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.

Wavelet transform methods for object detection and recovery

This article addresses the development of and recent advances in the rapidly growing field of optical pattern recognition. In optical pattern recognition there are two basic approaches; namely, matched filtering and associative memories. The first employs optical correlator architectures and the latter uses optical neural networks (NNs). This paper reviews various types of optical correlators and NNs applied to real-time pattern recognition and autonomous tracking. Techniques of scale and rotational invariant filtering are also given. Recent approaches using wavelet transform filtering, phase only filtering, high capacity composite filters and phase representation for improvement in pattern discrimination are also provided.

Optical pattern recognition: architectures and techniques

In recent years, correlation-filter (CF)-based face recognition algorithms have attracted increasing interest in the field of pattern recognition and have achieved impressive results in discrimination, efficiency, location accuracy, and robustness. In this tutorial paper, our goal is to help the reader get a broad overview of CFs in three respects: design, implementation, and application. We review typical face recognition algorithms with implications for the design of CFs. We discuss and compare the numerical and optical implementations of correlators. Some newly proposed implementation schemes and application examples are also presented to verify the feasibility and effectiveness of CFs as a powerful recognition tool.

New perspectives in face correlation research: a tutorial

Fourier optics has offered a powerful global information analysis and processing tool to optical domain signals and images and firmly locked its respectable position in the history of optics. The evolution of wavelet theory in the past decade, which has created significant impacts on many areas of information science and engineering, has recently been frequently mentioned in the optics community. Whether or not this locality-oriented signal analysis and processing tool can play a comparably significant role in optics remains to be answered. The present paper is intended to summarize important developments and recent progress in areas where novel wavelet processing concepts are incorporated into optics research.

Wavelet processing and optics

We describe a joint wavelet-transform correlator in which the wavelet function is combined with the input image as the input joint image to realize the wavelet transform of the objective image. The Haar wavelet and the Roberts filter are chosen as the wavelet functions to extract the features of the objective image. The relationship of the Haar wavelet and the Roberts filter is analyzed mathematically based on admissible condition of the wavelet. Computer simulations are provided to verify the theory and to illustrate the performance of this correlator.

Joint wavelet-transform correlator for image feature extraction

A joint transform correlation system based on wavelet transforms is introduced. The selection of wavelets and the optical wavelet transform of images enables this optical correlator to identify the specific features and distinguish similar characters. Preliminary experimental results are given.

X. J. Lu

Papers

Joint transform correlator that uses wavelet transforms