The Intensity Axis of Symmetry and Its Application to Image Segmentation
August 1993 (vol. 15 no. 8) pp. 753-770
The authors present the intensity axis of symmetry (IAS) method for describing the shape of structures in grey-scale images. They describe the spatial and intensity variations of the image simultaneously rather than by the usual two-step process of using intensity properties of the image to segment an image into regions and describing the spatial shape of these regions. The result is an image shape description that is useful for a number of computer vision applications. The method relies on minimizing an active surface functional that provides coherence in both the spatial and intensity dimensions while deforming into an axis of symmetry. Shape-based image segmentation is possible by identifying image regions associated with individual components of the IAS. The resulting image regions have geometric coherence and correspond well to visually meaningful objects in medical images.
[1] 753D. H. Ballard and C. M. Brown,Computer Vision. Englewood Cliffs, NJ: Prentice-Hall, 1982.
[2] H. Blum, "A geometry for biology,"Annals New York Acad. Sci., vol. 231, pp. 19-30 Apr. 1974.
[3] J. M. Gauch and S. M. Pizer, "Image description via the multiresolution intensity axis of symmetry, " inProc. Second Int. Conf. Comput. Vision(Tampa, FL), Dec. 1988.
[4] J. M. Gauch, "The multiresolution intensity axis of symmetry and its application to image segmentation," Ph.D. Dissertation, Univ. North Carolina, Chapel Hill, 1989.
[5] M. Brady and H. Asada, "Smoothed local symmetries and their implementation," MIT A.I. Memo 757, Feb. 1984.
[6] M. Leyton, "Smooth processes on shape," Draft Report, Harvard Univ., Feb. 1986.
[7] H. Blum and R. N. Nagel, "Shape description using weighted symmetric axis features,"Patt. Recogn., vol. 10, pp. 167-180, 1978.
[8] S. M. Pizer, W. R. Oliver, J. M. Gauch, and S. H. Bloomberg, "Hierarchical figure based shape description for medical imaging,"NATO ASI Math. Comput. Sci. Medical Imaging, 1986.
[9] A. R. Dill, M. D. Levine, and P. B. Noble, "Multiple resolution skeletons,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-9, pp. 495-504, July 1987.
[10] J. J. Koenderink, "The structure of images."Biolog. Cybern., vol. 50, pp. 363-370, 1984.
[11] J. M. Gauch, W. R. Oliver, and S. M. Pizer, "Multiresolution shape descriptions and their applications in medical imaging." inProc. 10th Inform. Processing Med. Imaging Conf. (IPMI 10)(Utrecht. Netherlands). June 1987.
[12] M. Morse and G. B. van Schaack, "'The critical point theory under general boundary conditions,"Ann. Math., vol. 35, no. 3, pp. 545-571, July 1934.
[13] A. P. Bilcher, "Edge detection and geometric methods in computer vision," Ph.D. dissertation, Stanford Univ., STAN-CS-85-1041, Feb. 1985.
[14] M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active contour models,"Int. J. Comput. Vision, vol. 1, pp. 321-331, 1987.
[15] J. Thorpe,Elementary Topics in Differential Geometry. New York: Springer-Verlag, 1979.
[16] A. Rosenfeld,Multiresolution Image Processing and Analysis. Berlin: Springer-Verlag, 1984.
[17] P.J. Burt, T. H. Hong, and A. Rosenfeld, "Segmentation and estimation of image region properties through cooperative hierarchical computation."IEEE Trans. Syst. Man Cybern., vol. SMC 11-12, pp. 802-809, Dec. 1981.
[18] L. M. Lifshitz, "Image segmentation using global knowledge and a priori information," Ph.D. dissertation, Univ. North Carolina, Chapel Hill, TR87-012, 1987.
[19] J. L. Crowley and A. C. Parker, "A representation for shape based on peaks and ridges in the difference of low-pass transform,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, no. 2, pp. 156-170, May 1984.
[20] T. Cullip, Personal correspondence, Dept. Comput. Sci., Univ. North Carolina, Chapel Hill, Feb. 1989.
[21] J. M. Coggins, T. Cullip, and S. M. Pizer, "A data structure for image region hierarchies," Int. Rep., Dept. of Comput. Sci., Univ. North Carolina, Chapel Hill, 1988.
[22] J. M. Gauch and S. M. Pizer, "Multiresolution analysis of ridges and valleys in grey-scale images,"IEEE Trans. Patt. Anal. Machine Intell., vol. 15, no. 6, pp. 635-646, June 1993.
[23] K. R. Castleman,Digital Image Processing. Englewood Cliffs, NJ: Prentice-Hall, 1979.
[24] S. M. Pizer et al., "Adaptive histogram equalization and its variations,"Comput. Vision Graphics Image Processing, vol. 39, pp. 355-368, 1987.
[25] 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.
[26] J. F. Canny, "Finding lines and edges in images," Artificial Intell. Lab., Massachusetts Inst. Technol., Tech. Rep. TM-720, 1983.
Index Terms:
spatial variations; shape structures; image processing; intensity axis; symmetry; image segmentation; grey-scale images; intensity variations; shape description; computer vision; geometric coherence; computer vision; image recognition; image segmentation
Citation:
J.M. Gauch, S.M. Pizer, "The Intensity Axis of Symmetry and Its Application to Image Segmentation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 8, pp. 753-770, Aug., 1993