This Article 
 Bibliographic References 
 Add to: 
A Curvature-Based Approach to Terrain Recognition
November 1989 (vol. 11 no. 11)
pp. 1213-1217

The authors describe an algorithm which uses a Gaussian and mean curvature profile for extracting special points on terrain and then use these points for recognition of particular regions of the terrain. The Gaussian and mean curvatures are chosen because they are invariant under rotation and translation. In the Gaussian and mean curvature image, the points of maximum and minimum curvature are extracted and used for matching. The stability of the position of those points in the presence of noise and with resampling is investigated. The input for this algorithm consists of 3-D digital terrain data. Curvature values are calculated from the data by fitting a quadratic surface over a square window and calculating directional derivatives of this surface. A method of surface fitting which is invariant to coordinate system transformation is suggested and implemented. The algorithm is tested with and without the presence of noise, and its performance is described.

[1] P. J. Besl and R. C. Jain, "Surface characterization for three-dimensional object recognition in depth maps," Univ. Michigan, Ann Arbor, Rep. RSD-TR-20-84, Dec. 1984.
[2] P. J. Besl and R. C. Jain, "Three-dimensional object recognition,"ACM Comput. Surveys, vol. 17, no. 1, pp. 75-145, Mar. 1985.
[3] M. Brady, J. Ponce, A. Yuille, and H. Asada, "Describing surfaces,"Comput. Vision, Graphics, Image Processing, vol. 32, pp. 1-28, 1985.
[4] P. J. Besl and R. C. Jain, "Segmentation through symbolic surface descriptions," inProc. CVPR, May 1986.
[5] T. J. Fan, G. Medioni, and R. Nevatia, "Description of surfaces from range data using curvature properties," inProc. CVPR, May 1986.
[6] H. H. Chen and T. S. Huang, "Maximal matching of two three-dimensional point sets," inProc. ICPR, Oct. 1986.
[7] B. O'Neill,Elementary Differential Geometry. New York: Academic, 1966.
[8] R.M. Haralick, S.R. Sternberg, and X. Zhuang, "Image analysis using mathematical morphology,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, no. 4, pp. 532-550, 1987.
[9] D. B. Goldgof, T. S. Huang, and H. Lee, "Feature extraction and terrain matching," inProc. IEEE Comput. Soc. Conf. Comput. Vision Pattern Recognition, Ann Arbor, MI, May 1988.
[10] M. Hebert and T. Kanade, "First results on outdoor scene analysis using range data," inProc. DARPA IUW, 1985.
[11] A. R. Seigel, "Aspects of information flow in VLSI circuits," inProc. 18th Annu. ACM Symp. Theory Comput., pp. 448-459, 1986.
[12] A. Goldberg and R. Tarjan, "A new approach to the maximum flow problem," inProc. 18th ACM Symp. Theory Comput., 1986, pp. 136-146.
[13] M. Daily, J. Harris, and K. Reiser, "An Operational Perception System for Cross-Country Navigation,"Proc. Image-Understanding Workshop, Morgan Kaufmann, San Mateo, Calif., 1988.
[14] D. B. Goldgof, T. S. Huang, and H. Lee, "Curvature based approach to terrain recognition," Coord. Sci. Lab., Univ. Illinois, Urbana-Champaign, Tech. Note ISP-910, Apr. 1989.

Index Terms:
Gaussian curvature; computerised pattern recognition; 3D digital terrain data; visual navigation; terrain recognition; mean curvature profile; mean curvature image; quadratic surface; square window; surface fitting; computerised navigation; computerised pattern recognition; computerised picture processing
D.B. Goldgof, T.S. Huang, H. Lee, "A Curvature-Based Approach to Terrain Recognition," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 11, pp. 1213-1217, Nov. 1989, doi:10.1109/34.42859
Usage of this product signifies your acceptance of the Terms of Use.