The nature of statistical learning theory
The nature of statistical learning theory
IEEE Transactions on Pattern Analysis and Machine Intelligence
Gaussian Scale-Space Theory
Pseudo-Linear Scale-Space Theory
International Journal of Computer Vision
Bayesian Detection of Random Signals on Random Backgrounds
IPMI '97 Proceedings of the 15th International Conference on Information Processing in Medical Imaging
Bayesian Detection with Amplitude, Scale, Orientation and Position Uncertainty
IPMI '97 Proceedings of the 15th International Conference on Information Processing in Medical Imaging
Linear Transformation Groups and Shape Space
Journal of Mathematical Imaging and Vision
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
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Object detection and localization are common tasks in image analysis. Correlation based detection algorithms are known to work well, when dealing with objects with known geometry in Gaussianly distributed additive noise. In the Bayes' view, correlation is linearly related to the logarithm of the probability density, and optimal object detection is obtained by the integral of the exponentiated squared correlation under appropriate normalization. Correlation with a model is linear in the input image, and can be computed effectively for all possible positions of the model using Fourier based linear filtering techniques. It is therefore interesting to extend the application to objects with many but small degrees of freedom in their geometry. These geometric variations deteriorate the linear correlation signal, both regarding its strength and localization with multiple peaks from a single object. Localization is typically preferred over detection, and Bayesian localization may be obtained as local integration of the probability density. In this work, Gaussian kernels of the exponentiated correlation are studied, and the use of Linear Scale-Space allows us to extend the Bayes detection with a well-posed localization, to extend the usage of correlation to a larger class of shapes, and to argue for the use of mathematical morphology with quadratic structuring elements on correlation images.