Distortion-invariant filter for nonoverlapping noise

A new heuristic filter based on the optimum filter for disjoint noise developed by Javidi and Wang [J. Opt. Soc. Am. A 11, 2604 (1995)] is presented. In this new filter a number of optimum filters built from single training images are combined linearly by use of the synthetic discriminant function (SDF) approach into a distortion-invariant filter for disjoint noise. Like the traditional SDF approach, this summation technique makes it possible to control the height of the correlation peak easily, for example, if a uniform filter response is needed. The filter is compared with the distortion-invariant version of the optimum filter on images with low contrast and high levels of nonoverlapping clutter. The new filter shows good results, demonstrating that it is, with very simple heuristic methods, possible to improve the performance of distortion-invariant filters for nonoverlapping noise.     

Comparative study of face recognition techniques that use joint transform correlation and principal component analysis

Face recognition based on principal component analysis (PCA) that uses eigenfaces is popular in face recognition markets. We present a comparison between various optoelectronic face recognition techniques and a PCA-based technique for face recognition. Computer simulations are used to study the effectiveness of the PCA-based technique, especially for facial images with a high level of distortion. Results are then compared with various distortion-invariant optoelectronic face recognition algorithms such as synthetic discriminant functions (SDF), projection-slice SDF, optical-correlator-based neural networks, and pose-estimation-based correlation.     

Projection-slice theorem: a compact notation

The notation normally associated with the projection-slice theorem often presents difficulties for students of Fourier optics and digital image processing. Simple single-line forms of the theorem that are relatively easily interpreted can be obtained for n-dimensional functions by exploiting the convolution theorem and the rotation theorem of Fourier transform theory. The projection-slice theorem is presented in this form for two- and three-dimensional functions; generalization to higher dimensionality is briefly discussed.     

Distortion-invariant fringe-adjusted joint transform correlation

A distortion-invariant joint transform correlator based on the concepts of the fringe-adjusted joint transform correlator and the synthetic discriminant function is presented. Computer-simulation results show that the proposed joint transform correlator is distortion-invariant for the target image from the training set and produces sharper correlation peaks and lower sidelobes compared with the classical joint transform correlator.     

Modified filter synthetic discriminant functions for improved optical correlator performance

By the filter modulation operator N, the modified filter synthetic discriminant function permits advantageous preprocessing of individual training-set images that are used in a linear combination to construct the filter synthetic discriminant function, which applies a modulation operator M to the synthetic discriminant function. A relaxation algorithm is used to satisfy the equal correlation peaks rule in the correlator output plane. As the filter modulation operators M and N can be given any functional form, the modified filter synthetic discriminant function design proposed is sufficiently general to be described as a unified filter modulation synthetic discriminant function design.     

Log-polar transform-based wavelet-modified maximum average correlation height filter for distortion invariance in a hybrid digital-optical correlator

We discuss and implement a log-polar transform-based distortion-invariant filter for automatic target recognition applications. The log-polar transform is a known space-invariant image representation used in several image vision systems to eliminate the effects of scale and rotation in an image. For in-plane rotation invariance and scale invariance, a log-polar transform-based filter was synthesized. In cases of in-plane rotation invariance, peaks shift horizontally, and in cases of scale invariance, peaks shift vertically. To achieve out-of-plane rotation invariance, log-polar images were used to train the wavelet-modified maximum average correlation height (WaveMACH) filter. The designed filters were implemented in the hybrid digital-optical correlation scheme. It was observed that, for a certain range of rotation and scale differences, the correlation signals merge with the strong dc. To solve this problem a shift was introduced in the log-polar image of the target. The use of a chirp function for dc removal has also been discussed. Correlation peak height and peak-to-sidelobe ratio have been calculated as metrics of goodness of the log-polar transform-based WaveMACH filter. Experimental results are presented.     

Pose and position tracking with super image vector inner products

We introduce a new and efficient distortion-invariant super image tracker and pose estimator based on a linear phase coefficient composite filter. The super image consists of a weighted sum of training images chosen to span the distortion range under analysis. Unlike correlation-based composite filter design, the super image is implemented by means of a complex vector inner product operation. A super image vector inner product is implemented by elementwise multiplication of a super image template by a window of interest in the input scene and summation of the elementwise operations. The resulting amplitude indicates target detection, and the resulting phase indicates the value of scale, orientation, or movement of the target object. The mathematical characteristics of the super image vector inner product are presented, and its application is demonstrated.     

Magnetic resonance brain tissue classification and volume calculation

This study develops a volume sphering analysis (VSA) approach to tissue classification and volume calculation of multispectral magnetic resonance (MR) brain images. It processes all multispectral MR image slices as an image cube while using only one set of training samples obtained from a single multispectral image slice to perform tissue classification as well as to calculate tissue volumes. In order to make a one slice set of training samples fit for all MR image slices a novel multispectral signature-specified extrapolation algorithm is particularly designed for this purpose so that the selected set of training samples can be extrapolated to create new data samples that are also applicable to other MR image slices. As a consequence, it significantly reduces the tremendous burden on radiologists for selection of training samples as well as computational cost. To further resolve instability and inconsistency issues which may be caused by training sample extrapolation, the proposed VSA also includes a support vector machine to refine training samples and develops an iterative Fisher’s linear discriminant analysis (IFLDA) to make VSA robust and insensitive to new generated training samples so as to improve the traditional slice-by-slice MR image classification. Experimental results demonstrate that VSA in conjunction with IFLDA not only performs comparably to approaches using training samples from individual image slices, but also saves significant time in selecting training samples and computational cost.     

Hybrid digital-optical correlation employing a chirp-encoded simulated-annealing-based rotation-invariant and distortion-tolerant filter

The simulated annealing (SA) algorithm based on entropy optimization is a technique of synthesizing distortion-invariant matched filters capable of discriminating very similar images. The synthesis of rotation-invariant filters using modified SA-based filter equations and their tolerance to distortions are studied. The filters are trained with true class images rotated in-plane at 3 degrees intervals between 0 degrees and 360 degrees . A total of seven filters are required over the whole range for both CCD or thermal images. Optical correlation in a hybrid digital-optical correlator results in an unwanted zero-order dc along with two first-order (+/-1) correlation peaks. A chirp function multiplied with the filter separates out the three peaks to three different planes, and only one peak in focus is captured in a camera. The performance of the modified SA-based filter has been studied in comparison to the conventional SA filter as well as with other filters.     

A simple and efficient methodology to approximate a general non-Gaussian stationary stochastic process by a translation process

Some widely used methodologies for simulation of non-Gaussian processes rely on translation process theory which imposes certain compatibility conditions between the non-Gaussian power spectral density function (PSDF) and the non-Gaussian probability density function (PDF) of the process. In many practical applications, the non-Gaussian PSDF and PDF are assigned arbitrarily; therefore, in general they can be incompatible. Several techniques to approximate such incompatible non-Gaussian PSDF/PDF pairs with a compatible pair have been proposed that involve either some iterative scheme on simulated sample functions or some general optimization approach. Although some of these techniques produce satisfactory results, they can be time consuming because of their nature. In this paper, a new iterative methodology is developed that estimates a non-Gaussian PSDF that: (a) is compatible with the prescribed non-Gaussian PDF, and (b) closely approximates the prescribed incompatible non-Gaussian PSDF. The corresponding underlying Gaussian PSDF is also determined. The basic idea is to iteratively upgrade the underlying Gaussian PSDF using the directly computed (through translation process theory) non-Gaussian PSDF at each iteration, rather than through expensive ensemble averaging of PSDFs computed from generated non-Gaussian sample functions. The proposed iterative scheme possesses two major advantages: it is conceptually very simple and it converges extremely fast with minimal computational effort. Once the underlying Gaussian PSDF is determined, generation of non-Gaussian sample functions is straightforward without any need for iterations. Numerical examples are provided demonstrating the capabilities of the methodology.     

Three-dimensional pattern recognition with a single two-dimensional synthetic reference function

A novel, to our knowledge, method of distortion-invariant three-dimensional (3-D) pattern recognition is proposed. A single two-dimensional synthetic discriminant function is employed as a reference function in the 3-D correlator. Thus the proposed system is able to identify and locate any true-class object in the 3-D scene. Preliminary simulation and experimental results are presented.     

Cone-beam reconstruction by backprojection and filtering

A new analytical method for tomographic image reconstruction from cone-beam projections acquired on the source orbits lying on a cylinder is presented. By application of a weighted cone-beam backprojection, the reconstruction problem is reduced to an image-restoration problem characterized by a shift-variant point-spread function that is given analytically. Assuming that the source is relatively far from the imaged object, a formula for an approximate shift-invariant inverse filter is derived; the filter is presented in the Fourier domain. Results of numerical experiments with circular and helical orbits are considered.     

First- and second-order information in natural images: a filter-based approach to image statistics

Previous analyses of natural image statistics have dealt mainly with their Fourier power spectra. Here we explore image statistics by examining responses to biologically motivated filters that are spatially localized and respond to first-order (luminance-defined) and second-order (contrast- or texture-defined) characteristics. We compare the distribution of natural image responses across filter parameters for first- and second-order information. We find that second-order information in natural scenes shows the same self-similarity previously described for first-order information but has substantially less orientational anisotropy. The magnitudes of the two kinds of information, as well as their mutual unsigned correlation, are much stronger for particular combinations of filter parameters in natural images but not in unstructured fractal images having the same power spectra.     

Biometric verification with correlation filters

Using biometrics for subject verification can significantly improve security over that of approaches based on passwords and personal identification numbers, both of which people tend to lose or forget. In biometric verification the system tries to match an input biometric (such as a fingerprint, face image, or iris image) to a stored biometric template. Thus correlation filter techniques are attractive candidates for the matching precision needed in biometric verification. In particular, advanced correlation filters, such as synthetic discriminant function filters, can offer very good matching performance in the presence of variability in these biometric images (e.g., facial expressions, illumination changes, etc.). We investigate the performance of advanced correlation filters for face, fingerprint, and iris biometric verification.     

A new approach to radionuclide imaging using compressed sensing

Abstract

Single-photon emission computerised tomography (SPECT) and positron emission tomography (PET) are essential medical imaging tools, with inherent drawback of slow data acquisition process. We present a novel compressed sensing-based reconstruction of these images from significantly fewer measurements than traditionally required, thus demonstrating potential of reduction in scan time and radiopharmaceutical doze with benefits for patients and health care economics. Our work effectively shows that high fidelity two-dimensional (2D) SPECT/PET image is reconstructed using compressive sensing with considerably reduced numbers of samples in acquisition stage. The reconstruction of tomographic images is realised by compressed sensing the 2D Fourier projections of k-space data. These 2D projections being sparse in transform domain need fewer samples in k-space and are reconstructed without loss of fidelity. These undersampled Fourier projections can then be backprojected by employing the iterative reconstruction approach for a complete three-dimensional (3D) volume. Compressed sensing of a phantom image and PET bone scintigraphy with radial Fourier samples are performed. The reconstructions of these images are compared to conventionally sampled images using image quality measures like mean square error, peak signal-to-noise ratio and structure similarity (SSIM) index, showing high-quality image reconstruction.     

General restoration filter for vibrated-image restoration

Mechanical vibrations are often the principal cause of image degradation. Low temporal-frequency mechanical vibrations involve random image degradation that depends on the instant of exposure. Exact restoration requires the calculation of a specific filter unique to each vibrated image. To calculate the restoration filter for each image, one needs the specific optical transfer function unique to the motion in the image. Therefore the instant of exposure and the motion function have to be measured or estimated by some other means. We develop a restoration filter for individual images blurred randomly by low-frequency mechanical vibrations. The filter is independent of the instant of exposure. The filter is designed to give its best performance averaged over a complete ensemble of vibrated images. Although when applying the new filter to any vibrated image the restoration achieved is slightly poorer than that achieved with an exact filter unique to the specific motion function, the new filter has the advantage of simplicity.     

Numerical evaluation of Hankel transforms for oscillating functions

Six methods for the numerical calculation of zero-order Hankel transforms of oscillating functions were evaluated. One method based on Filon quadrature philosophy, two published projection-slice methods, and a third projection-slice method based on a new approach to computation of the Abel transform were implemented; alternative versions of two of the projection-slice methods were derived for more accurate approximations in the projection step. These six algorithms were tested with an oscillating sweep signal and with the calculation of a three-dimensional diffraction-limited point-spread function of a fluorescence microscope. We found that the Filon quadrature method is highly accurate but also computationally demanding. The projection-slice methods, in particular the new one that we derived, offer an excellent compromise between accuracy and computational efficiency.     

Implementation of arbitrary real-valued correlation filters for the shadow-casting incoherent correlator

We describe an incoherent correlator, based on the shadow-casting principle, that is able to implement any real-valued linear correlation filter. The correlation filter and the input image are displayed on commercial liquid-crystal television (LCTV) panels. Although it cannot handle high-resolution images, the incoherent correlator is lensless, compact, low cost, and uses a white-light source. A bipolar technique is devised to represent any linear filter, computed from a single reference image or composite, in the correlator. We demonstrate experimentally the efficiency of the design in the case of optimal trade-off (OT) filters and optimal trade-off synthetic discriminant function (OT-SDF) filters.     

Composite versus multichannel binary phase-only filtering

Multichannel filtering and its inherent capacity for the implementation of data-fusion algorithms for high-level image processing, as well as composite filtering and its capacity for distortion-invariant pattern-recognition tasks, are discussed and compared. Both approaches are assessed by use of binary phase-only filters to simplify implementation issues. We discuss similarities and differences of these two solutions and demonstrate that they can be merged efficiently, giving rise to a new category of filters that we call composite-multichannel filters. We illustrate this comparison and the new filter design for the case of rotation-invariant fingerprint recognition. In particular, we show that the gain in terms of encoding capacity in the case of the composite-multichannel approach can be used efficiently to introduce multichannel-filter reconfigurability.     

Distortion-invariant pattern recognition with Fourier-plane nonlinear filters

The use of nonlinear techniques in the Fourier plane of pattern-recognition correlators can improve the correlators' performance in terms of discrimination against objects similar to the target object, correlation-peak sharpness, and correlation noise robustness. Additionally, filter designs have been proposed that provide the linear correlator with invariance properties with respect to input-signal distortions and rotations. We propose simple modifications to presently known distortion-invariant correlator filters that enable these filter designs to be used in a nonlinear correlator architecture. These Fourier-plane nonlinear filters can be implemented electronically, or they may be implemented optically with a nonlinear joint transform correlator. Extensive simulation results are presented that illustrate the performance enhancements that are gained by the unification of nonlinear techniques with these filter designs.