Abstract
The fundamental problem of local scale selection is addressed by means of a novel principle, which is based on maximum likelihood estimation. The principle is generally applicable to a broad variety of image models and descriptors, and provides a generic scale estimation methodology.
The focus in this work is on applying this selection principle under a Brownian image model. This image model provides a simple scale invariant prior for natural images and we provide illustrative examples of the behavior of our scale estimation on such images. In these illustrative examples, estimation is based on second order moments of multiple measurements outputs at a fixed location. These measurements, which reflect local image structure, consist in the cases considered here of Gaussian derivatives taken at several scales and/or having different derivative orders.
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References
ter Haar Romeny, B.: Front-end vision and multi-scale image analysis. Computational Imaging and Vision Series, vol. 27. Kluwer Academic Publishers, Dordrecht (2003)
Lindeberg, T.: Feature detection with automatic scale selection. International Journal of Computer Vision 30(2), 79–116 (1998)
Lindeberg, T.: Edge detection and ridge detection with automatic scale selection. International Journal of Computer Vision 30(2), 117–154 (1998)
Majer, P.: A Statistical Approach to Feature Detection and Scale Selection in Images. PhD thesis, University of Göttingen (2000)
Pedersen, K.S., Nielsen, M.: The Hausdorff dimension and scale-space normalisation of natural images. Journal of Visual Communication and Image Representation 11(2), 266–277 (2000)
Papandreou, G., Maragos, P.: Image denoising in nonlinear scale-spaces: Automatic scale selection through cross-validatory model selection. In: Proceeding of the International Conference on Image Processing (ICIP’05), Genova, Italy, September 2005, IEEE Computer Society Press, Los Alamitos (2005)
Bouman, C.A., Sauer, K.: Maximum likelihood scale estimation for a class of Markov random fields. In: Proceedings of ICASSP ’94. IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 537–540. IEEE Computer Society Press, Los Alamitos (1994)
Loog, M., Pedersen, K.S., Markussen, B.: Maximum likely scale estimation. In: Fogh Olsen, O., Florack, L.M.J., Kuijper, A. (eds.) DSSCV 2005. LNCS, vol. 3753, pp. 146–156. Springer, Heidelberg (2005)
Pentland, A.P.: Fractal-based description of natural scenes. IEEE Transactions on Pattern Analysis and Machine Intelligence 6(6), 661–674 (1984)
Pedersen, K.S.: Properties of brownian image models in scale-space. In: Griffin, L.D., Lillholm, M. (eds.) Scale-Space 2003. LNCS, vol. 2695, pp. 281–296. Springer, Heidelberg (2003)
Mandelbrot, B.B., van Ness, J.W.: Fractional brownian motions, fractional noises and applications. SIAM Review 10(4), 422–437 (1968)
Pesquet-Popescu, B., Vehel, J.L.: Stochastic fractal models for image processing. IEEE Signal Processing Magazine 19(5), 48–62 (2002)
Lowe, D.: Object recognition from local scale-invariant features. In: Proc. of 7th ICCV, pp. 1150–1157 (1999)
Schmid, C., Mohr, R., Bauckhage, C.: Evaluation of interest point detectors. International Journal of Computer Vision 37(4), 151–172 (2000)
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Pedersen, K.S., Loog, M., Markussen, B. (2007). Generic Maximum Likely Scale Selection. In: Sgallari, F., Murli, A., Paragios, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2007. Lecture Notes in Computer Science, vol 4485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72823-8_31
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DOI: https://doi.org/10.1007/978-3-540-72823-8_31
Publisher Name: Springer, Berlin, Heidelberg
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