Abstract
The parametric model of a certain class of characteristic intensity variations in Rohr (1990, 1992), which is the superposition of elementary model functions, is employed to identify corners in images. Estimates of the searched model parameters characterizing completely single grey-value structures are determined by a least-squares fit of the model to the observed image intensities applying the minimization method of Levenberg-Marquardt. In particular, we develop an analytical approximation of our model in such a way that function values can be calculated without numerical integration. Assuming the blur of the imaging system to be describable by Gaussian convolution our approach permits subpixel localization of the corner position of the unblurred grey-value structures, that is, to reverse the blur of the imaging system. By fitting our model to the original as well as to the smoothed original-image cues can be obtained for finding out whether the underlying model is an adequate description or not. Results are shown for real image data.
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Abramowitz, M., and Stegun, I.A. 1965.Handbook of Mathematical Functions: Dover Publications: New York
Beaudet, P.R. 1978. Rotationally invariant image operators,Proc. Intern. conf. Patt. Recog. Kyoto/Japan, pp. 579–583, November.
Bergholm, F. 1987. Edge focusing,IEEE Trans. Patt. Anal. Mach. Intell. 9: 726–741.
Bergholm, F. and Rohr, K. 1991. A comparison between two approaches applied for estimating diffuseness and height of step edges, Hausbericht Nr. 10262, Fraunhofer-Institut für Informations- und Datenverarbeitung (IITB), Karlsruhe/FR; and Tech. Rept. TRITA-NA-P9105, CVAP 83, Dept. of Num. Analysis and Comput. Science, Royal Institute of Technology, Stockholm. March.
Berzins, V. 1984. Accuracy of Laplacian edge detectors,Comput. Vis. Graph. Image Process. 27: 195–210.
Beymer, D.J. 1991. Finding junctions using the image gradient,Proc. Conf. Comput. Vis. Patt. Recog., Maui, Hawaii, June 3–6, pp. 720–721.
Bronstein, I.N., and Semendjajew, K.A. 1981.Taschenbuch der Mathematik, 19. Auflage, Verlag Harri Deutsch, Thun und Frankfurt/Main.
Canny, F. 1986. A computational approach to edge detection,IEEE Trans. Patt. Anal. Mach. Intell. 8:679–698.
Deriche, R., and Giraudon, G. 1990. Accurate corner detection: An analytical study,Proc. 3rd Intern. Conf. Comput. Vis. Dec. 4–7, Osaka/Japan, pp. 66–70, December.
Dreschler, L., and Nagel, H.-H. 1981. Volumetric model and 3D trajectory of a moving car derived from monocular TV-frame sequences of a street seene,Proc. Intern. Joint Conf. Artif, Intell., Vancouver, pp. 692–697: see alsoComput. Graph. Image Process. 20: 199–228, 1982.
Förstner, W. 1986. A feature based correspondence algorithm for image matching,Intern. Arch. Photogrammetry Remote Sens. 26(3/3):150–166.
Giraudon, G., and Deriche, R. 1991. On corner and vertex detection,Proc. Conf. Comput. Vis. Patt. Recog., Maui, Hawaii, pp. 650–655, June.
Guiducci, A. 1988. Corner characterization by differential geometry techniques.Patt. Recog. Lett. 8:311–318.
Hueckel, M.H. 1971. An operator which locates edges in digitized pictures,J. Assoc. Comput. Mach. 18(1):113–125.
Hueckel, M.H. 1973. A local visual operator which recognizes edges and lines,J. Assoc. Comput. Mach. 20(4):634–647.
Kitchen, L., and Rosenfeld, A. 1982. Gray-level corner detection,Patt. Recog. Lett. 1:95–102.
Korn, A. 1988. Towards a symbolic representation of intensity changes in images,IEEE Trans. Patt. Anal. Mach. Intell. 10: 610–625.
Li, D., Sullivan, G.D., and Baker, K.D. 1989. Edge detection at junctions,Proc. 5th Alvey Vision Conf., University of Reading. Reading/UK, pp. 121–125. September.
Marquardt, D. 1963. An algorithm for least-squares estimation of nonlinear parameters,J. Soc. Indust. Appl. Math. 11:431–441.
Marr, D., and Hildreth, E. 1980. Theory of edge detection,Proc. Roy. Soc. London B 207:187–217.
De, Micheli, E., Caprile, B., Ottonello, P., and Torre, V. 1989. Localization and noise in edge detection.IEEE Trans. Patt. Anal. Mach. Intell. 11:1106–1117.
Nalwa, V.S., and Binford, T.O. 1986. On detecting edges.IEEE Trans. Patt. Anal. Mach. Intell. 8(6):699–714.
Noble, J.A. 1987. Finding corners,Proc. 3rd Alvey Vision Conf., University of Cambridge, Cambridge/UK, pp. 267–274, September.
Powell, M.J.D. 1964. An efficient method for finding the minimum of a function of several variables without calculating derivatives.Computer Journal 7:155–162.
Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. 1988.Numerical Recipes, Cambridge University Press, Cambridge and New York.
Rangarajan, K., Shah, M. and Van, Brackle, D. 1989. Optimal corner detector.Comput. Vis. Graph. Image process. 48:230–245.
Rohr, K. 1990. Über die Modellierung und Identifikation charakteristischer Grauwertverläufe in Realweltbildern,12, DAGM—Symposium Mustererkennung, September, Oberkochen-Aalen, Informatik-Fachberichte 254, R.E., Großkopf (Hrsg.), Springer-Verlag Berlin Heidelberg, pp. 217–224.
Rohr, K. 1992. Modelling and identification of characteristic intensity variations,Image Vis. Comput. 10(2):66–76.
Rohr, K., and Schnörr, C. 1992. An efficient approach for identification of characteristic intensity variations, Tech. Rept. FBI-HH-M-242/92, FB Informatik, Universität Hamburg.
Waltz, D. 1975. Understanding line drawings of scenes with shadows, inThe Psychology of Computer Vision, P.H., Winston (ed.), McGraw-Hill, New York, pp. 19–91.
Zhang, W., and Bergholm, F. 1991. An extension of Marr's “signature” based edge classification,7th Scandinavian Conf. Image Anal., Aalborg/Denmark, August.
Zuniga, O.A., and Haralick, R.M. 1983. Corner detection using the facet model,Proc. IEEE Conf. Comput. Vis. Patt. Recog. Washington D.C., pp. 30–37, June 19–23.
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Rohr, K. Recognizing corners by fitting parametric models. Int J Comput Vision 9, 213–230 (1992). https://doi.org/10.1007/BF00133702
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DOI: https://doi.org/10.1007/BF00133702