Abstract
In this paper we address the problem of appropriately representing the intrinsic dimensionality of image neighborhoods. This dimensionality describes the degrees of freedom of a local image patch and it gives rise to some of the most often applied corner and edge detectors. It is common to categorize the intrinsic dimensionality (iD) to three distinct cases: i0D, i1D, and i2D. Real images however contain combinations of all three dimensionalities which has to be taken into account by a continuous representation. Based on considerations of the structure tensor, we derive a cone-shaped iD-space which leads to a probabilistic point of view to the estimation of intrinsic dimensionality.
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References
Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press, New York (1995)
Trunk, G.V.: Representation and analysis of signals: statistical estimation of intrinsic dimensionality and parameter identification. General System 13, 49–76 (1968)
Zetzsche, C., Barth, E.: Fundamental limits of linear filters in the visual processing of two dimensional signals. Vision Research 30 (1990)
Krieger, G., Zetzsche, C.: Nonlinear image operators for the evaluation of local intrinsic dimensionality. IEEE Transactions on Image Processing 5, 1026–1041 (1996)
Granlund, G.H., Knutsson, H.: Signal Processing for Computer Vision. Kluwer Academic Publishers, Dordrecht (1995)
Jähne, B.: Digitale Bildverarbeitung. Springer, Berlin (1997)
Bülow, T.: Hypercomplex Spectral Signal Representations for the Processing and Analysis of Images. PhD thesis, Christian-Albrechts-University of Kiel (1999)
Felsberg, M., Sommer, G.: Image features based on a new approach to 2D rotation invariant quadrature filters. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2350, pp. 369–383. Springer, Heidelberg (2002)
Förstner, W., Gülch, E.: A fast operator for detection and precise location of distinct points, corners and centres of circular features. In: ISPRS Intercommission Workshop, Interlaken, pp. 149–155 (1987)
Bigün, J., Granlund, G.H.: Optimal orientation detection of linear symmetry. In: Proceedings of the IEEE First International Conference on Computer Vision, London, Great Britain, pp. 433–438 (1987)
Förstner, W.: Statistische Verfahren für die automatische Bildanalyse und ihre Bewertung bei der Objekterkennung und -vermessung. C. Verlag der Bayerischen Akademie der Wissenschaften, vol. 370 (1991)
Ramanathan, J.: Methods of Applied Fourier Analysis. Birkhäuser, Basel (1998)
Farnebäck, G.: Fast and accurate motion estimation using orientation tensors and parametric motion models. In: Proceedings of 15th International Conference on Pattern Recognition (IAPR), vol. 1, pp. 135–139 (2000)
Bracewell, R.N.: The Fourier transform and its applications. McGraw Hill, New York (1986)
Harris, C.G., Stephens, M.: A combined corner and edge detector. In: 4th Alvey Vision Conference, pp. 147–151 (1988)
Krüger, N.: Learning object representations using a priori constraints within ORASSYLL. Neural Computation 13, 389–410 (2001)
Coexeter, H.S.M.: Introduction to Geometry, 2nd edn. Wiley & Sons, Chichester (1969)
Canny, J.: A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 8, 679–698 (1986)
Krüger, N., Felsberg, M.: A continuous formulation of intrinsic dimension. In: British Machine Vision Conference (2003) (submitted)
Felsberg, M.: Low-Level Image Processing with the Structure Multivector. PhD thesis, Institute of Computer Science and Applied Mathematics, Christian-Albrechts-University of Kiel, TR no. 0203 (2002), available at http://www.informatik.uni-kiel.de/reports/2002/0203.html
Krüger, N., Lappe, M., Wörgötter, F.: Biologically motivated multi-modal processing of visual primitives. In: AISB 2003 Convention: Cognition in Machines and Animals, Wales (2003)
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Felsberg, M., Krüger, N. (2003). A Probabilistic Definition of Intrinsic Dimensionality for Images. In: Michaelis, B., Krell, G. (eds) Pattern Recognition. DAGM 2003. Lecture Notes in Computer Science, vol 2781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45243-0_19
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DOI: https://doi.org/10.1007/978-3-540-45243-0_19
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