P. Karivaratha Rajan

Optimal real correlation filters

Expressions are derived for real filters that have a maximum correlation signal to noise ratio. Both continuous and discrete cases are treated and shown to have similar forms. The signal can be complex, and the case of a real signal is considered and related to previous results.

Design of synthetic estimation filters using correlation energy minimization

Synthetic estimation filters (SEFs) have been found useful for the determination of distortion parameters such as angle of rotation of objects from their images. Previous SEFs, designed using matched and phase-only filters required a knowledge of the exact location of the object to produce reasonable estimation accuracy. To overcome the limitation, use of minimum average correlation energy (MACE) filters is proposed for the construction of SEFs. Because the MACE filters are designed to have their peaks at the origin of the correlation plane, the peak can be detected without a knowledge of the exact position of the object. Computer simulations are used to study the performance of MACE-SEFs. It is found that significant errors result at rotation angles that are not part of the training set. An improved linearity leading to an increase in accuracy was realized when the minimum noise correlation energy (MINACE) concept was used in place of the MACE concept for the design of the SEFs.

Selection of LCTV operating curves for input and filter

A liquid crystal television (LCTV) SLMs phase, amplitude, and polarization all influence our selection of operating curves for input and filter. With its continuum of drive voltage, the LCTV permits grey-level control in both locations. Selection of an optimum curve depends on expected variations in signal amplitude, presence of input scene structured noise, and other factors. Using modulators obtained from a commercially available projection LCTV, and with no specifically added input noise present, we have obtained laboratory results in which the ratio of peak intensity to correlator system noise exceeded 100:1. Unfortunately, it was massively inefficient to implement the algorithm which had been developed as the abstract for this paper was submitted. Fortunately, we have quite recently developed two insights that will speed it by several orders of magnitude, and we shall report that result in the future. We will also extend the work to include clutter objects and additive input scene noise.

Symmetrical decomposition and transformation

This paper is concerned with the development of efficient procedures for the design of two-dimensional (2-D) finite impulse response (FIR) digital filters. Symmetry properties of 2-D real functions are employed to derive a number of results on the transformation functions useful in transformation based design. A procedure to decompose a given frequency response into symmetrical and antisymmetrical components is outlined. Application of symmetrical decomposition in optimization based 2-D FIR filter design is described. Examples are given to illustrate the efficiency of this procedure.

Design of SLM-constrained MACE filters using simulated annealing optimization

Among the available filters for pattern recognition, the MACE filter produces the sharpest peak with very small sidelobes. However, when these filters are implemented using practical spatial light modulators (SLMs), because of the constrained nature of the amplitude and phase modulation characteristics of the SLM, the implementation is no longer optimal. The resulting filter response does not produce high accuracy in the recognition of the test images. In this paper, this deterioration in response is overcome by designing constrained MACE filters such that the filter is allowed to have only those values of phase-amplitude combination that can be implemented on a specified SLM. The design is carried out using simulated annealing optimization technique. The algorithm developed and the results obtained on computer simulations of the designed filters are presented.

Real-valued composite filters for optical pattern recognition

The design of real-valued composite filters for optical pattern recognition and classification is considered. A procedure to design a real-valued minimum average correlation energy (MACE) filter is developed. Also, the design of a real MVSDF-MACE filter that minimizes the output variance due to input noise while maintaining a sharp correlation peak is developed. Computer simulation indicates that the performance of these real filters is almost as good as that of the complex filters.

Comparison of five types of synthetic estimation filters for pose parameter estimation

Synthetic estimation filters, introduced by Juday and Monroe, have been shown to be very useful in the estimation of pose parameters of objects from their images. These filters are designed from a composite image made up of a linear combination of images which have undergone variations in their position by a known amount. Each filter is designed such that its response for each of the constituent images lies on a straight line. The peak response of the filter was chosen as the response of interest. Though these filters were designed to have an affine response with respect to the pose parameter, the resulting response in general is not affine and this causes considerable error in the estimate. On a detailed study of the SEF filter design, it is found that this discrepancy results because of the use of the maximum response of the filter rather than the response at the origin. Hence, in this paper, new types of synthetic estimation filters constructed on the basis of the filter response at the origin are proposed. These filters, except the phase-only filters, yield exactly the desired response for the constituent images. Three filters of this type -- matched, phase-only, and composite phase filters -- are considered in this paper. Simulation results conducted on these filters using a set of images are presented. The accuracy of estimation is compared with the previous two SEFs - - matched and phase-only filters. It is found that the new filters possess better estimation accuracy. Noise analysis of these filters were also carried out. Both analytical and simulation studies were made. The matched SEFs designed on the basis of the response at the origin were found to possess good noise resistance characteristics.

Design of an optimal-weighted MACE filter realizable with arbitrary SLM constraints

A realizable optimal weighted minimum average correlation energy (MACE) filter with arbitrary spatial light modulator (SLM) constraints is presented. The MACE filter can be considered as the cascade of two separate stages. The first stage is the prewhitener which essentially converts colored noise to white noise. The second stage is the conventional synthetic discriminant function (SDF) which is optimal for white noise, but which uses training vectors subjected to the prewhitening transformation. So the energy spectrum matrix is very important for filter design. New weight function we introduce is used to adjust the correlation energy to improve the performance of MACE filter on current SLMs. The action of the weight function is to emphasize the importance of the signal energy at some frequencies and reduce the importance of signal energy at some other frequencies so as to improve correlation plane structure. The choice of weight function which is used to enhance the noise tolerance and reduce sidelobes is related to a priori pattern recognition knowledge. An algorithm which combines an iterative optimal technique with Judays minimum Euclidean distance (MED) method is developed for the design of the realizable optimal weighted MACE filter. The performance of the designed filter is evaluated with numerical experiments.

Iterative method for the design of SLM realizable minimum average correlation energy (MACE) filters

Design of optical pattern recognition filters taking into account the nonideal characteristics of the spatial light modulators on which the filters are implemented is an important research problem. In this paper, an iterative method is developed for the design of SLM constrained minimum average correlation energy (MACE) filters. The algorithm uses a relaxation algorithm in conjunction with Judays minimum euclidean distance (MED) mapping technique in an iterative manner. The performance of the filter designed using this method was evaluated using computer simulations and the results are compared with a constrained MACE filter designed using a software based on a simulated annealing technique. The new software requires much less computer time than the simulated annealing based software providing comparable response. The time taken by the new algorithm is more than that for the MED mapped design; but, the new algorithm provides less deviation from the specified response for training images than the MED mapped design.