Joint transform correlator that uses wavelet transforms

Wavelet filter for improving detection performance of compression-based joint transform correlator

A new method for improving fingerprint detections by a compression-based joint transform correlator (JTC) via wavelet filter is proposed. The simulation results show that the proposed method has advantages over the conventional compression-based JTC in that detection performance can be maximized to be higher than a classical JTC by using a smaller file size for the compressed-reference images.

Liquid crystal polarization-converting devices for edge and corner extractions of images using optical wavelet transforms

Optical properties of radially polarized light generated by liquid crystal (LC) polarization-converting devices with two LC molecular orientations (+/-180 degrees and +/-90 degrees twist modes) are measured and the applicability to optical wavelet transforms (WTs) are discussed. It is found that the radially polarized lights in both the +/-180 degrees and +/-90 degrees twist modes can be regarded as wavelets. Based on the principle of WT, feature extractions of a simple binary image are carried out by applying the LC polarization-converting device to a shadow-casting system. Unique feature extraction properties of the shadow-casting system using the LC polarization-converting device and a LC microlens array are discussed. It is experimentally confirmed that edge and corner features are successfully extracted using the LC polarization-converting device with +/-180 degrees and +/-90 degrees twist modes, respectively.

Two-dimensional optical wavelet decomposition with white-light illumination by wavelength multiplexing

We present a novel method for achieving in real time a two-dimensional optical wavelet decomposition with white-light illumination. The underlying idea of the suggested method is wavelength multiplexing. The information in the different wavelet components of an input object is transmitted simultaneously in different wavelengths and summed incoherently at the output plane. Experimental results show the utility of the new proposed method.

Morphologically preprocessed joint transform correlation

A morphologically preprocessed joint transform correlation is proposed that combines the techniques of morphological filtering and joint transform correlation. We improve on the performance of a joint transform correlator by eliminating noise with morphological preprocessing and by performing edge detection of input images. Computer simulation results show that the corresponding system contributes to a better discrimination capability than gradient operator-based and wavelet-based preprocessed joint transform correlation.

Continuous two-dimensional on-axis optical wavelet transformer and wavelet processor with white-light illumination

The wavelet transform can be expressed mathematically as a convolution between the input function and a continuous set of scaled wavelet mother functions. Optics has managed to implement only the hybrid wavelet transform in which the set of scaled wavelet mother functions is discrete but the shift is continuous. White-light illumination is used to obtain a two-dimensional, fully continuous, on-axis wavelet transformer. When the illumination source is also spatially incoherent, a complete wavelet processor may be constructed.

Improved Feature Extraction by use of a Joint Wavelet Transform Correlator

A new joint wavelet transform correlation-based technique is proposed for feature extraction such as the detection of edges in an unknown input scene. We exploited a modified version of the Roberts and the Sobel wavelet filters as reference images for extracting the edges of an unknown input scene. The performance of the proposed technique with the aforementioned wavelet filters is evaluated and compared by use of numerical simulations. For noise-free input scenes the Roberts wavelet filter was found to yield a superior output compared with that of the Sobel wavelet filter. However, for noisy input scenes the Sobel wavelet filter was found to yield a better output compared with the Roberts wavelet filter.

Joint wavelet representation correlator for pattern recognition

A joint wavelet representation correlator is proposed as a newarchitecture to combine wavelets and the joint transformcorrelator. It performs wavelet representation preprocessing andthe correlation operation simultaneously. An intensity filter usedfor wavelet representation is the power spectrum of the waveletfunction and can easily be synthesized and displayed. Computersimulation shows that, as compared with previous joint wavelettransform correlators, its discrimination capability is better and itsperformance is more stable under input noise.

Application of nonlinearity to wavelet-transformed images to improve correlation filter performance

A useful filter for pattern recognition must strike a compromise between the conflicting requirements of in-class distortion tolerance and out-of-class discrimination. Such a filter will be bandpass in nature, the high-frequency response being attenuated to provide less sensitivity to in-class variations, while the low frequencies must be removed, since they compromise the discrimination ability of the filter. A convenient bandpass is the difference of Gaussian (DOG) function, which provides a close approximation to the Laplacian of Gaussian. We describe the effect of a preprocessing operation applied to a DOG filtered image. This operation is shown to result in greater tolerance to in-class variation while maintaining an excellent discrimination ability. Additionally, the introduction of nonlinearity is shown to provide greater robustness in the filter response to noise and background clutter in the input scene.

Wavelet transform methods for object detection and recovery

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.

Two-dimensional wavelet transform by wavelength multiplexing

The wavelet transform is a useful tool for data compression, analysis of short transient pulses, optical correlators, etc. This transform was obtained optically by the use of the spatial or temporal multiplexing approaches. A two-dimensional wavelet transform is obtained with only one spatial channel. The information of the different scalings is carried in different wavelengths and summed incoherently at the output plane. Laboratory experimental results are demonstrated.

Two-dimensional wavelet processor

An optical implementation of the two-dimensional (2-D) wavelet transform and inverse wavelet transform is performed in real time by the exploitation of a new multichannel system that processes the different daughter wavelets separately. The so-coined wavelet-processor system relies on a multichannel replication array generated that uses a Dammann grating and is able to handle every wavelet function. All channels process in parallel using a conventional 2-D correlator. Experimental results applying the Mexican-hat wavelet-decomposition technique are presented.

Optical wavelet transform by the phase-only joint-transform correlator

A method is presented that performs the optical wavelet transform with liquid-crystal televisions as spatial light modulators operating only on the phase of the incident coherent light. The architecture is the joint-transform correlator, and the wavelets and the image to be transformed are encoded in the input plane of the system. The mathematical formalism describing the adaptation of the joint-transform correlator to the wavelet transform is given and extended to the operation of the phase-only joint-transform correlator. A new wavelet is described for two-dimensional image processing, and experimental results are presented for optical wavelet transforms done in real time by use of this wavelet in the phase-only joint-transform-correlator architecture. The analysis is extended to multiwavelet (multispectral) analysis by the joint-transform correlator, and simulation results are given. Finally experimental results with the phase-only joint-transform correlator applied to multi-wavelet analysis are presented.

Joint wavelet-transform correlator for image feature extraction

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.

Optical implementation of N-wavelet coding for pattern classification

A novel method, N-wavelet coding, for pattern detection and classification based on wavelet transform and coding theory is introduced. With this detection and classification technique it is possible to reduce the false-alarm rate while maintaining a constant probability of detection and noise level. A set of periodic continuous waveforms comprising six classes that span a cross-correlation coefficient between 0.68 and 0.99 is used to evaluate the N-wavelet coding technique. It is found that when the length N of the N-wavelet coding is increased it is possible to decrease the false-alarm rate while maintaining a constant probability of detection.