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Localization properties of direct corner detectors

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Abstract

In the past, several approaches for directly determining corners in gray-value images have been introduced. The accuracy of an approach has usually been demonstrated experimentally by comparing its results with those obtained by previous schemes. In this contribution we analyze localization properties of existing direct corner detectors by using an analytical model of gray-value corners. For the different approaches we derive implicit equations constraining the corner points and numerically evaluate their locations. Since a gray-value corner is generally defined as the curvature extremum along the edge line, we also compute this position and take it as the reference location for a comparison of the investigated approaches.

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References

  1. P.R. Beaudet, “Rotationally invariant image operators,” inProc. International Joint Conference on Pattern Recognition, Kyoto, Japan, 1978, pp. 579–583.

  2. F. Bergholm, “Edge focusing,”IEEE Trans. Patt. Anal. Mach. Intell., vol. PAMI 9, pp. 726–741, 1987.

    Google Scholar 

  3. F. Bergholm and K. Rohr, “A comparison between two approaches applied for estimating diffuseness and height of step edges,” Fraunhofer Institute for Information and Data Processing (IITB), Karlsruhe, Germany, House Rep. 10262, 1991; see also Department of Analysis and Computing Science, Royal Institute of Technology, Stockholm, Tech. Rep. TRITA-NA-P9105, CVAP 83, 1991.

    Google Scholar 

  4. V. Berzins, “Accuracy of Laplacian edge detectors,”Comput. Vis., Graph., Image Process., vol. 27, pp. 195–210, 1984.

    Google Scholar 

  5. J. Blom, B.M. ter Haar Romeny, and J.J. Koenderink, “Affine invariant corner detection,” submitted for publication; see also J. Blom, “Topological and geometrical aspects of image structure,” doctoral dissertation, University of Utrecht, The Netherlands, 1992.

  6. I.N. Bronstein and K.A. Semendjajew,Taschenbuch der Mathematik, 19th ed., Verlag Harri Deutsch: Frankfurt, 1981.

    Google Scholar 

  7. K. Brunnström, T. Lindeberg, and J.-O. Eklundh, “Active detection and classification of junctions by foveation with a head-eye system guided by the scale-space primal sketch,” inProc. 2nd European Conference on Computer Vision, S. Margherita, Italy, 1992; Lecture Notes in Computer Science, vol. 588, G. Sandini, (ed.), Springer-Verlag: Berlin, pp. 701–709, 1992.

    Google Scholar 

  8. F. Canny, “A computational approach to edge detection,”IEEE Trans. Patt. Anal. Mach. Intell., vol. PAMI-8, pp. 679–698, 1986.

    Google Scholar 

  9. R. Deriche and G. Giraudon, “Accurate corner detection: an analytical study,” inProc. 3rd International Conference on Computer Vision, Osaka, Japan, 1990, pp. 66–70.

  10. L. Dreschler, “Zur Reproduzierbarkeit von markanten Bildpunkten bei der Auswertung von Realwelt-Bildfolgen,” inModelle und Strukturen, DAGM Symposium, Hamburg, Germany, 1981, Informatik-Fachberichte 49, B. Radig, ed., Springer-Verlag: Berlin, 1981, pp. 76–82.

    Google Scholar 

  11. L. Dreschler and H.-H. Nagel, “Volumetric model and 3D-trajectory of a moving car derived from monocular TV-frame sequences of a street scene,” inProc. International Joint Conference of Artificial Intelligence, Vancouver, Canada, 1981, pp. 692–697; see alsoComputer Graph. Image Process. vol. 20, pp. 199–228, 1982.

  12. W. Förstner, “On the geometric precision of digital correlation,”Int. Arch. Photogramm. Remote Sensing, vol. 24, pp. 176–189, 1982.

    Google Scholar 

  13. W. Förstner, “A feature based correspondence algorithm for image matching,”Int. Arch. Photogramm. Remote Sensing vol. 26, pp. 150–166, 1986.

    Google Scholar 

  14. G. Giraudon and R. Deriche, “On corner and vertex detection,” inProc. IEEE Conference on Computer Vision and Pattern Recognition Lahaina, Maui, Hawaii, 1991, pp. 650–655.

    Google Scholar 

  15. A. Guiducci, “Corner characterization by differential geometry techniques,”Patt. Recog. Let., vol. 8, pp. 311–318, 1988.

    Google Scholar 

  16. L. Kitchen and A. Rosenfeld, “Gray-level corner detection,”Patt. Recog. Lett., vol. 1, pp. 95–102, 1982.

    Google Scholar 

  17. A. Korn, “Toward a symbolic representation of intensity changes in images,”IEEE Trans. Patt. Anal. Mach. Intell., vol. PAMI-10, pp. 610–625, 1988.

    Google Scholar 

  18. J. Martinet,Singularities of Smooth Functions and Maps, London Mathematical Society Lecture Note Series 58, Cambridge U. Press: Cambridge, England, 1982.

    Google Scholar 

  19. E. De Micheli, B. Caprile, P. Ottonello, and V. Torre, “Localization and noise in edge detection,”IEEE Trans. Patt. Anal. Mach. Intell., vol. PAMI-11, pp. 1106–1117, 1989.

    Google Scholar 

  20. H.-H. Nagel, “Displacement vectors derived from second-order intensity variations in image sequences,”Comput. Vis., Graph., Image Process., vol. 21, pp. 85–117, 1983.

    Google Scholar 

  21. H.-H. Nagel, “Constraints for the estimation of displacement vector fields from image sequences,”Proc. International Joint Conference on Artificial Intelligence, Karlsruhe, Germany, 1983, pp. 945–951.

  22. J.A. Noble, “Finding corners,” inProc. 3rd Alvey Vision Conference, Cambridge, England, 1987, pp. 267–274.

  23. J.H. Rieger, “Generic properties of edges and ‘corners’ on smooth greyvalue surfaces,”Biol. Cybernet. vol. 66, pp. 497–502, 1992.

    Google Scholar 

  24. K. Rohr, “Untersuchung von grauwertabhängigen Transformationen zur Ermittlung des optischen Flusses in Bildfolgen,” Diplomarbeit, Institut für Nachrichtensysteme, Universität Karlsruhe, Germany, 1987.

    Google Scholar 

  25. K. Rohr, “Über die Modellierung und Identifikation charakteristischer Grauwertverläufe in Realweltbildern,” in12th DAGM — Symposium Mustererkennung, Informatik-Fachberichte 254, R.E. Großkopf, ed., Springer-Verlag: Berlin, 1990, pp. 217–224.

    Google Scholar 

  26. K. Rohr, “Modelling and identification of characteristic intensity variations,”Image Vis. Comput., vol. 10, pp. 66–76, 1992.

    Google Scholar 

  27. K. Rohr, “Recognizing corners by fitting parametric models,”Int. J. Comput. Vis., vol. 9, pp. 213–230, 1992.

    Google Scholar 

  28. K. Rohr and C. Schnörr, “An efficient approach to the identification of characteristic intensity variations,”Image Vis. Comput., vol. 11, pp. 273–277, 1993.

    Google Scholar 

  29. M.A. Shah and R. Jain, “Detecting time-varying corners,”Proc. 7th International Conference on Pattern Recognition, Montreal, Canada, 1984, pp. 2–5.

  30. O.A. Zuniga and R.M. Haralick, “Corner detection using the facet model,” inProc. IEEE Conference on Computer Vision and Pattern Recognition, Washington, D.C. 1983, pp. 30–37.

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Authors and Affiliations

  1. Arbeitsbereich Kognitive Systeme, Fachbereich Informatik, Universität Hamburg, Vogt-Kölln-Str. 30, D-22527, Hamburg, Germany

    Karl Rohr

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  1. Karl Rohr
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Additional information

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) and by the European Union (EU), ESPRIT-Project VIVA (Viewpoint Invariant Visual Acquisition).

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Rohr, K. Localization properties of direct corner detectors. J Math Imaging Vis 4, 139–150 (1994). https://doi.org/10.1007/BF01249893

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