Optical implementations of threshold decomposition and morphological operations with dual-rail processing

Mathematical morphology on l-images

The concept of Euclidean and geodesic distance is of great importance in binary mathematical morphology (MM), and the grey-level MM deals mainly with neighborhood configuration analysis. This paper presents a novel approach to grey-level MM based on the concept of a distance function relative to topographical surfaces. By introducing the notions of connection cost and deviation cost, this paper defines the topographical and differential distances and develops a powerful theoretical framework for establishing the equivalence between the two fundamental notions of skeleton by influence zones (SKIZ) and watershed: the SKIZ of the set of the minima of a grey-level image f with respect to the differential distance function is exactly the watershed of f. This leads to a duality between binary and grey-level images and to new fast algorithms for computing the SKIZ and the watershed.

Constraints and proofs are provided by Shih and Pu (see ibid., vol.43, no.2, p.539, 1995) to justify their previous analysis of the idempotent soft morphological filters. It is shown that for a special case, the idempotency in Theorems 3 and 4 of a previous paper by the authors will not hold in the first stage, but the root signal will be produced in the second stage. The exact constraint is added to ensure the idempotency to be valid for the soft morphological closing and opening

Morphology is an image algebra technique whereby the shape and structure of an input object is transformed by a smaller object called the structuring element. The two most fundamental morphological operations, erosion and dilation, are usually defined in terms of set operations. Alternatively they can be understood in terms of a convolution followed by a threshold. In this paper we describe an iterative acoustooptic (AO) morphological image processor. The input to the system is displayed on a 128 × 128 magnetooptic spatial light modulator, and the system utilizes an AO Bragg cell in the Fourier plane of a coherent optical correlator to generate the desired structuring element. Thresholding is performed electronically in an image processing system. The feedback necessary for multiple erosions and dilations is provided electronically via a single computer that controls both an image processing system in the output image plane and the MOSLM.

A new type of nonlinear image processor based on morphological processing is demonstrated. Morphological image processing is based on the successive binary convolution of an image with a selectable convolution kernel. Its field of application includes numerical optical computing and binary image processing. Simple serial commands from a small electronic computer control the selection of the convolution kernels for a given iteration and consequently the parallel processing of very large optical data planes. 1.

A developed, binary, image-processing technique is proposed, and a dual-channel, optical, real-time morphological processor is developed. Nine binary image processings can be realized fully in parallel. The measures for compensating scale and rotation distortion for pattern recognition are provided. Some applications of optical, morphological binary image processing are studied and experimental results are listed.

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.

Chapter 3 - Fuzzy skeleton and skeleton by influence zones: a review

Development of industrial image processing applications is strictly governed by economical concerns. High demands with respect to recognition speed and certainty have to be satisfied by means of low-cost hardware implementations. Especially realization of such algorithms for extraction of regional information, e.g. for shape recognition, is thus a challenging task. The latter is addressed by investigating the implementability of binary morphological operations with large operator masks. The design procedure for implementation in low-cost FPGAs as well as a relatively accurate estimation of the required hardware effort is presented. Programmable operator mask sizes of up to 31 /spl times/ 31 pixels and a high data throughput of several giga-pixels per second can be obtained by the proposed methods.

Chapter 1 describes the early work of von Neumann (1951) on cellular automata. This work was not accompanied by reductions to practice in hardware as it was impractical at that time to build machines having the millions of devices required. Only with the development of high-density integrated circuitry in the 1970s has this feat now been accomplished (Chapter 11). Therefore, during the 1950s cellular automata were emulated using the general-purpose computers which were available at that time. The work of Moore (1966) and Kirsch (1957) at the National Bureau of Standards, of Ulam (1962) at the Atomic Energy Commission, and Unger (1959) at Bell Telephone Laboratories are outstanding examples of this work. All of these workers simplified von Neumann’s 29-state processing element and concentrated their efforts on studying arrays of 2-state (binary) processing elements. In the 1960s a new trend began with the construction of the first cellular logic machines by one of the authors (Preston, 1961). These and other special-purpose machines emulated the cellular automaton by using a single high-speed processing element to operate sequentially on an array of binary data. With the introduction of the diff3 in the 1970s (Graham, and Norgren, 1980) cellular logic machines were manufactured having several processing elements. Then Sternberg (1981) introduced a pipelined cellular logic machine, called the Cytocomputer, having approximately 100 processing elements. The Cytocomputer was also the first cellular logic machine to include numerical (multi-state) processing elements in addition to binary processing elements, thus making the transition from high-speed special-purpose machines limited to bilevel data to a system which could manipulate multi-state data. This chapter concentrates on the evolution and architecture of the cellular logic machines which have been built over the past two decades, all of which handle bilevel data arrays. Machines of this kind are currently in wide use both for commercial and research purposes in image processing. Despite their limitation to bilevel data, they are also useful in graylevel image processing due to their ability to convert graylevel images to binary images by multiple thresholding and, after performing logical operations at these thresholds, to convert results to graylevel output by arithmetic summation (Chapter 2).

We consider the problems of image segmentation and classification, and image restoration when the true image is made up of a small number of (unordered) colors. Our emphasis is on both performance and speed; speed has become increasingly important for analyzing large images and multispectral images with many bands, processing large image databases, real-time or near realtime image analysis, and the online analysis of video. Bayesian image analysis provides an elegant solution to these problems, but it is computationally expensive, and the solutions it provides may be sensitive to unrealistic global properties of the models on which it is based. The ICM algorithm is faster and based on the local properties of the models underlying Bayesian image analysis; parameter estimation is performed iteratively via pseudolikelihood. Mathematical morphology is faster again and is widely considered to perform well, but lacks a statistical basis; method selection (analogous to parameter estimation) is done in a rather ad hoc manner. We propose Bayesian morphology, a synthesis of these methods that attempts to combine the speed of mathematical morphology with the principled statistical basis of ICM. The key observation is that when the original image is discrete (or if an initial segmentation has been carried out), then, assuming a Potts model for the true scene and channel transmission noise, (1) the ICM algorithm is equivalent to a form of mathematical morphology and (2) the segmentation is insensitive to the precise values of the model parameters. Unlike in standard Bayesian images analysis and ICM, it is feasible to do maximum likelihood estimation of the parameters in this setting. For gray-level or multispectral images, we propose an initial segmentation based on the EM algorithm for a mixture model of the marginal distribution of the pixels. The resulting algorithm is much faster than ICM, with gains that increase for more bands and larger images, and has good performance in experiments and for real examples.

During the course of conventional multiscale morphological filtering, when the noise is filtered, the signals which are smaller than the structuring elements (SE) may be also removed. In this paper, a novel edge preserving multiscale filtering (EPMF) method based on mathematical morphology is proposed. The EPMF method adds the multiscale top-hat transformation and bottom-hat transformation to the conventional multiscale morphological opening and closing filtering. The two added transformations are used to extract and smooth the features which are smaller than the current scale. It is also found that the smaller features have greater possibilities to contain noise particles. Accordingly, the coefficients of top-hat transformation and bottom-hat transformation are modified. Simulation results on the standard gray-level images show that the proposed EPMF method can effectively remove noise and completely preserve the edge of images. It demonstrates better performance than the conventional filtering methods.

When considering ways to automate the generation of image processing algorithms for object recognition tasks, one critical element is the availability of measures to assess the potential and actual ability of individual operations for making a set of desired discriminations. This paper discusses the analysis and evaluation of grey-level image processing operators or algorithms from the perspective of trying to search automatically through a large space of them for one which satisfactorily performs a given recognition or discrimination task. Performance of an operator may be expressed in terms of accuracy, consistency, and cost, over an entire set of training images.The major issues of evaluating and choosing between operators in this context are discussed, and examples are given of measures which can be used to evaluate classes of operators for applicability, or to evaluate individual operators or parameter settings for actual performance. The paper first describes the form of the analysis for binary morphological operators, and then shows how it may be directly extended to grey-level morphological operators. Several examples are provided to show how grey-level pixel sets may be discriminated on the basis of various combinations of grey level and spatial criteria, as calculated by the basic morphological operators of erosion, dilation, opening, and closing.

Segmentation of ultrasound images is challenging because of the noisy nature and subtle boundaries of objects in ultrasound images. This paper discusses object segmentation and identification for ultrasound fetal images. The feature space for segmentation consists of information extracted from three sources: gray level, texture, and wavelet-based decomposition. Several texture features, including Laws' texture-energy measures and features based on local gray level run-length, were found useful for segmentation. An unsupervised clustering procedure was used to classify each pixel into its most probable class. Morphological operations were used to remove noisy structures from the original gray level images and to improve the boundaries of the segmented objects. An algorithm was developed to locate objects of interest based on a multiscale implementation of an image transform. Fetal heads were identified and their corresponding measurements are made automatically. The method was tested with a set of clinical images. The resulting images showed clearly the segmented objects. The measurements agreed closely with a sonographer's measurements. The purposed method holds promise for processing and analyzing ultrasound fetal images.

In digital topology, the use of a pair of connectivities is required to avoid topological paradoxes. In mathematical morphology, self-dual operators and methods also rely on such a pair of connectivities. There are several major issues: self-duality is impure, the image graph structure depends on the image values, it impacts the way small objects and texture are processed, and so on. A sub-class of images defined on the cubical grid, well-composed images, has been proposed, where all connectivities are equivalent, thus avoiding many topological problems. In this paper we unveil the link existing between the notion of well-composed images and the morphological tree of shapes. We prove that a well-composed image has a well-defined tree of shapes. We also prove that the only self-dual well-composed interpolation of a 2D image is obtained by the median operator. What follows from our results is that we can have a purely self-dual representation of images, and consequently, purely self-dual operators.KeywordsSelf-dual operatorsTree of shapesVertex-valued graphWell-composed gray-level imagesDigital topology