Binary Morphological Operations Research Articles

Real-time restoration of white-light confocal microscope optical sections

Confocal microscopes (CM) are routinely used for building 3-D images of microscopic structures. Nonideal imaging conditions in a white-light CM introduce additive noise and blur. The optical section images need to be restored prior to quantitative analysis. We present an adaptive noise filtering technique using Karhunen-Loéve expansion (KLE) by the method of snapshots and a ringing metric to quantify the ringing artifacts introduced in the images restored at various iterations of iterative Lucy-Richardson deconvolution algorithm. The KLE provides a set of basis functions that comprise the optimal linear basis for an ensemble of empirical observations. We show that most of the noise in the scene can be removed by reconstructing the images using the KLE basis vector with the largest eigenvalue. The prefiltering scheme presented is faster and does not require prior knowledge about image noise. Optical sections processed using the KLE prefilter can be restored using a simple inverse restoration algorithm; thus, the methodology is suitable for real-time image restoration applications. The KLE image prefilter outperforms the temporal-average prefilter in restoring CM optical sections. The ringing metric developed uses simple binary morphological operations to quantify the ringing artifacts and confirms with the visual observation of ringing artifacts in the restored images.

A Multi-dimensional Systems Theory Framework for Binary Mathematical Morphology

Binary mathematical morphology is a set theoretical approach to multidimensional signal processing. It enables extraction of shape features and is thus a well known and successfully applied kind of operation for image processing and recognition tasks. Nevertheless, a system theoretical treatment of these operations seems to be difficult, due to its mathematical origin of integral geometry. A system theoretical description of binary mathematical morphology is given in the present paper that allows to design realizations of binary morphological operations following methods from classical linear systems theory in a very favorable way. The advantage of the proposed correspondence description is exemplary shown in the development of a matching technique for shape varying object clusters.

FAST IMPLEMENTATION OF MORPHOLOGICAL OPERATIONS USING BINARY IMAGE BLOCK DECOMPOSITION

Morphological transformations are commonly used to perform a variety of image processing tasks. However, morphological operations are time-consuming procedures since they involve ordering and min/max computation of numbers resulting from image interaction with structuring elements. This paper presents a new method that can be used to speed up basic morphological operations for binary images. To achieve this, the binary images are first decomposed in a set of non-overlapping rectangular blocks of foreground pixels that have predefined maximum dimensions. Then off-line dilation and erosion of all rectangular blocks are arbitrary obtained and stored into suitable look-up array tables. By using the look up tables, the results of the morphological operations to the rectangular blocks are directly obtained. Thus, first all image blocks are replaced by their look-up array tables. Then the morphological operations are applied only to the limited number of the remaining pixels. Experimental results reveal that starting from a block represented binary image morphological operations can be executed with different types of structuring elements in significantly less CPU time. Using the block representation, we are able to perform dilation 16 times faster than non-fast implementations and 10 times faster than an alternative fast implementation based on contour processing. Significant acceleration is also recorded when using this approach for repeated application of dilation (for 10 iterations, dilation using the block representation is over 20 times faster than non-fast implementations and over four times faster than using the fast contour based approach).

Efficient binary and grey level morphological operations on a massively parallel processor

One of the most important features in image analysis and understanding is shape. Mathematical morphology is the image processing branch that deals with shape analysis. The definition of all morphological transformations is based on two primitive operations, i.e. dilation and erosion. Since many applications require the solution of morphological problems in real time, researching time efficient algorithms for these two operations is crucial. †The implementation of the above functions is beyond the scope of this paper. In this paper, efficient algorithms for the binary as well as the grey level dilation and erosion are presented and evaluated for an advanced associative processor. It is shown through simulation results that the above architecture is near optimal in the binary case and is also as efficient as the array processor with a 2D-mesh interconnection in the grey level case. Finally, it is proven that the implementation of this image processing machine is economically feasible.

Assessing Structural Changes in Knits During Processing

An automatic fabric evaluation system is developed to analyze knit structures and objectively evaluate fabric properties. Fabric images are captured with a CCD camera, and digital images are processed by histogram equalization, binary morphological operators, and pattern recognition. Six knitted fabrics are evaluated at different phases of manufac turing. Fabric construction parameters such as courses and wales per unit length, fabric cover, and areal density are measured and evaluated using the new approach and manual methods. Structural changes that occur in the fabrics at different levels of relaxation are also documented. Our image capturing and analysis system is capable of on-line control of knit structures' spatial characteristics before and after wet treatments.

Image processing of underwater multispectral imagery

Capturing in situ fluorescence images of marine organisms presents many technical challenges. The effects of the medium, as well as the particles and organisms within it, are intermixed with the desired signal. Methods for extracting and preparing the imagery for analysis are discussed in reference to a novel underwater imaging system called the low-light-level underwater multispectral imaging system (LUMIS). The instrument supports both uni- and multispectral collections, each of which is discussed in the context of an experimental application. In unispectral mode, LUMIS was used to investigate the spatial distribution of phytoplankton. A thin sheet of laser light (532 nm) induced chlorophyll fluorescence in the phytoplankton, which was recorded by LUMIS. Inhomogeneities in the light sheet led to the development of a beam-pattern-correction algorithm. Separating individual phytoplankton cells from a weak background fluorescence field required a two-step procedure consisting of edge detection followed by a series of binary morphological operations. In multispectral mode, LUMIS was used to investigate the bio-assay potential of fluorescent pigments in corals. Problems with the commercial optical-splitting device produced nonlinear distortions in the imagery. A tessellation algorithm, including an automated tie-point-selection procedure, was developed to correct the distortions. Only pixels corresponding to coral polyps were of interest for further analysis. Extraction of these pixels was performed by a dynamic global-thresholding algorithm.

Fast Implementation of Binary Morphological Operations on Hardware-Efficient Systolic Architectures

In this paper we present novel systolic architectures for the fast execution of common morphological operations, that is dilation, erosion, closing, and opening. Their novelty stems from the fact that the same unit, the combined Erosion-Dilation Architecture (EDA), is used to perform either dilation, or erosion, or both of them in parallel (depending on control signals). The proposed architectures show a major advantage on using reduced resources for storing the structuring element (SE), lead to full resource utilization, and provide high processing rates. We concentrate on 1-dim structuring elements and present an improved architecture, that performs dilation and erosion in half the time compared to other architectures, using a workload partitioning technique. Furthermore, the amenability of the EDA to VLSI implementation is exemplified by a processor that performs binary morphological operations with 1 × 3 structuring sets. Finally, we show that the modularity of the proposed architectures allows the direct extension to 2-dim morphology.

Statistical morphological skeleton for representing and coding noisy shapes

A new shape descriptor obtained by skeletonisation of noisy binary images is presented. Skeleton extraction is performed by using an algorithm based on a new class of parametrised binary morphological operators, taking into account statistical aspects. Parameters are adaptively selected during the successive iterations of the skeletonisation operation to regulate the characteristics of the shape descriptor. A probabilistic interpretation of the scheduling strategy used for parameters is proposed by analogy to stochastic optimisation techniques. Skeletonisation results on patterns extracted by a change-detection method in a visual-based surveillance application are reported. Results show the greater robustness of the proposed method as compared with other morphological approaches.

Implementation of binary and gray-scale mathematical morphology on the CNN universal machine

A cellular neural network(CNN)-based morphological engine is proposed. An effective implementation method of binary and gray-scale erosion, dilation, and reconstruction is introduced. The binary morphological operators are successfully implemented on an actual CNN universal chip. Experimental results are shown.

Implementation of mathematical morphological operations for spatial data processing

Mathematical morphology is a theory of image transformations which is based on set-theoretical, geometrical, and topological concepts. The methodology is useful particularly for the analysis of the geometrical structure in an image. Since many data types in the geosciences are related to spatial location, it is expected that the mathematical morphological operations are particularly important for geoscientific spatial data processing. In this paper, the binary mathematical morphological operations of dilation, erosion, opening, closing, hit/miss transform, and thinning are implemented using the C programming language and the PCIDSK C Toolbox. Dilation, erosion, opening, and closing operations are extended to gray-scale imagery. As an example, gray-scale image dilation and erosion operations are applied to an aeromagnetic image from the File Lake area, Manitoba, Canada for edge and linear feature detection. The detected edge and linear features are scaled into a binary image through thresholding, which allows for further binary morphological operations. Thinning operations are applied to binary images to obtain connected one-pixel thick skeletons. Trimming operations are tested to remove skeletal legs resulting from the thinning operation. Results from both binary and gray-scale images show that mathematical morphological operations can be applied efficiently to the processing of spatial data in the geosciences. The thinning operation makes it possible for edge and linear features to be vectorized and put directly into a geographic information system (GIS).

Two Image-Template Operations for Binary Image Processing

This paper presents two new image algebra image-template operationsmatch and mismatch derived from the general image-template product. These image algebra operations extend the binary morphological erosion and dilation operations and can be used to express elegantly most of binary image processing algorithms in a more natural way than binary morphological operations from the image processing viewpoint. In addition, the match and mismatch operations are easy to implement efficiently on SIMD bit-serial parallel computers.

Design and analysis of fuzzy morphological algorithms for image processing

A general paradigm for lifting binary morphological algorithms to fuzzy algorithms is employed to construct fuzzy versions of classical binary morphological operations. The lifting procedure is based upon an epistemological interpretation of both image and filter fuzzification. Algorithms are designed via the paradigm for various fuzzifications and their performances are analyzed to provide insight into the kind of liftings that produce suitable results. Algorithms are discussed for three image processing tasks: shape detection, edge detection, and clutter removal. Detailed analyses are given for the effect of noise and its mitigation owing to fuzzy approaches. It is demonstrated how the fuzzy hit-or-miss transform can be used in conjunction with a decision procedure to achieve word recognition.

Image morphological operations and edge detection using optical programmable logic neural networks

Based on the concept of 2-D programmable logic neural networks, an optical programmable image processor for neighborhood operations is proposed. The spatial polarization encoding and space-variant techniques are used in the design of an optical system which can perform multiple-instruction multiple-data image processing. The system is a cellular logic image processor with nine local neighbor inputs and three outputs. In particular, the applications of the optical scheme in binary image morphological operations and edge detection are described in detail. Simulation results are also presented.

THE FUNDAMENTALS OF FUZZY MATHEMATICAL MORPHOLOGY PART 2: IDEMPOTENCE, CONVEXITY AND DECOMPOSITION

Fuzzy mathematical morphology is an alternative extension of binary mathematical morphology to grayscale images. This paper discusses some of the more advanced properties of the fuzzy morphological operations. The possible extensivity of the fuzzy closing, anti-extensivity of the fuzzy opening and idem-potence of the fuzzy closing and fuzzy opening are studied in detail. It is demonstrated that these properties only partially hold. On the other hand, it is shown that the fuzzy morphological operations satisfy the same translation invariance and have the same convexity properties as the binary morphological operations. Finally, the paper investigates the possible decomposition, by taking (strict) α-cuts, of the fuzzy morphological operations into binary morphological operations.

Analysis of the properties of soft morphological filtering using threshold decomposition

We present the properties of soft morphological operations and the new definitions of binary soft morphological operations. It is shown that soft morphological filtering an arbitrary signal is equivalent to decomposing the signal into binary signals, filtering each binary signal with a binary soft morphological filter, and then reversing the decomposition. This equivalence allows problems in the analysis and the implementation of soft morphological operations in real time by using only logic gates for binary signals instead of sorting the numbers. The architectures of logic-gate implementation of soft morphological operations are also presented. Furthermore, unlike standard morphological filters, the soft morphological closing and opening are in general not idempotent. We develop the conditions and properties for a new class of idempotent soft morphological filters. >

THE FUNDAMENTALS OF FUZZY MATHEMATICAL MORPHOLOGY PART 1: BASIC CONCEPTS

Fuzzy mathematical morphology provides an alternative extension of the binary morphological operations to gray-scale images based on the theory of fuzzy sets. This paper introduces the basic concepts of fuzzy mathematical morphology, starting from the original definitions of the morphological operations by Serra. More specifically, the fuzzy dilation, erosion, closing and opening operations are introduced. Their basic properties such as monotonicity and interaction with union and intersection are discussed in detail. Some important relationships between the fuzzy erosion and fuzzy dilation are established.

An alternative to computing grey-scale mathematical morphological operations and its optical implementation

An alternative to the umbra definition on grey-scale mathematical morphology is proposed in this paper, which uses the top-surface set instead of the umbra to represent grey-scale structuring element. This algorithm greatly decreases the neighborhood connections for the binary morphological operation transformed from a grey-scale morphological operation. An optical incoherent correlator architecture with threshold device is developed to carry out the suggested algorithm, while a spatial digital coding method is used to represent input 3D binary data in a 2D arrangement. Experimental results are demonstrated too.

Morphological filtering as template matching

Binary morphological operations with single and multiple structuring elements are implemented using look-up table (LUT) driven templates. Many complex operations can be implemented in one pipeline processing cycle for 3*3 regions of support and in four or five cycles for 5*5 regions of support. The basis representation of the operations is used to specify the required templates.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Morphological Image Coding Based on a Geometric Sampling Theorem and a Modified Skeleton Representation

A new approach for gray-level image coding using binary morphological operations on the image bit-planes is presented. This approach is based on a Geometric Sampling Theorem (GST), and on a modified morphological skeleton. The theorem, which is proved in this paper, states conditions for the reconstruction of the boundary of a continuous two level image from a unique subset of points of its skeleton representation. This set of points, referred to as essential points, is found to play an important role in the skeleton representation of discrete binary images as well. The modified morphological skeleton (MMS) uses an exponentially increasing in size structuring element. The computational advantage of this representation was previously reported. A new approach to its development is presented here, and its advantage in image coding is demonstrated. The coding scheme consists of the following steps: First, the image is preprocessed by an error-diffusion technique in order to reduce the number of bit-planes from 8 to 4 without significant quality degradation. The pixel values are subsequently converted to Gray-code. The bit-planes are represented by the MMS. Redundancy in this representation is reduced using an algorithm motivated by the GST. These reduced modified morphological skeletons are coded with an entropy coding scheme particularly devised for efficient skeleton coding. The possibility of the introduction of geometric errors to reduce the bit-rate is also discussed. Compression ratios of up to 11:1 were obtained for satellite images.

Optimal mean-square N-observation digital morphological filters : I. Optimal binary filters

The present paper places binary morphological filtering into the framework of statistical estimation, the intent being to develop the theory of mean-square (MS) optimization. Classical binary morphological operations are interpreted as numerical functionals on binary N-vectors, so that in the random setting they can be treated as estimators dependent on N binary observation random variables. For single-erosion filters, optimization is achieved by finding the structuring element that minimizes MS error. Using the Matheron representation as a guide, we generalize the analysis to morphological filters given by unions of multiple erosions and optimize by minimizing MS error over all collections of erosions, or over a prefixed number of erosions. In all cases, MS error is relative to the estimation of an unobserved variable by a morphological function of observed variables. A key element in the method is use of the basis form of the Matheron expansion to reduce significantly the structuring-element search. The technique is adapted to special morphological filters by constraining the basis representation in accordance with the class of interest. It is demonstrated that optimization in terms of erosions is equivalent to optimization in terms of dilations.