Taking advantage of the new developments in mathematical statistics, a multiscale approach is designed to detect filament or filament-like features in noisy images. The major contribution is to introduce a general framework in cases when the data is digital. Our detection method can detect the presence of an underlying curvilinear feature with the lowest possible strength that are still detectible in theory. Simulation results on synthetic data will be reported to illustrate its effectiveness in finite digital situations.
In target recognition applications of discriminant of classification analysis, each 'feature' is a result of a convolution of an imagery with a filter, which may be derived from a feature vector. It is important to use relatively few features. We analyze an optimal reduced-rank classifier under the two-class situation. Assuming each population is Gaussian and has zero mean, and the classes differ through the covariance matrices: ∑1 and ∑2. The following matrix is considered: Λ=(∑1+∑2)-1/2∑1(∑1+∑2)-1/2. We show that the k eigenvectors of this matrix whose eigenvalues are most different from 1/2 offer the best rank k approximation to the maximum likelihood classifier. The matrix Λ and its eigenvectors have been introduced by Fukunaga and Koontz; hence this analysis gives a new interpretation of the well known Fukunaga-Koontz transform. The optimality that is promised in this method hold if the two populations are exactly Guassian with the same means. To check the applicability of this approach to real data, an experiment is performed, in which several 'modern' classifiers were used on an Infrared ATR data. In these experiments, a reduced-rank classifier-Tuned Basis Functions-outperforms others. The competitive performance of the optimal reduced-rank quadratic classifier suggests that, at least for classification purposes, the imagery data behaves in a nearly-Gaussian fashion.
We describe a multiscale pyramid of line segments and develop algorithms which exploit that pyramid to recover image features - lines, curves, and blobs - from very noisy data.
Recently many new methods of image representation have been proposed, including wavelets, cosine packets, brushlets, edgelets, and ridgelets. Typically each of these is good for a specific class of features, but not good for others. We propose method of combining two image representations based on 2D wavelet transform and edgelet transform. The 2D wavelet transform is good at capturing point singularities, while the newly proposed edgelet transform is good at capturing linear singularities (edges). Both transforms have fast algorithms for digital images.
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