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Transactions on Computational Science XIII pp 13–43Cite as

A Computational-Geometry Approach to Digital Image Contour Extraction

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Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 6750))

Abstract

We present a simple method based on computational-geometry for extracting contours from digital images. Unlike traditional image processing methods, our proposed method first extracts a set of oriented feature points from the input images, then applies a sequence of geometric techniques, including clustering, linking, and simplification, to find contours among these points. Extensive experimental results on synthetic and natural images show that our method can effectively extract contours from both clean and noisy images. Experiments on the Berkeley Segmentation Dataset also show that our proposed computational-geometry method can be linked with any state-of-the-art pixel-based contour extraction algorithm to remove noise and close gaps without severely dropping the contour accuracy. Moreover, contours extracted by our method have a much more compact representation than contours obtained by traditional pixel-based methods. Such a compact representation allows more efficient extraction of shape features in subsequent computer vision and pattern recognition tasks.

Supported in part by NSF grant DBI-0743670 and an ADVANCE grant from Utah State University. A preliminary version of this paper appeared in the Proceedings of the 21st Canadian Conference on Computational Geometry (CCCG’09) [53].

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References

  1. Arbeláez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 33, 898–916 (2011)

    Article  Google Scholar 

  2. Asano, T., Brimkov, V.E., Barneva, R.P.: Some theoretical challenges in digital geometry: A perspective. Discrete Applied Mathematics 157, 3362–3371 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bai, X., Yang, X., Latecki, L.J.: Detection and recognition of contour parts based on shape similarity. Pattern Recognition 41, 2189–2199 (2008)

    Article  MATH  Google Scholar 

  4. Bentley, J.L., Shamos, M.I.: Divide-and-conquer in multidimensional space. In: Proceedings of the 8th Annual ACM Symposium on Theory of Computing, pp. 220–230 (1976)

    Google Scholar 

  5. Bespamyatnikh, S.N.: An optimal algorithm for closest pair maintenance. In: Proceedings of the 11th Annual Symposium on Computational Geometry, pp. 152–161 (1995)

    Google Scholar 

  6. Canny, J.: A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 8, 679–698 (1986)

    Article  Google Scholar 

  7. Chan, W.S., Chin, F.: Approximation of polygonal curves with minimum numbers of line segments or minimum error. International Journal of Computational Geometry and Applications 6, 59–77 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dollár, P., Tu, Z., Belongie, S.: Supervised learning of edges and object boundaries. In: Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2006), pp. 1964–1971 (2006)

    Google Scholar 

  9. Duda, R.O., Hart, P.E.: Use of the Hough transformation to detect lines and curves in pictures. Communications of the ACM 15, 11–15 (1972)

    Article  MATH  Google Scholar 

  10. Ebbers-Baumann, A., Klein, R., Langetepe, E., Lingas, A.: A fast algorithm for approximating the detour of a polygonal chain. Computational Geometry: Theory and Applications 27, 123–134 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Elder, J.H., Goldberg, R.M.: Ecological statistics of Gestalt laws for the perceptual organization of contours. Journal of Vision 2, 324–353 (2002)

    Article  Google Scholar 

  12. Elder, J.H., Krupnik, A., Johnston, L.A.: Contour grouping with prior models. IEEE Transactions on Pattern Analysis and Machine Intelligence 25, 661–674 (2003)

    Article  Google Scholar 

  13. Elder, J.H., Zucker, S.W.: Computing contour closure. In: Buxton, B.F., Cipolla, R. (eds.) ECCV 1996. LNCS, vol. 1064, pp. 399–412. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  14. Eu, D., Toussaint, G.T.: On approximating polygonal curves in two and three dimensions. CVGIP: Graphical Models and Image Processing 56, 231–246 (1994)

    Google Scholar 

  15. Felzenszwalb, P.F., Huttenlocher, D.P.: Efficient graph-based image segmentation. International Journal of Computer Vision 59, 167–181 (2004)

    Article  Google Scholar 

  16. Felzenszwalb, P., McAllester, D.: A min-cover approach for finding salient curves. In: Proceedings of the 2006 Conference on Computer Vision and Pattern Recognition Workshop (CVPRW 2006), pp. 185–185 (2006)

    Google Scholar 

  17. Freeman, H.: Computer processing of line drawings. ACM Computing Surveys 6, 57–97 (1974)

    Article  MATH  Google Scholar 

  18. Goodman, J.E., O’Rourke, J.: Handbook of Discrete and Computational Geometry, 2 ed. CRC Press, Boca Raton (2004)

    Book  MATH  Google Scholar 

  19. Goodrich, M.T., Tamassia, R.: Algorithm Design: Foundations, Analysis, and Internet Examples. John Wiley & Sons, Chichester (2002)

    MATH  Google Scholar 

  20. Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 3rd edn. Pearson Prentice Hall (2008)

    Google Scholar 

  21. Grigorescu, C., Petkov, N., Westenberg, M.A.: Contour detection based on nonclassical receptive field inhibition. IEEE Transactions on Image Processing 12, 231–236 (2003)

    MATH  Google Scholar 

  22. Guy, G., Medioni, G.: Inferring global perceptual contours from local features. International Journal of Computer Vision 20, 113–133 (1996)

    Article  Google Scholar 

  23. Haris, K., Efstratiadis, S.N., Maglaveras, N., Katsaggelos, A.K.: Hybrid image segmentation using watersheds and fast region merging. IEEE Transactions on Image Processing 7, 1684–1699 (1998)

    Article  Google Scholar 

  24. Heckbert, P.S., Garland, M.: Survey of polygonal surface simplification algorithms, Technical Report, Carnegie Mellon University, School of Computer Science (1997)

    Google Scholar 

  25. Hérault, L., Horaud, R.: Figure-ground discrimination: a combinatorial optimization approach. IEEE Transactions on Pattern Analysis and Machine Intelligence 15, 899–914 (1993)

    Article  Google Scholar 

  26. Hunt, G.C., Nelson, R.C.: Lineal feature extraction by parallel stick growing. In: Proceedings of the Third International Workshop on Parallel Algorithms for Irregularly Structured Problems, pp. 171–182 (1996)

    Google Scholar 

  27. Huttenlocher, D., Klanderman, G., Rucklidge, W.: Comparing images using the hausdorff distance. IEEE Transactions on Pattern Analysis and Machine Intelligence 15, 850–863 (1993)

    Article  Google Scholar 

  28. Huttenlocher, D., Olson, C.: Automatic target recognition by matching oriented edge pixels. IEEE Transactions on Image Processing 6, 103–113 (1997)

    Article  Google Scholar 

  29. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. International Journal of Computer Vision 1, 321–331 (1988)

    Article  MATH  Google Scholar 

  30. Klette, R., Rosenfeld, A.: Digital Geometry: Geometric Methods for Digital Picture Analysis. Morgan Kaufmann, San Francisco (2004)

    MATH  Google Scholar 

  31. Koffka, K.: Principles of Gestalt Psychology. Harcourt, Brace & Company, New York (1935)

    Google Scholar 

  32. Konishi, S., Yuille, A.L., Coughlan, J.M., Zhu, S.C.: Statistical edge detection: learning and evaluating edge cues. IEEE Transactions on Pattern Analysis and Machine Intelligence 25, 57–74 (2003)

    Article  Google Scholar 

  33. Latecki, L.J., Lakämper, R., Eckhardt, U.: Shape descriptors for non-rigid shapes with a single closed contour. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 424–429 (2000)

    Google Scholar 

  34. Mahamud, S., Williams, L.R., Thornber, K.K., Xu, K.: Segmentation of multiple salient closed contours from real images. IEEE Transactions on Pattern Analysis and Machine Intelligence 25, 433–444 (2003)

    Article  Google Scholar 

  35. Malik, J., Belongie, S., Leung, T., Shi, J.: Contour and texture analysis for image segmentation. International Journal of Computer Vision 43, 7–27 (2001)

    Article  MATH  Google Scholar 

  36. Mansouri, A., Malowany, A.S., Levine, M.D.: Line detection in digital pictures: A hypothesis prediction verification paradigm. Computer Vision, Graphics, and Image Processing 40, 95–114 (1987)

    Article  Google Scholar 

  37. Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings of the 8th International Conference on Computer Vision (ICCV 2001), pp. 416–423 (2001)

    Google Scholar 

  38. Martin, D.R., Fowlkes, C., Malik, J.: Learning to detect natural image boundaries using local brightness, color, and texture cues. IEEE Transactions on Pattern Analysis and Machine Intelligence 26, 530–549 (2004)

    Article  Google Scholar 

  39. Moore, G.A.: Automatic scanning and computer processes for the quantitative analysis of micrographs and equivalent subjects. Pattern Recognition: Pictorial Pattern Recognition 1, 275–326 (1969)

    Google Scholar 

  40. Nelson, R.C.: Finding line segments by stick growing. IEEE Transactions on Pattern Analysis and Machine Intelligence 16, 519–523 (1994)

    Article  Google Scholar 

  41. Nevatia, R., Babu, K.R.: Linear feature extraction and description. Computer Graphics and Image Processing 3, 257–269 (1980)

    Article  Google Scholar 

  42. Paparilow, G., Petkov, N.: Edge and line oriented contour detection: state of the art. Image and Vision Computing 29, 79–103 (2011)

    Article  Google Scholar 

  43. Pelli, D.G., Majaj, N.J., Raizman, N., Christian, C.J., Kim, E., Palomares, M.C.: Grouping in object recognition: The role of a Gestalt law in letter identification. Cognitive Neuropsychology 26, 36–49 (2009)

    Article  Google Scholar 

  44. Ren, M., Yang, J., Sun, H.: Tracing boundary contours in a binary image. Image and Vision Computing 20, 125–131 (2002)

    Article  Google Scholar 

  45. Ren, X.: Multi-scale improves boundary detection in natural images. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part III. LNCS, vol. 5304, pp. 533–545. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  46. Robinson, G.S.: Detection and coding of edges using directional masks. In: Proceedings SPIE Conference on Advances in Image Transmission Techniques, pp. 117–125 (1976)

    Google Scholar 

  47. Sarkar, S., Boyer, K.L.: Quantitative measures of change based on feature organization: eigenvalues and eigenvectors. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 1996), pp. 478–483 (1996)

    Google Scholar 

  48. Sha’ashua, A., Ullman, S.: Structural saliency: the detection of globally salient structures using a locally connected network. In: Second International Conference on Computer Vision (ICCV 1988), pp. 321–327 (1988)

    Google Scholar 

  49. Sobel, I.E.: Camera models and machine perception, Ph.D. dissertation, Stanford University, CA, USA (1970)

    Google Scholar 

  50. Shotton, J., Blake, A., Cipolla, R.: Multiscale categorical object recognition using contour fragments. IEEE Transactions on Pattern Analysis and Machine Intelligence 30, 1270–1281 (2008)

    Article  Google Scholar 

  51. Stahl, J.S., Oliver, K., Wang, S.: Open boundary capable edge grouping with feature maps. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPRW 2008), pp. 1–8 (2008)

    Google Scholar 

  52. Stahl, J.S., Wang, S.: Convex grouping combining boundary and region information. In: Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV 2005), pp. 946–953 (2005)

    Google Scholar 

  53. Tejada, P.J., Qi, X., Jiang, M.: Computational geometry of contour extraction. In: Proceedings of the 21st Canadian Conference on Computational Geometry (CCCG 2009), pp. 25–28 (2009)

    Google Scholar 

  54. Toussaint, G.T.: Computational geometry and computer vision. Contemporary Mathematics 119, 213–224 (1991)

    Article  MATH  Google Scholar 

  55. Wang, S., Ge, F., Liu, T.: Evaluating edge detection through boundary detection. EURASIP Journal on Applied Signal Processing 2006, 1–15 (2006)

    Google Scholar 

  56. Wang, S., Kubota, T., Siskind, J.M., Wang, J.: Salient closed boundary extraction with ratio contour. IEEE Transactions on Pattern Analysis and Machine Intelligence 27, 546–561 (2005)

    Article  Google Scholar 

  57. Wang, S., Siskind, J.M.: Image segmentation with ratio cut. IEEE Transactions on Pattern Analysis and Machine Intelligence 25, 675–690 (2003)

    Article  Google Scholar 

  58. Williams, L.R., Jacobs, D.W.: Stochastic completion fields: a neural model of illusory contour shape and salience. In: Proceedings of the Fifth International Conference on Computer Vision (ICCV 1995), pp. 408–415 (1995)

    Google Scholar 

  59. Williams, L.R., Thornber, K.K.: A comparison of measures for detecting natural shapes in cluttered backgrounds. International Journal of Computer Vision 34, 81–96 (1999)

    Article  Google Scholar 

  60. Zhu, Q., Song, G., Shi, J.: Untangling cycles for contour grouping. In: Proceedings of the 11th IEEE International Conference on Computer Vision (ICCV 2007), pp. 1–8 (2007)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Utah State University, Logan, Utah, 84322-4205, USA

    Minghui Jiang, Xiaojun Qi & Pedro J. Tejada

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  1. Minghui Jiang
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  2. Xiaojun Qi
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  3. Pedro J. Tejada
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  1. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  2. Exascala Ltd., Unit 9, 97 Rickman Drive, B15 2AL, Birmingham, UK

    C. J. Kenneth Tan

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Jiang, M., Qi, X., Tejada, P.J. (2011). A Computational-Geometry Approach to Digital Image Contour Extraction. In: Gavrilova, M.L., Tan, C.J.K. (eds) Transactions on Computational Science XIII. Lecture Notes in Computer Science, vol 6750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22619-9_2

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  • DOI: https://doi.org/10.1007/978-3-642-22619-9_2

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