Showing papers on "Structuring element published in 1995"

Decomposition of arbitrarily shaped morphological structuring elements

Abstract: For image processing systems that have a limited size of region of support, say 3/spl times/3, direct implementation of morphological operations by a structuring element larger than the prefixed size is impossible. The decomposition of morphological operations by a large structuring element into a sequence of recursive operations, each using a smaller structuring element, enables the implementation of large morphological operations. In this paper, the authors present the decomposition of arbitrarily shaped (convex or concave) structuring elements into 3/spl times/3 elements, optimized with respect to the number of 3/spl times/3 elements. The decomposition is based on the concept of factorization of a structuring element into its prime factors. For a given structuring element, all its corresponding 3/spl times/3 prime concave factors are first determined. From the set of the prime factors, the decomposability of the structuring element is then established, and subsequently the structuring element is decomposed into a smallest possible set of 3/spl times/3 elements. Examples of optimal decomposition and structuring elements that are not decomposable are presented. >

Recursive erosion, dilation, opening, and closing transforms

Abstract: A new group of recursive morphological transforms on the discrete space Z/sup 2/ are discussed. The set of transforms include the recursive erosion transform (RET), the recursive dilation transform (RDT), the recursive opening transform (ROT), and the recursive closing transform (RCT), The transforms are able to compute in constant time per pixel erosions, dilations, openings, and closings with all sized structuring elements simultaneously. They offer a solution to some vision tasks that need to perform a morphological operation but where the size of the structuring element has to be determined after a morphological examination of the content of the image. The computational complexities of the transforms show that the recursive erosion and dilation transform can be done in N+2 operations per pixel, where N is the number of pixels in the base structuring element. The recursive opening and closing transform can be done in 14N operations per pixel based on experimental results. >

Morphological pyramids with alternating sequential filters

Abstract: The aim of this paper is to find a relationship between alternating sequential filters (ASF) and the morphological sampling theorem (MST) developed by Haralick et al. (1987). The motivation behind this approach is to take advantage of the computational efficiency offered by the MST to implement morphological operations. First, we show alternative proofs for opening and closing in the sampled and unsampled domain using the basis functions. These proofs are important because they show that it possible to obtain any level of a morphological pyramid in one step rather than the traditional two-step procedure. This decomposition is then used to show the relationship of the open-closing in the sampled and unsampled domain. An upper and a lower bound, for the above relationships, are presented. Under certain circumstances, an equivalence is shown for open-closing between the sampled and the unsampled domain. An extension to more complicated algorithms using a union of openings and an intersection of closings is also proposed. Using the Hausdorff metric, it is shown that a morphologically reconstructed image cannot have a better accuracy than twice the radius of the reconstruction structuring element. Binary and gray scale examples are presented. >

A background based adaptive page segmentation algorithm

Abstract: A novel page segmentation algorithm is provided in this paper. Based on the extraction of the background, it offers the benefit of being adaptive to the context of the document and to be insensitive to the orientation of the text blocks. It involves a two-dimensional isotropic structuring element used to characterized the white streams. This element is a disk approximated by a regular octagon which can be recursively generated. Another advantage of the proposed method is that a hierarchical segmentation can be derived from the image built upon the octagonal pattern. This tree allows to perform an isotropic multi-scale smearing, which leads to a physical segmentation. The algorithms are based on an input-time tracing principle and use a single scan of the image, they are very well suited to a real-time implementation.

Morphological Operations for Color-Coded Images

Abstract: The subject of this paper is the semantically based postprocessing of color-coded images such as classification results. We outline why the classical definition of mathematical morphology suffers if it is used for processing of coded image data. Therefore we provide an extension for morphological operations such as dilation, erosion, opening, and closing. With a new understanding of morphology we introduce bridging and tunneling as further combinations of dilation and erosion. The extensions are applied to medical image data, where the semantic rules stem from basic anatomical knowledge.

Morphological operations on fuzzy sets

Abstract: One can analyse the structure of a binary image by looking at patterns of a certain shape at different places on the image. This idea of describing the image by looking at similar patterns at various locations is quantified in mathematical morphology by the concept of a structuring element. Binary images can be regarded as subsets of Euclidean or digital space. Fuzzy sets have proven to be useful to model grey-tone images. As shown by Werman and Peleg (1985), morphology techniques used for analysis of binary images can be applied to grey-tone images using fuzzy logic. In the present paper a redefinition of Werman and Peleg's fuzzy morphology operations is given. This redefinition employs the more general indicator framework, given by Sinha and Dougherty (1992).

Automatic line detection in document images using recursive morphological transforms

Abstract: In this paper, we describe a system that detects lines of various types, e.g., solid lines and dotted lines, on document images. The main techniques are based on the recursive morphological transforms, namely the recursive opening and closing transforms. The advantages of the transforms are that they can perform binary opening and closing with any sized structuring element simultaneously in constant time per pixel, and that they offer a solution to morphological image analysis problems where the sizes of the structuring elements have to be determined after the examination of the image itself. The system is evaluated on about 1,200 totally ground-truthed IRS tax form images of different qualities. The line detection output is compared with a set of hand-drawn groundtruth lines. The statistics like the number and rate of correct detection, miss detection, and false alarm are calculated. The performance of 32 algorithms for solid line detection are compared to find the best one. The optimal algorithm tuning parameter settings could be estimated on the fly using a regression tree.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Statistical evaluation of sequential morphological operations

Abstract: In order to properly apply sequential morphological operations to random signals in applications concerned with noise suppression, the authors have examined their statistical properties using different structuring elements. The performance of flat and triangular structuring elements has been evaluated for signals with uniform, Gaussian, and Rayleigh density functions. In particular, the statistical properties of sequential morphological operations (i.e,, dilation, closing, clos-erosion, and clos-opening) are examined as a function of the parameters of the structuring element through Monte Carlo simulation, which overcomes the statistical dependency problem arising in the processed signal at different stages of morphological operations. The simulated results and their statistics (mean, variance, and skewness) present an interpretation of the signal root, biasing effects, and noise suppression capability of morphological filters. >

Realisation of morphological operations

Abstract: Multi-input min and max operators are two essential components for dilation and erosion, which are two basic building units for morphological filtering. Many of the more complicated operations of morphological filtering can be decomposed by them. The min or max operator cascades after a bit-serial adder or subtractor is equal to a dilation or erosion operator. In the paper, an efficient algorithm and its implementation architecture for the min/max operation are proposed. The proposed algorithm and architecture can process bit by bit directly for all input signals without using threshold decomposition which requires more complicated hardware design. Any shape and size of the filtering window or structuring element can be realised. For a fixed window size, the shape of window is programmable by changing some input initial conditions. The computation time is independent of, and the hardware complexity is linear to, the window size. This implies that a very high throughput rate can be attained after an initial latency period required to fill up the pipeline. The proposed architecture is modular, regular and of local interconnections; and therefore amenable for VLSI implementation.

A CMOS wave-pipelined image processor for real-time morphology

Abstract: This paper presents the implementation of a high-speed morphological image processor using CMOS wave-pipelining. A modular and expandable architecture, based on wave-pipelined transmission gate logic, has been developed for gray-scale and binary morphological operators. Using this architecture, 3/spl times/3 (2-dimensional) structuring element binary dilation and erosion units, and a two-stage morphological skeleton transform filter have been implemented in CMOS 1.2 /spl mu/m technology. The operating frequency is 333 MHz, which exceeds the speeds reported in literature for this functionality. Simulation results indicate a speed-up of 4-5 compared to non-pipelined processor implementations. The wave-pipelined implementation also offers a significant reduction in latency and hardware complexity compared to regular pipelined architectures.

Image manipulation using m-filters in a pyramidal computer model

Abstract: This paper presents how morphological transformations can be related to representations of a set on different lattices. A hierarchical definition of structuring element conveys to a class of multigrid transformations /spl Psi//sub k/ that handle changes on discrete representations of regions. The transformations correspond to upward and downward processes in a hierarchical structure. Based on multigrid transformations, a method to delineate not-perfectly-isolated objects in an nxn image requiring O(log n) time is presented. The approach considers grey level regions as sets and processes through a pyramid to carry out geometric manipulations. Extending the concept of boundary to cope with hierarchical representations of a set, a second method which identifies the boundaries in an image is discussed. >

Analogue VLSI morphological image processing circuit

Abstract: An analogue VLSI circuit that performs morphological image processing operations on the focal plane is presented. The circuit has been fabricated using a standard digital CMOS process. We exploit the parallelism of morphological image processing operations by using the massively parallel architecture of analogue VLSI arrays, achieving both high-speed and low-power computation. The analogue circuit presented computes the grey-scale morphological operation of dilation. This system also allows for programmability of the structuring element used in the dilation operation.

Decomposition of Arbitrarily Shaped

Abstract: For image processing systems that have a limited size of region of support, say 3 x 3, direct implementation of mor- phological operations by a structuring element larger than the prefixed size is impossible. The decomposition of morphological operations by a large structuring element into a sequence of re- cursive operations, each using a smaller structuring element, en- ables the implementation of large morphological operations. In this paper, we present the decomposition of arbitrarily shaped (convex or concave) structuring elements into 3 x 3 elements, op- timized with respect to the number of 3 x 3 elements. The decom- position is based on the concept of factorization of a structuring element into its prime factors. For a given structuring element, all its corresponding 3 x 3 prime concave factors are first deter- mined. From the set of the prime factors, the decomposability of the structuring element is then established, and subsequently the structuring element is decomposed into a smallest possible set of 3 x 3 elements. Examples of optimal decomposition and structur- ing elements that are not decomposable are presented.

Morphological contour coding using structuring functions optimized by genetic algorithms

Abstract: Shape representation is an important image analysis task which can be used for contour coding and feature extraction. The morphological skeleton is a geometrical shape description by means of maximal inscribed structuring elements. The form of the structuring element is usually chosen a priori, and we show how genetic algorithms can be used for an automatic optimization of an arbitrary shaped structuring element. It permits improved progressive contour transmission and the extraction of shape features.

Partial closing filters for image restoration

Abstract: A partial closing is class of edge preserving operators where a dilation-like operation is followed by an erosion with a convex structuring element. These operators are increasing, and edge preserving, but in general satisfy none of the other formal properties of the standard morphological closing which is a special case of this operator. The purpose of the partial closing is the restoration of certain classes of images by filling in gaps caused by noise. However, the examples and analysis to be given involves one dimensional images. The method can be applied to two dimensional images that are comprised of short line segments that occur for example in character strokes or image edges after an edge detection operation. One type of partial closing is an order statistic filter followed by an erosion. Another type-a dilation partial closing is a dilation with a sparse structuring element followed by an erosion with a convex structuring element. Dilation partial closings exist that are excellent approximations to the median filters with sliding windows of diameters 3, 5, and 7. The use of dilation partial closings in place of the median filters results in a considerable savings in computer time. The statistics of the partial closings are independent of the threshold. Thus the filters can be generalized to gray levels using stack filters. The dilation partial filters are then expressed in terms of minima and maxima.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Removing Impulse Noise from Human Head Scan Data.

Abstract: : This report presents a mathematical morphological filtering technique to eliminate impulse noise from human head surface data generated by laser surface scanning technologies. In the area of image processing, mathematical morphology refers-to a branch of nonlinear filters which use geometric form and structure to alter a signal. Several structuring elements were investigated with a spherical structuring element being selected as the best candidate. A spherical element is the ideal shape since protruding shapes like spikes on the human head are best removed using a structuring element that has an omni-directional behavior. A spherical structuring element having a radius of 3.Omm to 3.5mm represented the best trade-off between identification of impulse noise and loss of good data points. (AN)

Texture analysis: pretopological approach versus morphology approach

Abstract: This paper deals with the problem of texture classification: a new coding images has been developed. The first interest of this article is the presentation of a new approach for texture analysis based on pretopology: pretopology is a mathematical area which generalizes, in our case, mathematical morphology. Instead of using only one structuring element to make transformations on an image, we can use a basis of structuring elements. We can recreate the mathematical-morphology transformations like dilation and erosion, but we can build new transformations, thinner or coarser than dilation or erosion. More over, we can use the all mathematical knowledges of pretopology. The second part of this article presents the coding images based on the pretopological approach: it uses a basis of four structuring elements. One gray scale image is coded by two images of 15 colors. We try to determinate the discrimining capacity of the coding images.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Multivariate morphological granulometric texture classification using Walsh and wavelet features

Abstract: As introduced by Matheron, granulometries depend on a single sizing parameter for each structuring element forming thefilter. The size distributions resulting from these granulometries have been used successfully to classify texture by using as features the moments of the normalized size distribution. The present paper extends the concept of granulometry in such a way that each structuring element has its own sizing parameter and the resulting size distribution is multivariate. Classification is accomplished by taking either the Walsh or wavelet transform of the multivariate size distribution, oh- taming a reduced feature set by applying the Karhunen-Loeve transform to decorrelate the Walsh or wavelet features, andclassifying the textures via a Gaussian maximum-likelihood classifier. 1. Introduction Binary granulometries were introduced by Matheron to characterize size and shape information in random sets [1]. He defined granulometries axiomatically and provided a general representation theory. For purposes of the present paper, webriefly describe the most important class of granulometries, leaving the general theory and details to the literature [2, 3].Let B =

Optimal implementation of morphological operations on neighborhood-connected parallel computers

Abstract: To efficiently perform morphological operations on neighborhood-processing-based parallel image computers, we need to decompose structuring elements larger than the neighborhood that can be directly handled into neighborhood subsets. In the special case that the structuring element is a convex polygon, there are known decomposition algorithms in the literature. In this paper, we give an algorithm for the optimal decomposition of arbitrarily shaped structuring elements, enabling an optimal implementation of morphological operations on neighborhood-connected parallel computers in the general case.

Distance-morphological transformations of digital images

Abstract: Digital mathematical morphology (MM) and the distance transform (DT) have many points of intersection. The DT combines numerical features and object shapes. Usual application of mathematical morphology uses distance transforms based on the trivial city-block or chessboard metrics like digital representation of continuous ball. In this paper we concern structuring element as oriented neighborhood structures (ONSs) defined in the digital space; wider class of digital metrics and nonmetric functions defined on these NSs. We show that basic morphological operations may be performed by a thresholding of results of local propagations based on this class of digital functions. Such approach simplifies a description of some structuring elements and some operations of image analysis.

Adaptive multiparameter openings

Abstract: Adaptation of an opening possessing a multiparameter structuring element is studied in the context of Markov chains by treating the multiple parameters as a vector r defining the state of the system and considering the operativefilter Ar to be opening by reconstruction. Adaptation of Ar (transition of r) is in accordance to whether or not Ar conectly or incorrectly passes signal and noise grains sampled from the image. Signal and noise are modeled as unions ofrandomly parameterized and randomly translated primary grains. Transition probabilities are discussed fortwo adaptation protocols and the state-probability increment equations are deduced from the appropriate Chapman- Kolmogorov equations. Adaptation convergence is characterized by the steady-state distributions of the Markov chains and these are computed numerically. 1. INTRODUCTION Analytic derivation of optimal binary openings was first treated for a restricted model in which grains were assumedto be disjoint homothetics of some basic generating shape that also served as the opening structuring element [1]. A

Optimal single-stage restoration of subtractive noise corrupted images by a morphological closing

Abstract: Restoration of subtractive noise on a binary image by a single morphological operation, closing, is analyzed. Restoration by closing alone is appropriate under particular explicitly defined random noise models, based respectively on erosion, independent pixel subtractive noise, and independent pixel subtractive noise followed by dilation. Since in general it is not possible to perfectly restore subtractive noise, we use the Hausdorff metric to measure the residual error in restoration. This metric is an appropriate one because of its geometric interpretation in terms of set coverings. We describe a best first search procedure to find a structuring element for closing that is optimal in the sense of minimizing the mean Hausdorff error. The search procedure's utility function is based on the calculation of certain probabilities related to the noise model, namely the probability of one set being the subset of another set and some related probabilities. We describe how a bound on these probabilities can be efficiently computed to speed up the search process.

Fast binary segmentation of gray-level images using a morphological operator

Abstract: During the binary segmentation an image transforms into a binary representation, in which the regions of interest as objects (or their parts) for further analysis are detected as connected components. The underlying image model for binary segmentation and analysis is composed of two separated parts: the first one is to model image domain by using notions and operations of mathematical morphology and the second one is to model the values of intensity function, defined on this domain. The proposed morphological operator transforms gray-scale images into binary ones by comparing image local properties within the structuring elements or structuring regions with a tolerance threshold, giving eroded objects as connected components and dilated contours for further analysis. Since the implementation of this operation is rather complicated, fast algorithms to calculate local properties of intensity function (e.g. mean, square deviation, median, absolute deviation, etc.), using spatial recursion, have been developed. They give a speed-up of order O(N), where N equals L X L is the structuring element size, for computing, e.g. local mean and variance, as compared with their naive calculation.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.