Synthetic Discriminant Function Filters Research Articles

Research on Distortion Invariant Recognition of a Planar Integrated Optical Correlator

In this paper, an optical correlator which adopts planar integrated 2F structure and optimal tradeoff synthetic discriminant function filter is proposed to improve the system integration and the recognition ability. The specialized digital microlens is designed for the correlator to replace the physical lens. By the theoretical analysis, the structural design conditions and parameters of the correlator are given, and the system volume is 63.1 cm3 which is only half of the planar integrated 4F optical correlator. Moreover, simulations and experimental research works reveal that the correlator can achieve stable recognition to the input object of distortion with scaling (52%, 150%), rotation (–50°, +42°), and existed scaling (72%, 130%) and rotation (–36°, +38°) simultaneously. Theoretical analysis and experimental results indicate that the planar integrated optical correlator with compact structure and high integration has good performance of distortion invariant recognition.

Distortion-invariant recognition of volume holographic correlator based on morphological algorithm and synthetic discriminant function

We proposed a novel method based on mathematical morphological algorithm and space domain synthetic discriminant function (SDF) for distortion-invariant recognition of volume holographic correlator (VHC). To suppress the effect of pattern-dependent behavior, a new morphological algorithm is introduced, which can process the gray-scale images into strong and clean edge maps without redundancy and irrelevant detail. Using these edge maps, SDF filters are synthesized for detecting distorted targets on VHC system. Experimental results demonstrate that the proposed method can achieve both rotation and scale invariant recognition.

Content-addressable holographic data storage system for invariant pattern recognition of gray-scale images

Conventionally a holographic data storage system uses binary digital data as the input pages. We propose and demonstrate the use of a holographic data storage system for the purpose of invariant pattern recognition of gray-scale images. To improve the correlation accuracy for gray-scale images, we present a coding technique, phase Fourier transform (phase-FT) coding, to code a gray-scale image into a random and balanced digital binary image. In addition to the fact that a digital data page is obtained for incorporation into a holographic data storage system, this phase-FT coded image produces dc-free homogenized Fourier spectrum. This coded image can also be treated as an image for further processing, such as synthesis of distortion-invariant filters for invariant pattern recognition. A space-domain synthetic discriminant function (SDF) filter has been synthesized using these phase-FT coded images for rotation-invariant pattern recognition. Both simulation and experimental results are presented. The results show good correlation accuracy in comparison to correlation results obtained for SDF filter synthesized using the original gray-scale images themselves.

Optoelectronic 3-D Object Classification From 2-D Images

The task of object classification is complicated by variations in the 3-D object, which translate into distortions in 2-D images. The pattern matching for 3-D invariance classification requires a large amount of data and computation time. Proposed here is an efficient 3-D object classification algorithm for real-time fringe-adjusted joint transform correlator (FJTC)-based automatic target recognition (ATR) system. The proposed classification technique employed a fragment-based recognition approach and a new type of synthetic discriminant function filter in the generation of distortion-invariant correlation filter sets. The optoelectronic FJTC is then used to provide correlation of the filter sets with the input under a proper arrangement. This classification method is simple and fast, hence is suitable to be in use by real-time ATR systems. For the conclusion, simulation results are provided to prove the effectiveness of the proposed system in the classification of objects invariant to 3-D out-of-plane rotation distortion.

Adaptive synthetic discriminant function filters for pattern recognition

New adaptive correlation filters based on a conventional synthetic discriminant function (SDF) for reliable recognition of an object in cluttered background are proposed. The information about an object to be recognized, false objects, and a background to be rejected is utilized in an iterative training procedure to design a correlation filter with a given value of discrimination capability. Computer simulation results obtained with the proposed adaptive filter in test scenes are discussed and compared with those of various correlation filters in terms of discrimination capability, tolerance to input additive noise that is always present in image sensors, and to small geometric image distortions.

Generalization of the Jared and Ennis method of complex transmittance objects for the generation of synthetic discriminant function filters

We present a simple method of constructing synthetic discriminant function filters optimized to take into account the modulation of liquid-crystal devices. This relaxation algorithm, a generalization of the Jared and Ennis method, is an iterative method that includes arbitrary modulations for both scene and filter, extending the problem to the complex plane. Simulated and experimental results obtained in a VanderLugt correlator are presented for a two-class recognition problem. The optimal number of images needed to describe an object in a filter generated in this way is discussed, and the influence of the spatial light modulation resolution on the correlation is studied.

A distortion-tolerant photorefractive joint transform correlator

A distortion-tolerant recognition process has been successfully implemented in an optical joint transform correlator operating with a liquid crystal television display in the input plane and a photorefractive crystal in the Fourier plane. We have generated the reference by retaining the phase information of the Fourier transform of a constrained phase-only minimum Euclidean distance synthetic discriminant function filter. This gave rise to a process that successfully detects the target also for distortions not included in the training set. Experimental and theoretical results are shown.

Distortion-invariant pattern recognition based on a synthetic hit-miss transform

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.

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.

Rotation-invariant synthetic discriminant function filter for pattern recognition

The ring synthetic discriminant function (RSDF) filter for rotation-invariant response is discussed for pattern recognition. This method uses one half of a slice of the Fourier transform of the object to generate the transfer function of the filter. This is accomplished by rotating the one half of a slice in the Fourier domain through 2? rad about the zero-frequency point of the Fourier plane. This filter has the advantage of always matching at least one half of a slice of the Fourier transform of any rotation of the image. An analytical discussion of the filter construction and correlation results are presented along with simulated correlation results for a particular target image. These results and established metrics are used for comparison with benchmark algorithms.

Circular optimal trade-off and distance-classifier correlation filters

We use circular versions of advanced distortion-invariant filters such as optimal trade-off synthetic discriminant function and distance classifier correlation filters to obtain rotation invariance with an optical correlator. The filter noise performance is compared using a common measure of probability of error because the filters have different characteristics. The filters are real-valued so they can be implemented on a variety of SLMs. The circular symmetry of the filters significantly decreases their computational requirement.

Data reduction via the wavelet transform for the synthesis of the projection-slice filter

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)

Gray-level computer-generated hologram filters for multiple-object correlation

Synthesis of gray-level computer-generated holograms allows for an increase of the information storage capability that is usually achieved with conventional binary filters. This is mainly because more degrees of freedom are available. We propose to profit from this feature by synthesizing complex filters formed by many superimposed holograms, each with a different carrier frequency. We apply these gray-level filters to perform multichannel correlation and in this way enhance the capability of optical correlators to process the information in parallel and simultaneously. First, we analyze the behavior of some performance criteria on the impulse response and on the correlation as a function of the number of holograms that are multiplexed. Then we show the results of two experiments: In the first a composed phase-only filter is used in a multiple-object recognition process. In the second a composed synthetic discriminant function filter is used to implement an object classification by means of a binary code.

Optical Pattern Recognition System Based on Parallel Spatial Filtering Using Synthetic Discriminant Function

In this paper, we propose an optical pattern recognition system based on spatial filtering using a synthetic discriminant function (SDF). In this system, the input image is multiplexed by a microlens array under incoherent illumination, and then the optical inner product of input images and SDF filters is optically conducted. The image is recognized by thresholding the optical inner product values. The present SDF filter was constructed with pseudogradation transparent filters fabricated by electron-beam lithography. We performed an experiment that involved the recognition of ten Arabic numerals and evaluated the discriminating characteristics of parallel pattern recognition. We confirm that the proposed system can function as a parallel recognition system without the need to scan images.

Synthetic discriminant function filter employing nonlinear space-domain preprocessing on bandpass-filtered images

Previously [Appl. Opt. 36, p. 9212 (1997)] we examined the performance of the linear and nonlinear preprocessed difference-of-Gaussians filter, and it was shown that this operation results in greater tolerance to in-class variations while maintaining excellent discrimination ability. The introduction of nonlinearity was shown to provide greater robustness to the filter's response to noise and background clutter in the input scene. We incorporate this new operation into the synthesis of a modified synthetic discriminant function filter. The filter is shown to produce sharp peaks, excellent discrimination without the need to include out-of-class objects, and good invariance to out-of-plane rotation over a distortion range of up to 90 degrees . Additionally, the introduction of nonlinearity is shown to provide greater robustness of the filter response to background clutter in the input scene.

One-dimensional logarithmic harmonic synthetic discriminant function filters for shift-, scale-, and projection-invariant pattern recognition

We introduce a new approach for shift-, scale-, and projection-invariant pattern recognition that combines the harmonic expansion and the synthetic discriminant function approaches by use of a synthetic discriminant function filter with equal-order one-dimensional logarithmic harmonic components. Because projection invariance in one direction is guaranteed by the harmonics, the required number of training images is much fewer than with classical synthetic discriminant function filters.

Projection-slice synthetic discriminant functions for optical pattern recognition

The projection-slice synthetic discriminant function (PSDF) filter is introduced and proposed for distortion-invariant pattern-recognition applications. The projection-slice theorem, often used in tomographic applications for medical imaging, is utilized to implement a distortion-invariant filter. Taking M projections from one training image and combining them with (N - 1)M projections taken from another N - 1 training image accomplishes this. With the projection-slice theorem, each set of these M projections can be represented as M one-dimensional slices of the two-dimensional Fourier transform of the particular training image. Therefore, the PSDF filter has the advantage of matching each of the training images with at least M slices of their respective Fourier transforms. This filter is theoretically analyzed, numerically simulated, and experimentally implemented and tested to verify the simulation results. These tests show that the PSDF filter significantly outperforms the matched-filter and the basic synthetic discriminant function technique for the particular images used.

Automated detection of macromolecules from electron micrographs using advanced filter techniques

We have addressed the problem of automated detection of biological macromolecules from electron micrographs by designing a detection filter which combines conventional correlation technique with a synthetic discriminant function (SDF) in conjunction with the constraint to minimize the energy in the correlation plane and that of noise. Combining the constrained SDF filter with circular harmonic expansion results in rotational invariance of the detection process. We define measures to evaluate filter performance by test calculations and discuss the choice of parameters for filter development. Compared with the conventional matched filter, improved recognition and discrimination of objects to be detected is achieved. Applications of the filter to detect biological macromolecules in electron micrographs are presented, demonstrating the improvements in object detection as well as the limitations of the method.

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.

Experimental implementation of a joint transform correlator using synthetic discriminant functions

A joint transform correlator (JTC) was implemented in the Optical Science Department at CERT. In order to ensure a rotational invariance, the reference image is replaced by a synthetic discriminant function (SDF) image displayed on an amplitude spatial light modulator (SLM). Numerical simulations are performed and then compared to experiments. We show that the pseudo-inverse SDP (PI-SDF) gives accurate experimental results. The training ability of the PI-SDF allows it to recognize the reference object unambiguously, even if the input view does not explicitly belong to the training set. Then, we propose to replace our amplitude device with a ternary phase and amplitude device, in order to display positive and negative images: this allows us to display any kind of SDF filters, e.g. OT-SDF or MINACE-SDF, which reduce the side lobes, with a good resistance to noise.