Wavelet transform methods for object detection and recovery

Abstract
We show that a biorthogonal spline wavelet closely approximates the prewhitening matched filter for detecting Gaussian objects in Markov noise. The filterbank implementation of the wavelet transform acts as a hierarchy of such detectors operating at discrete object scales. If the object to be detected is Gaussian and its scale happens to coincide with one of those computed by the wavelet transform, and if the background noise is truly Markov, then optimum detection is realized by thresholding the appropriate subband image. In reality, the Gaussian may be a rather coarse approximation of the object, and the background noise may deviate from the Markov assumption. In this case, we may view the wavelet decomposition as a means for computing an orthogonal feature set for input to a classifier. We use a supervised linear classifier applied to feature vectors comprised of samples taken from the subbands of an N-octave, undecimated wavelet transform. The resulting map of test statistic values indicates the presence and location of objects. The object itself is reconstructed by using the test statistic to emphasize wavelet subbands, followed by computing the inverse wavelet transform. We show two contrasting applications of the wavelets-based object recovery algorithm. For detecting microcalcifications in digitized mammograms, the object and noise models closely match the real image data, and the multiscale matched filter paradigm is highly appropriate. The second application, extracting ship outlines in noisy forward-looking infrared images, is presented as a case where good results are achieved despite the data models being less well matched to the assumptions of the algorithm.

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