This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Scale-Based Detection of Corners of Planar Curves
April 1992 (vol. 14 no. 4)
pp. 430-449

A technique for detecting and localizing corners of planar curves is proposed. The technique is based on Gaussian scale space, which consists of the maxima of absolute curvature of the boundary function presented at all scales. The scale space of isolated simple and double corners is first analyzed to investigate the behavior of scale space due to smoothing and interactions between two adjacent corners. The analysis shows that the resulting scale space contains line patterns that either persist, terminate, or merge with a neighboring line. Next, the scale space is transformed into a tree that provides simple but concise representation of corners at multiple scales. Finally, a multiple-scale corner detection scheme is developed using a coarse-to-fine tree parsing technique. The parsing scheme is based on a stability criterion that states that the presence of a corner must concur with a curvature maximum observable at a majority of scales. Experiments were performed to show that the scale space corner detector is reliable for objects with multiple-size features and noisy boundaries and compares favorably with other corner detectors tested.

[1] I. M. Anderson and J. C. Bezdek, "Curvature and tangential deflection of discrete arcs: A theory based on the commutator of scatter matrix pairs and its application to vertex detection in planar shape,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, no. 1, pp. 27-40, Jan 1984.
[2] H. Asada and M. Brady, "The curvature primal sketch,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 1, pp. 2-14, 1986.
[3] F. Attneave, "Some informational aspects of visual perception,"Psychol. Rev., vol. 61, no. 3, pp. 183-193, 1954.
[4] J. Babaud, A. P. Witkin, M. Baudin, and R. O. Duda, "Uniqueness of the Gaussian kernel for scale-space filtering,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 26-33, Jan. 1986.
[5] P. J. Burt, "Fast filter transform for image processing,"Comput. Vision Graphics Image Processing, vol. 16, pp. 20-51, 1981.
[6] P. J. Burt and E.H. Adelson, "The Laplacian pyramid as a compact image code,"IEEE Trans. Commun., vol. COM-31, pp. 532-540, Apr. 1983.
[7] J. J. Clark, "Singularity theory and phontom edges in scale space,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-10, no. 5, pp. 720-727, 1988.
[8] H. Freeman and L. S. Davis, "A corner-finding algorithm for chain-coded curves,"IEEE Trans. Comput., vol. C-26, pp. 297-303, Mar. 1977.
[9] D. Langride, "On the computation of shape," inFrontiers of Pattern Recognition(S. Watanabe, Ed.) New York: Academic, 1972, pp. 347-365.
[10] D. Marr and E. C. Hildreth, "Theory of edge detection,"Proc. Roy. Soc. London B, vol. 270, pp. 187-217, 1980.
[11] P. Meer, E. S. Baugher, and A. Rosenfeld, "Frequency domain analysis and synthesis of image pyramid generating kernels,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, pp. 512-522, 1987.
[12] P. Meer, E. S. Baugher, and A. Rosenfeld, "Extraction of trend lines and extrema from multiscale curves,"Pattern Recogn. vol. 21, no. 3, pp. 217-226, 1988.
[13] F. Moktarian and A. Mackworth, "Scale-based description and recognition of planar curves and two-dimensional shapes,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 1, pp. 34-43, Jan. 1986.
[14] M. A. Piech, "Comment on fingerprints of two-dimensional edge models,"Comput. Vision Graphics Image Processing, vol. 42, pp. 381-386, 1988.
[15] A. Rosenfeld and E. Johnston, "Angle detection on digital curves,"IEEE Trans. Comput., vol. C-22, pp. 875-878, Sept. 1973.
[16] A. Rosenfeld and J. S. Weazka, "An improved method of angle detection on digital curves,"IEEE Trans. Comput.vol. C-24, pp. 940-941, Sept. 1975.
[17] P. Saint-Marc and G. Medioni, "Adaptive smoothing for feature extraction," inProc. Image Understanding, Apr. 1988, pp. 1110-1113, vol. II.
[18] P. V. Sankar and C. V. Sharma, "A parallel procedure for the detection of dominant points on a digital curves,"Comput. Vision Graphics Image Processing, vol. 7, pp. 403-412, 1978.
[19] M. Shah, A. Sood, and R. Jain, "Pulse and staircase edge models",Comput. Vision Graphics Image Processing, vol. 34, pp. 321-343, 1986.
[20] C. Teh and R. T. Chin, "On the detection of dominant points on digital curves,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-11, no. 8, pp. 859-872, Aug. 1989.
[21] A. P. Witkin, "Scale-space filtering,"Proc. 8th Int. Joint Conf. Artificial Intell.(Kalsruhe, West Germany), 1983, pp. 1019-1021.
[22] A. Yuille and T. Poggio, "Scaling theorems for zero crossings,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 1, pp. 15-25, 1986.

Index Terms:
pattern recognition; picture processing; scale-based corners detection; planar curves; Gaussian scale space; maxima of absolute curvature; boundary function; line patterns; tree; multiple-scale corner detection; coarse-to-fine tree parsing technique; stability criterion; filtering and prediction theory; pattern recognition; picture processing; trees (mathematics)
Citation:
A. Rattarangsi, R.T. Chin, "Scale-Based Detection of Corners of Planar Curves," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 4, pp. 430-449, April 1992, doi:10.1109/34.126805
Usage of this product signifies your acceptance of the Terms of Use.