–281, 1984.

[52] L. Bers and F. Karal, Calculus, New York: Holt, Rinehart and Winston, New York, 1976.

[53] J.C. Latombe, “Motion planning: A journey of robots, molecules, digital actors, and other artifacts,” International Journal of Robotics Research, vol. 18, no. 11, pp. 1119–

1128, Nov. 1999.

[54] T. Lozano-Perez and M.A. Wesley, “An algorithm for planning collision-free paths among polyhedral obstacles,” Communications. ACM, vol. 22, no. 10, pp. 560–570, 1979.

[55] T. Laliberte and C. Gosselin, “Efficient algorithms for the trajectory planning for redundant manipulators with obstacle avoidance,” Proc. IEEE Intl. Conf. on Robotics and Automation, pp. 2044–2049, 1994.

[56] R. Nevatia and T.O. Binford, “Description and recognition of curved objects,” Artificial Intelligence, vol. 8, no. 1, pp. 77–98, 1977.

[57] C.I. Connolly and R.A. Grupen, “Path planning using laplace’s equation,” IEEE Intl.

Conf. of Robotics and Automation, pp. 2102–2106, 1990.

[58] D.E. Koditschek, “Exact robot navigation by means of potential functions: Some topological considerations,” IEEE Intl. Conf. of Robotics and Automation, pp. 1–6, 1987.

[59] O. Brock and L.E. Kavraki, “Decomposition-based motion planning: A framework for real-time motion planning in high-dimensional configuration spaces,” IEEE Intl. Conf.

of Robotics and Automation, pp. 1469–1474, 2001.

[60] K.K. Gupta, “Fast collision avoidance for manipulator arms: A sequential search strat-egy,” IEEE Trans. on Robot. and Auto., vol. 6, no. 5, pp. 522–532, Oct. 1990.

[61] C.C. Lin, C.C. Pan, and J.H. Chuang, “A novel potential-based path planning of 3-D articulated robots with moving bases,” Proc. IEEE International Conference on Robottic and Automation, pp. 3365–3370, 16-18 Sep 2003, in Taipei, Taiwan, R.O.C.

[62] J.H. Chuang, N. Ahuj, C.C. Lin, C.H. Tsai, and C.H. Chen, “A potential-based gener-alized cylinder representation,” accepted by Computers and Graphics, 2004.

[63] E.C. Sherbrooke, N.M. Patrikalakis, and E. Brisson, “An algorithm for the medial axis transform of 3-D polyhedral solids,” IEEE Trans. Visualization and Computrer Graphics, vol. 2, no. 1, pp. 44–61, Mar. 1996.