Correlation Synthetic Discriminant Functions for Object Recognition and Classification in High Clutter

Conventional Synthetic Discriminant Function (SDF) filter fermulations employ the same real correlation output(at origin) for all input training images from the same class, but this leads to poor discrimination. However, this canbe overcome by using complex correlation constraints in the SDF filter design. In this paper, we characterize therecognition sets for such SDF filters.I. INTRODUCTION Synthetic Discriminant Function (SDF) filters [1] present one approach to obtaining distortion tolerance incorrelation filters. The earliest SDF filters were designed to yield equal correlation outputs (at the origin) for all training images from a given class. Subsequently, these basic SDF designs were improved by minimizing outputnoise variance and by minimizing correlation plane energy, among other things.A common feature in several advanced SDF filter designs is the condition that the correlation outputs (at the origin) be the same real constant whenever the input is a training image from the desired class. An undesirableconsequence of this is that the resulting SDF filter will recognize as belonging to that class any image that is amember of the convex hull of the training set [2]. Many images in this convex hull bear little resemblance to the

A new nonlinear morphological detection algorithm is proposed for input scenes with a number of objects present in a clutter. It uses a synthetic discriminant function (SDF) to form the matched spatial filter (MSF) of the structuring element (SE) used in the hit-miss transform (HMT) detection. The SDF synthetic technique is used to adapt intraclass distortions and interclass similarity, where an HMT is used to adapt noisy and cluttered scenes. Simulation results show the proposed algorithm is an attractive nonlinear optical image processing technique that can be applied to an HMT detection to improve both the false alarm rate and its ability to detect multiple-object with distortions and clutter.

A novel method for three-dimensional (3-D) object rotation-invariant recognition by use of perspective array and the Synthetic Discriminant Function (SDF) is proposed. With high relevancy of perspective array, the conversion of depth information of 3-D object to 2-D perspective images by use of microlens array makes 3-D object recognition is possible accomplished through the technology of 2-D image. The SDF is synthesized by use of the computer, and 3-D object rotation-invariant recognition is accomplished with the aberration-invariant characteristic of SDF. Correlative analysis has been done for the conversion and recognition process, the SDF has been synthesized by use of Matlab process, and rotation-invariant recognition of dice, a 3-D object, has been accomplished by use of the method of match filtering. The result showed that the proposed method is performed better.

A power-law correlation based on an inverse filter Fourier-Radon-transform synthetic discriminant function (SDF) for facial recognition is proposed. In order to avoid spectral overlap and nonlinear crosstalk, superposition of rotationally variant sets of inverse filter Fourier-transformed Radon-processed templates is used to generate the SDF. For the inverse filter, the Fourier transform of M projections (Radon Transform) from one training image is combined with (N-1) M Fourier transform of M projections taken from another N-1 training image. This synthetic SDF filter has a very high discrimination capability; however, it is not noise robust. To overcome this problem, a power-law dynamic range compression is added to the correlation process. The proposed filter has three advantages: (1) high discrimination capability as an inverse filter, (2) noise robustness due to dynamic range compression, and (3) crosstalk-free nonlinear processing. The filter performance was evaluated by established metrics, such as peak-to-correlation energy (PCE), Horner efficiency, and correlation-peak intensity. The results showed significant improvement as the power-law filter compression increased.

We describe a binary joint transform correlator (JTC) that uses a synthetic discriminant function (SDF) at the input plane to store the reference images. The SDF is displayed at the input plane side by side the input scene. The input scene, the SDF, and their joint power spectrum are thresholded to only two values. Thus, binary spatial light modulators (SLMs) can be used to implement the correlator. The correlation performance of the SDF-based binary JTC is compared to that of the classical SDF-based correlator in the areas of correlation peak intensity, peak to sidelobe ratio, signal-to-noise ratio, and correlation width. We show that the SDF-based binary JTC outperforms the classical correlator in all these areas. Furthermore, a single binary SLM can be used to read in sequentially the binarized input signals and the binarized joint power spectrum which results in a significant reduction in cost, size, and complexity of the system.

New approach for intensity distortion-invariant OPR

The projection-slice synthetic discriminant function, which was described earlier, reduces significant portions of the training data in the synthesis process as compared to the normal synthetic discriminant function filters. This enables the matching of particular features of each training image. The wavelet transform is utilized to further reduce the data in the synthesis stage and thereby reduce the data overlap in filters. The method for this type of filter synthesis is discussed and simulation results of the algorithms involved are presented to show that the relative performance of the newly synthesized filter is improved, while the data representing the training images has been reduced. © 2000 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(00)01505-1)

A distortion-invariant joint transform correlation (JTC), based on the fractional power fringe-adjusted joint transform correlation and synthetic discriminant function, is investigated. By suitably adjusting the parameters used to characterize the fractional power fringe-adjusted fil- ter formulation, we obtain JTC-based classical matched filtering, fringe- adjusted filtering, and amplitude-modulated phase-only filtering. Com- puter simulation results show that the proposed joint transform correlation is distortion-invariant for the target image from the training set. © 1998 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(98)00501-7) Subject terms: recognition techniques; synthetic discriminant function; joint trans- form correlation; fractional power fringe-adjusted joint transform correlation; joint power spectrum.

A modified form of a composite or multiplexed matched filter has been computer simulated and tested. The modification consists of using only the phase function and setting the amplitude function equal to unity—a so-called phase-only filter (POF). The original filter was D. Casasent's synthetic discriminant function (SDF) filter. The filter and test images were made from actual IR imagery. The results are compared in terms of efficiency, correlation peak height and width, and signal/noise ratio. A binary phase version of the SDF/POF was also tested. Its performance is between the SDF and the SDF/POF.

A new synthetic hit-miss transform (SHMT) algorithm is proposed for distortion-invariant recognition of various objects in noisy and cluttered input images. The proposed SHMT algorithm uses synthetic structuring elements (SEs), which are synthesized based on a synthetic discriminant function (SDF) filter algorithm. The synthetic hit SE is composed of the linear combination of the reference hit SEs, and the synthetic miss SE is composed of the linear combination of the reference miss SEs. Based on various simulations, it is shown that the proposed algorithm can be applied to an HMT correlator to improve its ability to detect various objects with distortions in noisy and cluttered scenes.

A new method is proposed to correct the nonlinear distortion of a practical hardware optical implementation system. The on-line optical-computer feedback technique and off-line digital iterative algorithm are used to correct the correlation matrix of a SDF and the input-output vector respectively. As a result, a optimum SDF with very good correlation S/N, minimum peak variance, is obtained. Experiments demonstrate that this method is very effective for correcting the nonlinear distortion of a real-world nonideal optical and optoelectric system, so it could be applied to 3D distortion invariant real-time optical correlation filtering and optical pattern recognition.

Most of captured images present degradations due to blurring and additive noise; moreover objects of interest can be geometrically distorted. The classical methods for pattern recognition based on correlation are very sensitive to intensity degradations and geometric distortions. In this work, we propose an adaptive generalized filter based on synthetic discriminant function (SDF). With the help of computer simulation we analyze and compare the performance of the adaptive correlation filter with that of common correlation filters in terms of discrimination capability and accuracy of target location when input scenes are degraded and a target is geometrically distorted.

: In an optical correlator, binary phase-only filters (BPOFs) that recognize objects that vary in a nonrepeatable way are essential for recognizing objects from actual sensors. An approach is required that is as descriptive as a BPOF yet robust to object and background variations of an unknown or unrepeatable type. We investigated the use of BPOFs to recognize objects undergoing unknown variations. In our study, we developed a BPOF that was more robust than other designs. This was done by creating a filter that retained the invariant features of a training set. Our feature-based filter offered a range of performance by setting a parameter to different values. At one extreme, the filter offered similar performance to that of a synthetic discriminant function (SDF) filter. As the value of the parameter was changed, correlation peaks within the training set became more consistent and broader. In addition, the feature-based filter was potentially useful for recognizing objects outside the training set. Furthermore, the feature-based filter was more easily calculated and trained than an SDF filter. Pattern Recognition, Optical Correlation, Binary Phased-Only Filter.

We propose here a simple way to synthesize a shift, rotation and limited size correlation filter, making use of the idea of synthetic discriminant functions (SDF). The SDF is synthesized by superimposing four 2nd order circular harmonics of a training reference pattern in 4 different sizes. Computer simulation experiments have shown that the filter is indeed shift, fully rotation and limited size invariant over a size range from 1 to 1.75. The invariant range can be increased if more training patterns are used.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Face recognition based on independent component analysis (ICA) has emerged as a popular approach for face recognition application. In this paper we present a comparison between various optoelectronic face recognition techniques and ICA based face recognition. Computer simulations are used to study the effectiveness of the fastICA algorithm in recognizing facial images with a high level of three-dimensional (3-D) distortion. Results are then compared to 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.