Showing papers on "Structuring element published in 1994"

Morphological Area Openings and Closings for Grey-scale Images

Abstract: The filter that removes from a binary image the components with area smaller than a parameter λ is called area opening. Together with its dual, the area closing, it is first extended to grey-scale images. It is then proved to be equivalent to a maximum of morphological openings with all the connected structuring elements of area greater than or equal to λ. The study of the relationships between these filters and image extrema leads to a very efficient area opening/closing algorithm. Grey-scale area openings and closings can be seen as transformations with a structuring element which locally adapts its shape to the image structures, and therefore have very nice filtering capabilities. Their effect is compared to that of more standard morphological filters. Some applications in image segmentation and hierarchical decomposition are also briefly described.

Evolution equations for continuous-scale morphological filtering

Abstract: Multiscale signal analysis has emerged as a useful framework for many computer vision and signal processing tasks. Morphological filters can be used to develop nonlinear multiscale operations that have certain advantages over linear multiscale approaches in that they preserve important signal features such as edges. The authors discuss several nonlinear partial differential equations that model the scale evolution associated with continuous-space multiscale morphological erosions, dilations, openings, and closings. These equations relate the rate of change of the multiscale signal ensemble as scale increases to a nonlinear operator acting on the space of signals. The nonlinear operator is characterized by the shape and dimensionality of the structuring element used by the morphological operators, generally taking the form of a nonlinear function of certain partial differential operators. >

A Euclidean distance transform using grayscale morphology decomposition

Abstract: A fast and exact Euclidean distance transformation using decomposed grayscale morphological operators is presented. Applied on a binary image, a distance transformation assigns each object pixel a value that corresponds to the shortest distance between the object pixel and the background pixels. It is shown that the large structuring element required for the Euclidean distance transformation can be easily decomposed into 3/spl times/3 windows. This is possible because the square of the Euclidean distance matrix changes uniformly both in the vertical and horizontal directions. A simple extension for a 3D Euclidean distance transformation is discussed. A fast distance transform for serial computers is also presented. Acting like thinning algorithms, the version for serial computers focuses operations only on the potential changing pixels and propagates from the boundary of objects, significantly reducing execution time. Nonsquare pixels can also be used in this algorithm. An example application, shape filtering using arbitrary sized circular dilation and erosion, is discussed. Rotation-invariant basic morphological operations can be done using this example application. >

Optimal decomposition of convex morphological structuring elements for 4-connected parallel array processors

Abstract: A morphological operation using a large structuring element can be decomposed equivalently into a sequence of recursive operations, each using a smaller structuring element. However, an optimal decomposition of arbitrarily shaped structuring elements is yet to be found. In this paper, we have derived an optimal decomposition of a specific class of structuring elements/spl mdash/convex sets/spl mdash/for a specific type of machine/spl mdash/4-connected parallel array processors. The cost of morphological operation on 4-connected parallel array processors is the total number of 4-connected shifts required by the set of structuring elements. First, the original structuring element is decomposed into a set of prime factors, and then their locations are determined while minimizing the cost function. Proofs are presented to show the optimality of the decomposition. Examples of optimal decomposition are given and compared to an existing decomposition reported by Xu (1991). >

A mathematical morphology approach to image formation and image restoration in scanning tunnelling and atomic force microscopies

Abstract: In the nanometer resolution range, image formation in STM and AFM cannot be described by a convolution process but is essentially governed by the geometrical interaction between the specimen surface and the tip surface. This non-linear process can be simply described by a dilation of the surface profile by a three-dimensional structuring element which has the shape of the tip. Accordingly, the restoration procedure using these concepts consists in performing the erosion of the image by the same structuring element. A preliminary investigation of a possible blind restoration procedure (i.e. restoration without a very precise knowledge of the tip shape and without the need of using a known test object) is performed.

Application of SKIPSM to grey-level morphology

Abstract: 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

A fast implementation of 1-D grayscale morphological filters

Abstract: This paper presents an algorithm for the fast implementation of 1-D grayscale morphological filters with set structuring elements. The algorithm is developed by filter property analysis, instead of by architecture design. It performs an opening or closing with a single pass procedure. The average number of operations required is less than three comparisons per sample for openings and closings, which is independent of the size of the structuring element used. >

Decomposition of morphological structuring elements

Abstract: Mathematical morphology has become an important tool for machine vision since the influential work by Serra (1982). It is a branch of image analysis based on set-theoretic descriptions of images and their transformations. As is well known, the chain rule for basic morphological operations, i.e., dilation and erosion, lends itself well to pipelining. Specialized pipeline architecture hardware built in the past decade is capable of efficiently performing morphological operations. The nature of specialized hardware depends on the strategy for morphologically decomposing a structuring element. The two-pixel decomposition technique and the cellular decomposition technique are the two main techniques for morphological structuring-element decomposition. The former was used by the image flow computer and the latter by the cytocomputer.

Image Analysis Methods Based on Hierarchies of Graphs and Multi-Scale Mathematical Morphology

Abstract: This thesis is about image analysis methods based on hierarchical graph represen-tations. A hierarchical graph representation of an image is an ordered set of graphs that represent the image on different levels of abstraction. The vertices of the graph represent image structures (lines, areas). Its edges represent the relations between those structures (adjacency, collinearity). Graphs on higher levels of the hierarchy give a more global and abstract representa-ti-on of the image. A number of image analysis methods based on hierarchical graph repre-senta-tions were developed. These methods were applied to image segmentation, detection of linear structures and edge detection. It is found that a hierarchical graph is an attractive framework for image analysis, because it can easily encode and handle different structures, and because structures and there relations are encoded in the same repre-sentation. The only restriction of the method is its 'bottom-up' character. However it is suggested how this can be remedied by a 'top-down' analysis in a later stage of the proces. The second part of this study is about multiresolution morphology. Discs defined by weighted metrics were used as structuring elements. Weighted metrics can approximate the Euclidian metric to within a few percent. Algorithms were developed to perform the elementary morphological operations (erosion, dilation, opening, closing), and some advanced operations as the medial axis transform, the opening transform, and the patttern spec-trum-transform. The computational costs of these methods is comparable to the cost of conventional morphological methods using square structuring elements.

Image enhancement using mathematical morphology with adaptive structuring elements

Abstract: Mathematical morphology has been widely used in recent years in the image processing area. Due to the nonlinear nature of morphological operations, their application to some image noise removal problems have achieved very impressive results. However, of the morphological algorithms by far most use only a single structuring element. To optimize the performances on various parts of an image, we introduce morphological operations using an adaptive structuring element for noise removal of binary and grayscale images. These techniques were used in the preprocessing of character recognition problems at CEDAR, SUNY at Buffalo, New York. Demonstrations of the improved performance of the algorithm are provided.

A Spatially Variant, Locally Adaptive, Background Normalization Operator

Abstract: This paper describes a spatially variant, locally adaptive, background normalization operator that is defined in terms of morphological openings and closings. The variable opening (and closing) residue operators address the problems that can occur when one attempts to choose a single structuring element size for background normalization purposes, in cases where the objects of interest have multiple or unknown widths. The operators attempt to assign a natural width to each pixel in an image, based on the opening or closing size that causes the largest change in its value. This size then also determines a local contrast value for that pixel. The size, local contrast and original grey values of pixels in an image can be used to cluster pixels as an aid to performing image segmentation, or foreground-background discrimination. This paper describes and illustrates the algorithm, and discusses how its outputs may be used for image analysis and parameter selection.

Fast morphology hardware using large‐sized structuring element

Abstract: Mathematical morphology is one of the data processing methods that is extremely useful for image processing and has many applications, such as, noise elimination, shape description, texture analysis, and so on. The mathematical base of morphological processing is dilation and erosion which are described by set analysis and can be expressed in logical AND, OR notation. Localized parallel processing including morphological processing is not suitable to Neumann architecture because of the memory access bottleneck which makes it hard to achieve the high throughout data processing required in applications such as video image processing. Also the cytocomputer aimed at fast image processing has a drawback in that it can handle only very small structuring elements. In this paper, first, an algorithm is presented which accelerates morphological image processing. Next, the algorithm to design a specialized hardware which processes the real-time video image is implemented and finally, an application of this specialized hardware for medical use is described.

Texture Classification Using Neural Networks and Local Granulometries

Abstract: This paper presents a method for segmenting interstitium and tubules in images of kidneys’ biopsies. Openings by structuring elements of increasing size, forming a granulometry, were performed on the entire image. For every pixel x and for each size of the structuring element the volume over a small window centered at x was measured (a local Granulometry). The vectors defined as the volume gradient served as an entry to a neural network (NN). The NN was taught to discriminate between vectors corresponding to pixels of the interstitium (textured region) and vectors corresponding to pixels of the tubules (non-textured region). The correlation factor between the area of the interstitium and the renal function was computed and compared to the results obtained with the manual procedure and two other automatic procedures.

An Efficient Implementation Technique of Adaptive Morphological Operations

Abstract: In the paper the implementation aspects of mathematical morphology based on a new formalization of the window operation is presented. The proposed technique called the Reverse Window Operation (RWO) can also be applied to adaptive morphological operations. In order to reduce the control complexity an algorithm is proposed, which uses a region-based parameter modification for the structuring element adaptation. Finally, an application of a data-dependent processing technique using the adaptive filter scheme is demonstrated.

C-Factor: A Morphological Shape Descriptor

Abstract: Mathematical morphology is a relatively new approach that is being applied to image processing and analysis. Mathematical morphology is based on shape. Hence morphological tools are well suited to problems of shape analysis. Shape is conceptually quite abstract, and it is rather difficult to quantify. In this paper a simple quantitative shape descriptor based on a modified image-skeleton spectrum is defined, and experiments to validate its use are described. We attempted to incorporate human ideas of shape into the new shape descriptor. Throughout this paper it is assumed that the reader has a good knowledge of the basic morphological operations and of the skeletonization procedure.

Properties of Image Sequences Generated Through Opening Residuals

Abstract: This paper states and proves a number of properties of the tophat and the tophat spectrum. These include: the tophat is antiextensive and idempotent (but not increasing); each image in the tophat spectrum is size-limited and open; the structuring element family need not be mutually open to generate a tophat spectrum; if the SE family is mutually open, and the original image is binary, each image in the tophat spectrum includes the open part of the corresponding image from the opening spectrum; and, the tophat spectrum is identical to the opening spectrum created with a family of flat, 1D structuring elements.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Fast algorithms for grayscale morphological operations

Abstract: This paper presents efficient real time implementation methods for grayscale composite (opening and closing) function processing (FP) systems. The proposed method is based on a matrix representation of the composite FP system using a basis matrix. However, the straightforward implementation of the FP opening and closing has a complexity of O(N/sup 2/), where N is the size of the structuring element. In order to improve the computational efficiency of the proposed implementation method, we present a recursive algorithm based on redundancy of the basis matrix and input matrices. It is shown that, with the proposed scheme, both opening and closing can be determined by 2N-2 additions and 2N-2 comparisons.

Multiple structuring element neural learning via cellular logic

Abstract: Multiple Structuring Element Neural Learning Via Cellular LogicLan Shao, Liren Liu, Guoqiang Li and Xuejun ZhangShanghai Institute of Optics and Fine Mechanics, Academia SinicaP.O.Box 800-211, Shanghai 201800, P.R.ChinaABSTRACTAn idea for the construction of morphological structuring elements byneural learning from multiple targets is proposed. Accordingly, neuralerosion is developed. Thus multi-character recognition and multi-to-onesymbolic substitution can be easily realized. Optical implementationbased on incoherent optical correlation is illustrated.

Neural network implementation of mathematical morphology operation

Abstract: This paper proposes a feedforward neural network structure to realize the mathematical morphology operations (MMO), namely: HMT (Hit and Miss Transformation), dilation, erosion, opening, closing, and the union and intersection (for multistructuring elements and multioperators) of them. Different kinds of operations can be implemented by assigning the weights, the threshold values and the architecture of the network according to the operation itself to be implemented. A general expression relating the weight value, threshold value to the configuration of the structuring element for different operations is derived, the assigning of the values becomes merely straight-forward training procedure of the proposed network. Also, it is proved that with a single hidden layer, all the MMO can be implemented by the ANN. The most interesting aspect of the method proposed is the reduction of on-line operation steps, which for conventional MMO algorithm consist of a series of operations processed consecutively. As a extension of the method, Boolean function implementations of the operations are also proposed, in which, the concept of collection of basic `And' structuring elements is presented. We prove that all MMO sequence can be implemented by a 2-layer logic gate array (or 3 layers in the sense of node levels).

Design of Morphological Processors for Ultrasonic Nondestructive Evaluation of Materials — A Review

Abstract: Sequential morphological operations are capable of extracting signal features while suppressing random noise and undesired signal patterns (e.g., speckles in ultrasonic imaging). They utilize a structuring element which interacts with the signal in order to suppress noise and enhance certain desirable information. In this paper we identify a group of sequential morphological processors that exhibit a performance similar to lowpass, bandpass and highpass filters. Furthermore, a class of morphological processors are presented which offer peak detection and edge detection. Deterministic and stochastic properties of combinational (parallel and/or serial) morphological processors have been studied. In particular, the information content of ultrasonic signals has been used to design a suitable structuring element with optimal performance. The results obtained by applying morphological processors to experimental ultrasonic signals show that combinational morphological processors can improve flaw detection when the signal is contaminated by impulsive thermal noise and/or microstructure scattering echoes.

3‐D spatiotemporal subband decomposition of image sequences by mathematical morphology

Abstract: An efficient 3‐D spatiotemporal image sequence decomposition method using mathematical morphology is described in this paper. The method can be used to decompose the spectrum of the input signal into 8 and 4 spatiotemporal subband images. It does this using two different sets of structuring elements. After decomposition, each band image can be decimated and coded for data transmission. This subband pyramid scheme preserves the number of pixels which existed in the original image, has an efficient hierarchical data structure, and allows parallel implementation. Therefore, this scheme has great potential for High Definition Television (HDTV) coding, multimedium video compression, etc. As regards filtering, the unique advantages of morphology over the linear filtering approach are: 1) it utilizes direct geometric interpretations; and 2) it is simple and efficient when used in conjunction with parallel/pipelining hardware. Some image sequence examples are given to show the effectiveness of this approach.

Morphological pattern restoration: optimal structuring elements

Abstract: — In this paper, we derive the optimal structuring elements of morphological filters in image restora-tion. The expected pattern transformation of random sets is presented. An estimation theory framework for randomsets is subsequently proposed. This framework is based on the least mean difference (LMD) estimator. The leastmean difference (LMD) estimator is defined to minimize the cardinality of the expected pattern transformation of theset-difference of the parameter and the estimate. Several important results for the determination of the least meandifference (LMD) estimator are derived. The least mean difference (LMD) structuring elements of morphologicalfilters in image restoration are finally derived.Keywords: mathematical morphology, nonlinear filtering, pattern restoration, random set theory. I. Introduction Pattern restoration is an important problem in image processing and analysis applications. Various methods havebeen proposed for pattern restoration. Among the most important techniques is the median filter (and its repeatediterations) [1-2]. The median filter has been proven to minimize the absolute-value of the error [1]. The ubiquity ofthe median filter (and its repeated iterations) is further attributed to its superior performance in pattern restorationapplications [2]. The implementation of this technique, however, results in a high computational complexity due tothe large number of iterations required.A more recent approach to pattern restoration is based on morphological filters (i.e., increasing and idempotentoperators) [3-9]. In [10-13] morphological filters have been demonstrated to provide an approximation of medianfilters. The popularity of morpholoigcal filters in pattern restoration applications is ultimately attributed to theirperformance [14-19]. The main advantage of morphological filters is due to their idempotence (i.e., single iterationfilters) [3-9]. Fast algorithms for the implementation of morphological filters have also been proposed [20]. As aresult, a very low computational complexity is required for the implementation of morphological filters.In the theory of mathematical morphology an image is probed by a siruduring element which interacts withthe image in order to extract useful information about the geometrical structure of the image {3-9J. A fundamentalproblem in the application of mathematical morphology is the determination of the optimal structuring element. Theperformance of the morphological filters in pattern restoration is critically dependent on the choice of the structuringThis work was supported by the Office of Naval Research Award N00014-91-J-1725.

Optimal single stage restoration of split-beam sonar images via mathematical morphology

Abstract: Split-beam sonar binary images are inherently noisy and have large quantities of shot noise as well as many missing data points. We address the problem of their restoration via mathematical morphology. Conventional restoration techniques for these types of images do not make use of any of the spatial relationships between data points, such as a qualitative observation that outliers tend to have much larger distances to neighboring pixels. We first define an explicit noise model that characterizes the image degradation process for split-beam sonar images. A key feature of the model is that the degradation is split into two parts, a foreground component and a background component. The amount of noise occurring in the background decreases with distance from the underlying signal object. Thus outliers in the model have the same statistical properties as those observed in training data. Next we propose two different restoration algorithms for these kinds of images based respectively on morphological distance transforms and dilation with a toroid shaped structuring element followed by intersection. Finally we generalize to processing other kinds of imagery where applicable.