Fuzzy reasoning morphological operators and their optical implementation

A programmable opto-electronic analogic CNN computer (POAC) provides an efficient frame for diverse image processing applications, as it combines the enormous inherent computational capabilities of our new, massively parallel, but flexibly programmable optical CNN implementation with the capabilities of a visual CNN-UM chip. Our optical CNN implementation is based on an original, semi-incoherent optical correlator architecture, which is superior to other optical implementations in several respects. It makes real time reprogramming of a new type of joint Fourier transform correlator (t/sub 2/-JTC) possible while preserving the inherent speed of VanderLugt type of systems. Furthermore the POAC architecture overcomes the main limitations of both the microelectronic (VLSI) and other optical implementations. In this paper it will be shown that this device is particularly useful in image-processing algorithms, which cannot be fulfilled real time by any other existing optical or digital system due to the high number of pattern matching tasks required.

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.

A generic language for optical parallel processing image logic algebra (ILA), is proposed. In ILA a neighborhood configuration pattern (NCP) is introduced, and image transformations are defined by the use of NCP operations. The comprehensive relationship of ILA to symbolic substitution, optical array logic, mathematical morphology, and binary image algebra are clarified. Furthermore, an architecture that is suited for ILA and its optical implementations is proposed.

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.

The mathematical morphology was applied to high-speed automaton fault diagnosis in this paper, which a new method was proposed to diagnosis high-speed automaton fault based on mathematical morphology and the combination of fuzzy clustering. Take a high-speed automaton fault data in laboratory tests for example; various types were analyzed for the fault signal. The results demonstrated that the combination of mathematical morphology and fuzzy clustering applied on a high-speed automaton can effectively diagnose faults, providing a new way for high-speed automata fault diagnosis.

Mathematical morphology on l-images

An overview of SKIPSM (eparated-Kemel Jinage rocessing using Finite state Machines), a powerful new way to implement many standard image processing operations, is presented in a two companion ape2 This paper describes the application of SKJPSM to grey-level morphology, which involves . in some cases, the reformulation of the grey-level morphology problem as a set of binary morphology operations, . the separation of 2-D morphological operations into a row operation followed by a column operation, . the formulation of these row and column operations in a form compatible with pipelined operation, S the implementation of the resulting operations as simple finite-state machines, and S theautomated generation of the finite-state machine configuration data. Grey-level morphology presents some difficulties to the SKJPSM paradigm having to do with word length. In spite of this, some very useful results can be obtained. Some key features of SKIPSM, as applied to grey-level morphology, are S There is a tradeoffbetween structuring element (SE) size and number of grey levels. . The SEs can be arbitrary . With currently-available components, SEa up to 5x5 and larger can be obtained. S Jfl certain special cases, SEs up to 9x9 and larger can be obtained. . Multiple SEs can be applied simultaneously in a single pipeline pass. S The user specifies the SE or SEs. All other steps can be automated. This paper includes some simple examples of the results and gives implementation feasibility guidelines based on SE size and number of grey levels. The limitations of SKIPSM in this application all relate to the capabilities of the available RAM microchips. As chip capabilities expand, larger SE sizes and greater numbers of grey levels will become feasible. KEYWORDS: image processing, separability, real time, implementations, finite-state machines, grey-level morphology

An automated mathematical morphology driven algorithm for water body extraction from remotely sensed images

A method for processing microfocus X-ray images is described. It is based on high-frequency filtration and morphological image processing, which increases the contrast of the X-ray details. One of the most informative X-ray techniques is microfocus X-ray. In some cases, microfocus X-ray images cannot be reliably analyzed due to the peculiarities of the shooting method. So, the main disadvantages of microfocus X-ray images are most often an uneven background, distorted brightness characteristics and the presence of noise. The proposed method for enhancing the contrast of fine image details is based on the idea of combining high-frequency filtering and morphological image processing. The method consists of the following steps: noise suppression in the image, high-frequency filtering, morphological image processing, obtaining the resulting image. As a result of applying the method, the brightness of the contours in the image is enhanced. In the resulting image, all objects will have double outlines. The method was tested in the processing of 50 chest radiographs of patients with various pathologies. Radiographs were performed at the Mariinsky Hospital of St. Petersburg using digital stationary and mobile X-ray machines. In most of the radiographs, it was possible to improve the images contrast, to highlight the objects boundaries. Besides, the method was applied in microfocus X-ray tomography to improve the information content of projection data and improve the reconstruction of the 3D image of the research object. In both the first and second cases, the method showed satisfactory results. The developed method makes it possible to significantly increase the information content of microfocus X-ray images. The obtained practical results make it possible to count on broad prospects for the method application, especially in microfocus X-ray.

SKIPSM (separated-kernel image processing using finite state machines) is a technique for implementing large-kernel binary- morphology operators and many other operations. While earlier papers on SKIPSM concentrated mainly on implementations using pipelined hardware, there is considerable scope for achieving major speed improvements in software systems. Using identical control software, one-pass binary erosion and dilation structuring elements (SEs) ranging from the trivial (3 by 3) to the gigantic (51 by 51, or even larger), are readily available. Processing speed is independent of the size of the SE, making the SKIPSM approach practical for work with very large SEs on ordinary desktop computers. PIP (prolog image processing) is an interactive machine vision prototyping environment developed at the University of Wales Cardiff. It consists of a large number of image processing operators embedded within the standard AI language Prolog. This paper describes the SKIPSM implementation of binary morphology operators within PIP. A large set of binary erosion and dilation operations (circles, squares, diamonds, octagons, etc.) is available to the user through a command-line driven dialogue, via pull-down menus, or incorporated into standard (Prolog) programs. Little has been done thus far to optimize speed on this first software implementation of SKIPSM. Nevertheless, the results are impressive. The paper describes sample applications and presents timing figures. Readers have the opportunity to try out these operations on demonstration software written by the University of Wales, or via their WWW home page at http://bruce.cs.cf.ac.uk/bruce/index.html .

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.

This paper gives a novel concept of what we call as Geometric Filters defined over a 3-D rectangular grid of pixels. These G-Filters have potential applications to processing of volumetric images. In addition, the paper describes in brief the algebra of G-Filters by formulating a lattice of convex polyhedrons (structuring elements) constructed in a 3X3X3 grid of pixels. The results are visualized as a distributive lattice. Mathematical morphology is an application of lattice theory .Many applications of mathematical morphology like erosion, dilation etc, use structuring elements. The work discussed in this paper is systematically generating the 3-D structuring elements by using geometric filters (G-Filters) for mathematical, morphological operations.

Mathematical Morphology (MM) is a general method for image processing based on set theory. The two basic morphological operators are dilation and erosion. From these, several non linear filters have been developed, usually with polynomial complexity and this because the two basic operators depend strongly on the definition of the structural element. Most efforts to improve the algorithm's speed for each operator are based on structural element decomposition and/or efficient codification. In this second part, the concepts developed in part I (see Diaz de Leon and Sossa Azuela, “Mathematical morphology based on linear combined metric spaces on Z^1 (part I): Fast distance transforms,” Journal of Mathematical Imaging and Vision, Vol. 12, No. 2, pp. 137–154, 2000) are used to prove that it is possible to reduce the complexity of the morphological operators to zero complexity (constant time algorithms) for any regular discrete metric space and to eliminate the use of the structural element. In particular, this is done for an infinite family of metric spaces further defined. The use of the distance transformation is proposed for it comprises the information concerning all the discs included in a region to obtain fast morphological operators: erosions, dilations, openings and closings (of zero complexity) for an infinite (countable) family of regular metric spaces. New constant time, in contrast with the polynomial time algorithms, for the computation of these basics operators for any structural element are next derived by using this background. Practical examples showing the efficiency of the proposed algorithms, final comments and present research are also given here.

The two fundamental operations in morphological image processing are dilation and erosion. These processes are defined via structuring elements. It is of practical interest to consider a variety of structuring element shapes. The realisation of dilation/erosion for convex structuring elements by use of partial differential equations (PDEs) allows for digital scalability and subpixel accuracy. However, numerical schemes suffer from blur by dissipative artifacts. In our paper we present a family of so-called flux-corrected transport (FCT) schemes that addresses this problem for arbitrary convex structuring elements. The main characteristics of the FCT-schemes are: (i) They keep edges very sharp during the morphological evolution process, and (ii) they feature a high degree of rotational invariance. We validate the FCT-scheme theoretically by proving consistency and stability. Numerical experiments with diamonds and ellipses as structuring elements show that FCT-schemes are superior to standard schemes in the field of PDE-based morphology.