Image logic algebra and its optical implementations

An implementation method for an inference engine using optical array logic is presented. Optical array logic is a technique for parallel neighborhood operation using spatial coding and 2-D correlation. For efficient execution of inference in artificial intelligence problems, a large number of data must be searched effectively. To achieve this demand, we apply a template matching technique to the inference operation. By introducing a new function of data conversion, the inference operation can be implemented with optical array logic, which utilizes parallelism in optical techniques.

Binary image algebra and optical cellular logic processor design

In this paper, we propose a novel inference method for a gene network using optical array logic (OAL).1–3) OAL is utilized as a descriptive language for multipurpose parallel information processing on general electronic hardware. We develop an effective algorithm to extract direct regulations in a redundant gene network provided by biological experiments. In the proposed method, a gene interaction matrix is converted into a two-dimensional discrete binary image. The image is processed using parallel operations provided by OAL. After several steps of OAL operations indirect regulations in the gene network can be eliminated. The algorithm is believed to avoid undesired elimination of links caused by loop structures. In the simulation using artificial network data, the proposed technique achieves more than 90% sensitivity.

In this paper we present a two-dimensional cellular hypercube architecture for image processing that combines features of the conventional hypercube and cellular logic architectures for 2-D computation cells. A unified theory of parallel binary image processing, binary image algebra (BIA), serves as a software tool for designing parallel image processing algorithms. To match the hardware to the software, we characterize the cellular processors using the same algebraic structure as BIA. The two-dimensional cellular hypercube image processor is a cellular SIMD machine with N2 cells and has a simple overall organization, low cell complexity and fast processing ability. An optical cellular hypercube implementation of BIA is proposed which offers parallel input/output and global interconnection capabilities which are difficult to do in planar VLSI technology.

A new version of an experimental system of an optoelectronic hybrid optical parallel array logic system is constructed. The experimental system is composed of a two-dimensional correlator with selectable holographic filters and parallel electronic circuits. The system can process images consisting of 3 × 3 pixels at a time. Several types of processing are achieved both without and with dynamic selection of the holographic filters. On the experimental system, parallel operations of several logical functions and data transmission are demonstrated. Processing rates of iterative operation without and with filter selection are 278 and 143 frames/s, respectively.

A simulator for exponential function in Shor's quantum algorithm is presented. It is based on optical array logic (OAL) which is one of paradigm for digital optical computing. In the method, a quantum statement with superposition and entanglement is represented by two-dimensional spatial pattern. Parallel processing set by OAL simulates quantum properties.

A new nonlinear spatial encoding method for cascadable fuzzy logic

Fuzzy-reasoning theory is widely used in industrial control. Mathematical morphology is a powerful tool to perform image processing. We apply fuzzy-reasoning theory to morphology and suggest a scheme of fuzzy-reasoning morphology, including fuzzy-reasoning dilation and erosion functions. These functions retain more fine details than the corresponding conventional morphological operators with the same structuring element. An optical implementation has been developed with area-coding and thresholding methods.

Fast parallel processing of gray-scale images and exact hard-clip thresholding are two important functionalities necessary in optoelectronic implementations of structural processors. The parallel nature of processing stems from optical implementation of local operations with arrays of active smart pixels. We have demonstrated a morphological image processor composed of arrays of bistable optoelectronic transceivers which are connected in differential pairs and work as comparators. The use of differential pairs of optical thyristors fabricated in GaAs technology allows to realize a dual rail architecture for this photonic morphological image processor. The processor consists of a thresholding module and a binary morphological processing module. The thresholding module decomposes gray level images into series of binary slices. In the binary morphological processing module operations are performed within a neighborhood defined by a structuring element implemented as a diffractive fan-out element. In the prototype set-up we demonstrate median filtering, dilation and erosion operations performed for an image of 8x8 pixels and threshold decomposition of 6 gray level images. In principle all rank order as well as morphological filters can be optically calculated in the set-up. Additional functionality of the processor is achieved with use of the electronic layer with digital cellular processors. The electronic layer, designed as an array of simple digital processors, realizes a set of operations on binary images using 4 bit programmable weights. Simulation results for 0.8 µm CMOS technology are presented. We discuss the limitations of the photonic morphological image processing with respect to bandwidth, parallelism and architecture of the processor.

A hit-or-miss transform architecture and a canonical Boolean logic format and threshold decomposition algorithm are proposed to process binary and gray-tone images with morphological combined operations. The transformation of morphological combined image processing functions to hit-or-miss transforms is explicit: Binary functions are formulated by a summation of hit-or-miss transforms and gray-tone functions formulated by a double summation. A simple optical hit-or-miss transform processor is suggested on the basis of incoherent two-channel correlation with dual-rail spatial coding. The hit-or-miss transforms can be realized optically in one parallel processing step. Thus, binary and gray-tone image processing functions can be implemented by the repeated use of the optical processor with different structuring elements.

In this paper, a novel image denoising method with a morphological opening is proposed. In many image recovery, the regularization has been introduced to prevent overfitting between a recovered image and a noisy observation. In the regularization of an image, the smoothness of the image is assumed. The cost function, which is minimized during the regularization, is defined as a sum of the approximation error term and the smoothness penalty of the image. In morphological image processing, an image is approximated as a union of structuring elements (SEs) by the morphological image opening. In the approximation with the opening, the SE represents the local intensity surface of the image. We hence impose the smoothness penalty on the SE, instead of the recovered image itself, and propose an image opening method with the regularization penalty for the SE. In denoising, the approximation error is minimized under the constraint of the penalty for the SE. In experiments, we show that the proposed filtering method has ability to remove impulsive noises from degraded texture images.

Recent Developments in Image Algebra

This paper presents a new efficient enhanced automatic target recognition approach based on hybrid feature and intensity based methods. The proposed approach is based on comparison and matching between the acquired target image and the stored database images through edge detection, morphological operation, image transformation, image histogram matching and mutual information for both target and stored database images. Sobel operator is used to detect edges in both acquired target image and the stored database images. Hough transform is used as an image transformation which groups the extracted edge points in edged images to an appropriate set of lines which helps in features extraction and matching processes in both of target and stored database images. This gives an initial indication about realization and recognition between target image and its corresponding database image. Comparisons of image histogram and mutual information for both target and database images are finally used to emphasize the recognition of the target image and its verification with its corresponding database image. The proposed recognition approach passed through four stages which are: edge detection by Sobel edge detector, thinning as a morphological operation, Hough transformation, matching process using median deviation and finally histogram matching and measuring the mutual information between target and the available database images. The experimental results proved that the proposed hybrid target recognition approach gives a more accurate and successful recognition rate than other techniques which depend on using feature based methods or intensity based methods.

Power consumption is often a major advantage of optics. When access to power is limited, such as for a satellite in geosynchronous orbit, power is often not only important, but critically important. Satellites rely on power for motion control, controlling yaw, pitch, and roll. An optical Fuzzy controller would overcome the problem of limited power. This paper explores the possibility of optical implementation of fuzzy logic for low-power optical fuzzy controllers. Recent advances in optical logic have suggested ways to overcome the problems that have plagued that field for over 40 years. In this paper the authors overviews recent advances in the optical implementation of Boolean logic and explores whether these or similar technologies might feasibly be applied to optical implementation of fuzzy logic. Specifically, the authors examines whether fuzzy logic might be productively implemented in an interferometric network in which weighting is accomplished by optical phase shifting of mutually coherent beams of light. This paper produces a optical fuzzy OR and lays the foundation for other fuzzy operators based on an interferometric network.

A morphological image enhancement method based on the GAN (General Adaptive Neighborhood) structuring elements is proposed for some problems such as low overall contrast, noise and inter-target edge of some remote sensing images. Firstly, a pixel to be processed is selected as a seed point, and an adaptive neighborhood is defined according to the image pixel characteristic and the neighborhood constraint relation to obtain the self-adaptive structuring elements set. A corresponding self-adaptive morphological operation based on the self-adaptive structuring elements set is constructed with reference to the classical morphological operation definition, and the self-adaptive alternative filter is constructed by using the adaptive morphological operation combination so as to realize the enhancement of the remote sensing image. The experimental results show that the method can preserve the accurate positioning of the objects edge while enhancing the image, avoid the loss of information, has better noise removing performance. Compared with the classical morphological filter operator, the single-scale Retinex algorithm and bi-histogram equalization (BHE) algorithm, the contrast ratio and the signal-to-noise ratio of the enhanced image are improved.