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Directional Analysis of Images in Scale Space
November 1991 (vol. 13 no. 11)
pp. 1185-1192

The authors propose a computational technique for the directional analysis of piecewise linear patterns in images based on the notion of zero crossings in gradient images. A given image is preprocessed by a sequence of filters that are second derivatives of 2-D Gaussian functions with different scales. This gives a set of zero-crossing maps (the scale space) from which a stability map is generated. Significant linear patterns are detected from measurements on the stability map. Information regarding orientation of the linear patterns in the image and the area covered by the patterns in specific directions is then computed. The performance of the method is illustrated through applications to a simple test image made up of straight bar patterns as well as to scanning electron microscope images of collagen fibrils in rabbit ligaments. The method has significant applications in quantitative analysis of ligament healing and in comparison of treatment methods for ligament injuries.

[1] H. H. Arsenault, M. K. Seguin, and N. Brousseau "Optical filtering of aeromagnetic maps,"Appl. Optics, vol. 13, no. 5, pp. 1013-1017, May 1974.
[2] 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.
[3] V. Berzins, "Accuracy of Laplacian detectors,"J. Comput. Vision Graphics Image Processing, vol. 27, pp. 195-210, 1984.
[4] V. Bezvoda and K. Segeth, "Directional and frequency filtering of geophysical data, measured in a rectangular net,"Gerlands Beitr. Geophys.(Germany), vol. 90, pp. 133-146, 1981.
[5] T. Binford, "Image understanding: Intelligent systems," inProc. DARPA Image Understanding Workshop, vol. I, pp. 18-31, Feb. 1987.
[6] W. F. Bischof and T. M. Caelli, "Parsing Scale-space and spatial stability analysis,"J. Comput. Vision Graphics Image Processing, vol. 42, pp. 192-205, 1988.
[7] L. T. Bruton, N. R. Bartley, and R. A. Stein, "The design of stable high-quality two-dimensional recursive filters for seismic signal processing,"Advances Geophysical Data Processing, vol. 2, pp. 223-261, 1985.
[8] T. M. Caelli, "On the specification of coding principles for visual image processing," inFigural Synthesis(P.C. Dodwell and T. M. Caelli, Ed.), NJ: Erlbaum, 1984.
[9] T. M. Caelli, W. F. Bischof, and Z. Q. Liu, "Filter-based approaches to pattern recognition,"Patt. Recogn., vol. 6, no. 6, pp. 639-650, Dec. 1988.
[10] S. Chaudhuri, H. Nguyen, R. M. Rangayyan, S. Walsh, and C. B. Frank, "A Fourier domain directional filtering method for analysis of collagen alignment in ligaments,"IEEE Trans. Biomed. Eng., vol. BME-34, no. 7, pp. 509-517, July 1987.
[11] S. Chaudhuri, R. M. Rangayyan, S. Walsh, and C. B. Frank, "Quantitative analysis of ligament healing via directional filtering," inProc. 13th Canadian Med. Biological Eng. Conf.(Halifax, Nova Scotia), June 9-12, 1987, pp. 109-110.
[12] S. Chaudhuri, R. M. Rangayyan, S. Walsh, and C. B. Frank, "The role of the supercomputer in image processing: Quantitative analysis of collagen alignment in ligaments," inProc. Supercomput. Symp. '87(Calgary, Alberta), June 15-16, 1987, pp. 5-9.
[13] J. S. Chen, A. Huertas, and G. Medioni, "Fast convolution with Laplacian-of-Gaussian masks,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-9, pp. 584-590, July 1987.
[14] J. S. Chen and G. Medioni, "Detection, localization, and estimation of edges,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, no. 2, pp. 191-198, Feb. 1989.
[15] J. J. Clark, "Authenticating edges produced by zero crossing algorithms,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, no. 1, pp. 43-57, Jan. 1989.
[16] R. Deriche, "Using Canny's criteria to derive a recursively implemented optimal edge detector,"Int. J. Comput. Vision, vol. 1, pp. 167-187, 1987.
[17] R. Deriche, "Fast algorithms for low-level vision," inIEEE Proc. 9th. Int. Conf. Patt. Recogn., 1988, pp. 434-438.
[18] M. B. Dobrin, A. L. Ingalls, and J. A. Long, "Velocity and frequency filtering of seismic data using laser light,"Geophys., vol. 30, no. 6, pp. 1144-1178, Dec. 1965.
[19] J. Duvernoy and K. Chalasinka-Macukow, "Processing measurements of the directional content of Fourier spectra,"Appl. Optics, vol. 20, pp. 136-144, 1981.
[20] A. P. Pentland, "A new sense for depth of field,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-9, no. 4, pp. 523-531, July 1987.
[21] P. Embree, J. P. Burg, and M. M. Bacus, "Wide-band velocity filtering--The Pie-slice process,"Geophys., vol. 28, pp. 948-974, 1963.
[22] W. E. L. Grimson, and E. C. Hildreth, "Comments on 'Digital step edges from zero crossings of second directional derivatives,'"IEEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-7, no. 1, pp. 121-126, Jan. 1985.
[23] E. L. Hall,Computer Image Processing and Recognition, New York: Academic, 1979.
[24] A. Huertas, and G. Medioni, "Detection of intensity changes with subpixel accuracy using Laplacian-Gaussian masks,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-8, no. 5, pp. 651-664, Sept. 1986.
[25] R. A. Hummel, "Representations based on zero-crossings in scale-space," inIEEE Proc. Conf. Comput. Vision Patt. Recogn(Miami Beach, FL), 1986, pp. 204-209.
[26] A. Ikonomopoulos, and M. Kunt, "Directional filtering, zero crossing edge detection, and image coding," inSignal Processing II: Theories and Applications(H. W. Schussler, Ed.), New York: Elsevier, 1983, pp. 203-206.
[27] A. Ikonomopoulos, and M. Unser, "A directional filtering approach to texture discrimination," inProc. IEEE 7th Int. Conf. Patt. Recogn.(Montreal), 1984, pp. 87-89.
[28] M. Kass and A. Witkin, "Analyzing oriented patterns," inProc. 9th Int. Joint Conf. Artificial Intell.(Los Angeles, CA), 1985, pp. 944-952.
[29] I. Katz, "Coaxial stereo and scale-based matching," Tech. Rep. 85-13, Dept. Comput. Sci., Univ. British Columbia, Vancouver, Canada, 1985.
[30] H. S. Lim, and T. O. Binford, "Survey of parallel computers," inProc. DARPA Image Understanding Workshop, Feb. 1987, pp. 644-654, vol. II.
[31] J. O. Limb and C. B. Rubenstein "A model of threshold vision incorporating inhomogeneity of the visual fields,"Vision Res., vol. 17, no. 4, pp. 571-584, 1977.
[32] Z. Q. Liu, R. M. Rangayyan, and C. B. Frank, "A scale-space approach to directional analysis of images," inProc. Canadian Conf. Elect. Comput. Eng.(Vancouver, Canada), Nov. 3-4, 1988, pp. 755-759.
[33] Z. Q. Liu, R. M. Rangayyan, and C. B. Frank, "Linear pattern analysis using scale-space techniques," inProc. Supercomput. Symp. '89(Toronto), June 19-21, 1989, pp. 111-123.
[34] Z. Q. Liu, R. M. Rangayyan, and C. B. Frank, "Statistical analysis of collagen alignment in ligaments by scale-space analysis,"IEEE Trans. Biomed. Eng., vol. 38, pp. 580-588, 1991.
[35] D. Marr and E. Hildreth, "Theory of edge detection," inProc. Royal Soc.(London), 1980, pp. 187-217, Ser. B, vol. 207.
[36] D. Marr and T. Poggio, "Some comments on a recent theory of stereopsis," Memo 558, M .I. T. Artif. Intell. Lab., July 1980.
[37] 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.
[38] G. K. Moore, and F. A. Waltz, "Objective procedures for lineament enhancement and extraction,"Photogram. Eng. Remote Sensing, vol. 49, pp. 641-647, 1983.
[39] N. Ranganathan, and M. Shah, "A VLSI architecture for computing scale-space,"Comput. Vision Graphics Image Processing, vol. 43, no. 2, pp. 178-204, Aug. 1988.
[40] C. B. Franket al., "A quantitative analysis of matrix alignment in ligament scars: A comparison of movement versus immobilization in an immature rabbit model,"J. Orthopaedic Res., vol. 9, pp. 219-227, 1991.
[41] A. Rosenfeld and A. Kak,Digital Picture Processing, New York: Academic, 1976.
[42] D. Rotem, and Y. Y. Zeevi, "Image reconstruction from zero-crossings,"IEEE Trans. Acoustics Speech Signal Processing, vol. ASSP-34, no. 5, pp. 1269-1277, Oct. 1986.
[43] G. E. Sotak and K. L. Boyer, "The Laplacian-of-Gaussian kernel: A formal analysis and design procedure for fast, accurate convolution and full-frame output,"Comput. Vision Graphics Image Processing, vol. 48, no. 2, pp. 147-189, 1989.
[44] K. A. Stevens, "Computation of locally parallel structure,"Bio. Cybern., vol. 29, pp. 19-28, 1978.
[45] H. Takahashi, "A Iineament enhancement technique for active fault analysis," inMachine Processing Remotely Sensed Data Symp., 1981, pp. 103-112.
[46] S. Treitel, J. L. Shanks, and C. W. Frasier, "Some aspects of fan filtering,"Geophys., vol. 32, pp. 789-806, 1967.
[47] J. Richter and S. Ullman, "Non-linearities in cortical simple cells and the possible detection of zero-crossings,"Biol. Cybern., vol. 53, pp. 195-202, 1986.
[48] A. P. Witkin, "Scale-space filtering," inProc. Int. Joint Conf. Artificial Intell.(Karlsrhue, West Germany), Aug. 1983, pp. 1019-1022.
[49] 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.
[50] Y. T. Zhou, V. Venkateswar, and R. Chellappa, "Edge detection and linear feature extraction using a 2-D random field model,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, no. 1, pp. 84-95, Jan. 1989.
[51] S. W. Zucker, "Early orientation selection: Tangent fields and the dimensionality of their support,"Comput. Vision Graphics Image Processing, vol. 32, no. 1, pp. 74-103, 1985.

Index Terms:
scale space images; directional analysis; piecewise linear patterns; zero crossings; gradient images; 2-D Gaussian functions; stability map; orientation; scanning electron microscope images; collagen fibrils; rabbit ligaments; ligament healing; treatment methods; ligament injuries; biology computing; computer vision; filtering and prediction theory
Z.Q. Liu, R.M. Rangayyan, C.B. Frank, "Directional Analysis of Images in Scale Space," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 11, pp. 1185-1192, Nov. 1991, doi:10.1109/34.103277
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