This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Pessimal Guesses may be Optimal: A Counterintuitive Search Result
November 1988 (vol. 10 no. 6)
pp. 949-955

A particular style of search is considered that is motivated by the problem of reconstructing the surface of three-dimensional objects given a collection of planar contours representing cross-sections through the objects. An improvement on the simple divide-and-conquer method is presented. The key idea is to locate bottlenecks (minimal separators), which markedly reduces the number of searches required but reduces other measures (e.g. nodes expanded) by only a constant factor. It is observed that for well-behaved search spaces, the search efficiency can be improved further by making 'pessimal guesses'. This suggests a style of search in which the region of the search space thought to be close to the optimal solution (on whatever grounds are available) is examined last, while the outlying regions (the pessimal guesses) are examined first.

[1] J. D. Boissonnat and O. D. Faugeras, "Triangulation of 3D objects," inProc. IJCAI-81, pp. 658-660.
[2] H. N. Christiansen and T. W. Sederberg, "Conversion of complex contour line definitions into polygonal element mosaics,"Comput. Graphics, vol. 13, no. 2, Aug. 1978.
[3] L. T. Cook, P. N. Cook, K. R. Lee, S. Batnitzky, B. Y. S. Wong, S. L. Gritz, J. Ophir, S. J. Dwyer III, L. R. Bihongiari, and A. W. Templeton, "An algorithm for volume estimation based on polyhedral approximation,"IEEE Trans. Biomed. Eng., vol. BME-27, no. 9, Sept. 1980.
[4] L. T. Cook, S. J. Dwyer III, S. Batnitzky, and K. Rak Lee, "A three-dimensional display system for diagnostic imaging applications,"IEEE Comput. Graphics Applications, vol. 3, no. 5, pp. 13-19, Aug. 1983.
[5] C. A. Curcio, and K. R. Sloan, Jr., "A computer-system for combined neuronal mapping and morphometty,"J. Neuroscience Methods 4, 1981.
[6] H. Fuchs. Z. M. Kedem, and S. P. Uselton, "Optimal surface reconstruction from planar contours,"Commun. ACM, vol. 20, Oct. 1977.
[7] S. Ganapathy and T. G. Dennehy, "A new general triangulation method for planar contours,"Comput. Graphics, vol. 16, no. 3, July 1982.
[8] E. Keppel, "Approximating complex surfaces by triangulation of contour lines,"IBM J. Res. Develop., vol. 19, Jan. 1975.
[9] J. O'Rourke, "Polyhedra of minimal area as 3D object models," inProc. IJCAI-81, Aug. 1981, pp. 664-666.
[10] U. Shani, "Understanding three dimensional images: The recognition of abdominal anatomy from computed axial tomograms (CAT)," Ph.D. dissertation, Dep. Comput. Sci., Univ. Rochester, 1980.
[11] K. R. Sloan, Jr. and L. Hrechanyk, "Surface reconstruction from sparse data," inProc. Pattern Recognition and Image Processing, Dallas, TX, Aug. 1981.
[12] K. R. Sloan and J. Painter, "Contours to surfaces: Testbed and initial results," inProc. CHI+GI'87, Toronto, Canada, Apr. 1987, pp. 115-120.
[13] Y. F. Wang and J. K. Aggarwal, "Construction of surface representation from 3-D volumetric scene description," inProc. Computer Vision and Pattern Recognition, San Francisco, CA, June 1985.

Index Terms:
3-D object surface reconstruction; picture processing; pattern recognition; counterintuitive search; planar contours; divide-and-conquer method; search spaces; search efficiency; pattern recognition; picture processing
Citation:
K.R. Sloan, J. Painter, "Pessimal Guesses may be Optimal: A Counterintuitive Search Result," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 6, pp. 949-955, Nov. 1988, doi:10.1109/34.9117
Usage of this product signifies your acceptance of the Terms of Use.