Showing papers on "Structuring element published in 1997"

Mathematical morphology for angle-valued images

Abstract: Mathematical morphology (MM) can be defined in terms of complete lattices. Thus, MM is useful for the processing of binary images or of single-valued intensity images - images for which a partial ordering, hence a lattice structure, is apparent. The lattice structure of an intensity image is manifest through set inclusion with ordering on intensity. It is always possible to define majorants and minorants for collections of sets that are intensities with spatial support. Not all the components of a color image can be ordered trivially. In particular, hue is angle-valued. Consequently, MM has not been as useful for color image processing because it has not been clear how to define set inclusion for angle-valued images. This paper contains definitions for erosion, dilation, opening, and closing for angle-valued images using hue as the exemplar. The fundamental idea is to define a structuring element (SE) with a given hue or hues. From each image neighborhood of the SE, the erosion operation returns the hue value that is closest to the hue of the corresponding SE member. Examples of the effects of the operators on a color noise field are shown. Histograms demonstrate the effects of the operators on the hue distributions.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Rotated texture classification by improved iterative morphological decomposition

Abstract: An improved algorithm based on iterative morphological decomposition (IMD) proposed by Wang et al. (1993) is described. The proposed algorithm requires less computation than the original IMD algorithm. The improved iterative morphological decomposition (IIMD) is compared with granulometric moments, multiresolution rotation-invariant SAR (MRRISAR) models and multichannel Gabor filters. It is found that IIMD is superior to granulometric moments and MRRISAR in rotated texture classification. IIMD may also perform better than multichannel Gabor filters by employing many different kinds of structuring elements. In the study, three kinds of pseudo rotation-invariant structuring elements, namely the disc, octagon and square, as well as a line structuring element are tested. Since the line structuring element is rotation-variant in nature, the image is rotated to different orientations of equal angular separation to find a set of primitive features. A Fourier transform is then applied to convert these features to rotation-invariant. An accuracy rate as high as 96% is achieved in classifying 30 classes of textured images in the experiment. It is also demonstrated that using both the normalised variance and the mean can give better classification accuracy rate than using both the variance and the mean when classified by simplified Bayes or Mahalanobis distance measure.

Initial investigation of mathematical morphology for the digital extraction of the skeletal characteristics of trabecular bone

Abstract: OBJECTIVE To develop a filter utilizing mathematical theory to extract the skeletal patterns of trabecular bone. METHODS Studies of morphology in the extraction of patterns of calcification in mammograms provided the theoretical framework. Using these studies as a basis, a morphological filter was applied to extract skeletal patterns from digital images of trabecular bone. Sequential images (subset) were combined in a structured fashion to create an aggregate (sumset) which compared with the original images, skeleton and line skeleton images. RESULTS Binary images of the skeletal patterns in continuous, round and mesh-like forms were obtained from the original images by processing with the skeleton operation using a disc-shaped single structuring element. The line skeleton operation using line structuring elements with constant directions allowed the extraction of linear and discontinuous patterns. Both the skeleton and line skeleton operations extracted binary subset images which depicted skeletal patter...

Method and device for automatic segmentation of a digital image using a plurality of morphological opening operation

Abstract: A method of processing a digital image representing ribbon-shaped objects of non-uniform intensity contrasting with a background of lower intensity includes an automatic segmentation phase having one or more morphological opening operations effected, respectively, with one or more three-dimensional structuring elements. The latter have a two-dimensional base parallel to the image plane and have a non-binary intensity function in a third dimension. Preferably, the automatic segmentation phase is carried out by means of a set of two-dimensional spatial structuring elements with a third intensity dimension. The set contains N anisotropic structuring elements oriented from π/N to π/N and one isotropic structuring element.

Real-time implementation of grey-scale morphological operators

Abstract: The authors improve and generalise real-time implementations of GS (grey-scale) morphological operators proposed by Morales et al. (see IEEE Trans. Image Process., vol. 5, no. 6, p. 1073-7, 1996) for any GSE (grey-scale structuring element) having its centre in any position of the defined domain.

Decomposition of gray-scale morphological templates using the rank method

Abstract: Convolutions are a fundamental tool in image processing. Nonlinear convolutions are used in such operations as the median filter, the medial axis transform, and erosion and dilation as defined in mathematical morphology. For large convolution masks or structuring elements, the computation cost resulting from implementation can be prohibitive. However, in many instances, this cost can be significantly reduced by decomposing the templates representing the masks or structuring elements into a sequence of smaller templates. In addition, such decomposition can often be made architecture specific and, thus, resulting in optimal transform performance. In this paper we provide methods for decomposing morphological templates which are analogous to decomposition methods used in the linear domain. Specifically, we define the notion of the rank of a morphological template which categorizes separable morphological templates as templates of rank one. We establish a necessary and sufficient condition for the decomposability of rank one templates into 3/spl times/3 templates. We then use the invariance of the template rank under certain transformations in order to develop template decomposition techniques for templates of rank two.

Software implementation of 2-D grey-level dilation using SKIPSM

Abstract: The earlier papers on SKIPSM (Separated-Kernel Image Processing using finite State Machines) concentrated mainly on implementations using pipelined hardware. Because of the potential for significant speed increases, the technique has even more to offer for software implementations. However, the gigantic structuring elements (e.g., 51x51 in one pass) readily available in binary morphology using SKIPSM are not practical in grey-level morphology. Nevertheless, useful structuring element sizes can be achieved. This paper describes two such applications: dilation with a 7x7 square and a 7x7 octagon. Previous 2-D SKIPSM implementations had one row machine and one column machine. Two of the implementations described here follow this pattern, but the other has four machines: row, column, and the two 45-degree diagonals. In operation, all of these are one-pass algorithms: The next pixel is fetched from the input device, the two (or four) machines are updated in turn, and the resulting output pixel is written to the output device. All neighborhood information needed for processing is encoded in the state vectors of the finite-state machines. Therefore, no intermediate image stores are needed. Furthermore, even the input and output image stores can be eliminated if the image processor can keep up with the input pixel rate. Comparisons are provided between these finite-state-machine implementations and conventional implementation of the 2-step and 4-step decompositions, all based on the same structuring elements.

Binary dilation using SKIPSM: some interesting variations

Abstract: The morphological image processing operation of binary dilation, as usually defined, cannot be implemented as a single-pass pipelined operation because it is a 'one-pixel-to- many-pixels' operation, whereas pipelining is possible only for 'one-to-one' or 'many-to-one' operations. Fortunately, there is an indirect equivalent (negate-erode-negate) which can be pipelined, and which can therefore be implemented in either hardware or software using the single-pass SKIPSM FSM (finite-state machine) paradigm. The great speed advantage of SKIPSM, which offers execution time independent of structuring element size, can therefore be extended to binary dilation also. This paper provides a procedure for incorporating these negations into SKIPSM erosion lookup tables, thus creating dilation lookup tables. It also discusses the relationship between FSM initial conditions and image boundary conditions, and 180-degree structuring element rotation. Examples are included.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Hardware architectures for image dilation and erosion operations

Abstract: A hardware architecture for mathematical morphology operations such as dilation and erosion of an image signal is provided A hardware architecture for an image dilation operation includes: a plurality of adders corresponding to the size of the structuring element for adding the image signal and a structuring element symmetrical to the image signal with respect to the origin to output the result; a plurality of stores for temporarily storing the signals output from the plural adders; a comparator for comparing data stored in the plural stores with feedback data to output the maximum data; and an outputting device for outputting the output signal of the comparator as a dilation operation value if the dilation operation with respect to all structuring elements for one image signal is completed and feeding back the output signal of the comparator as input data of the comparator if not Therefore, the elementary operations such as dilation and erosion with respect to a gray-level image signal can be attained by a simple arithmetic operation, that is, by finding the maximum/minimum value using an adder Also, since the hardware architecture for the dilation and erosion operations adopts a feedback structure, the volume of the hardware linearly increases even though the size of the structuring element increases in geometrical progression

Implementation of SKIPSM for 3D binary morphology

Abstract: The SKIPSM finite-state machine image processing paradigm can be extended to 3-dimensional (and to n-dimensional) image processing in a very straightforward way. Two-dimensional SKIPSM involves an R-machine (row machine) and a C-machine (column machine) in sequence (in either order). Three- dimensional SKIPSM uses what will be called X-machines, Y- machines, and Z-machines (in any order). This means that large 3-D structuring elements can be applied to 3-D images in a single scan through the image, with three lookup-table accesses per volume element, and no other operations, regardless of the size of the structuring element. It is even possible to apply more than one 3-D structuring element simultaneously, with no increase in execution time. For binary erosion, which has interesting applications to the 3-D packing problem, many of the same lookup tables used for 2-D erosion can be used for 3-D erosion. This implies that the same software programs used to create these 2-D lookup tables can be used for 3-D tables, so that no new tools are required. For 3-D dilation, some changes are required, but all the tables needed can be created in a routine way from the corresponding 3-D erosion tables. A brief discussion of the use of SKIPSM for 3-D operations other than binary erosion and dilation is also included.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Direct implementation of open-closing in morphological filtering

Abstract: An algorithm for the direct implementation of commonly used 1-D morphological filters is presented. Open-closing and close-opening operations are performed with a single-pass procedure, resulting in a substantial increase in speed, proportional to the length of the structuring element, over alternative implementations.

Fuzzy reasoning morphological operators and their optical implementation.

Abstract: Fuzzy-reasoning theory is widely used in industrial control. Mathematical morphology is a powerful tool to perform image processing. We apply fuzzy-reasoning theory to morphology and suggest a scheme of fuzzy-reasoning morphology, including fuzzy-reasoning dilation and erosion functions. These functions retain more fine details than the corresponding conventional morphological operators with the same structuring element. An optical implementation has been developed with area-coding and thresholding methods.

Change detection from remotely sensed multi-temporal images using morphological operators

Abstract: This paper presents a new approach to spatial change detection. The algorithms developed are based on the use of basic morphological filters and on more advanced concepts such as geodesic transformations. Such techniques are able to overcome the traditional problems associated with change detection from remotely sensed multi-temporal images. As a matter of fact it is already known that traditional methods using the concept of direction variation of the change vector are inadequate for a precise detection. These frequential techniques lay on very limitative statistical hypotheses: gaussian distribution, a priori determined ratio of change, very large images and relatively small ratio of change. However in a prior study, it was determined that the basic operators of mathematical morphology were partly corrupting the results of change detection by introducing bias on the shape of the objects and also by shifting the edges in the displacement direction of the structuring element. The geodesic transformations are correcting these topological difficulties in an elegant way. The usual threshold step is replaced by appropriate structuring element interval of sizes. Thus, it becomes possible to treat the spatial change detection problem by using a single formalism. The first results show that the particles of change are detected even for very slight radiometric variations, with the advantage of taking into account the configuration of the neighbourhood.

Recursive morphological operators for gray image processing. Application in granulometry analysis

Abstract: This paper presents a new algorithm for an efficient implementation of morphological operations for gray images. It defines a recursive morphological decomposition method of convex structuring elements by only causal two pixel structuring elements. Whatever the element size, erosion or/and dilation can then be performed during a unique raster-like image scan, involving a fixed reduced analysis neighborhood. The resulting process offers a low computational complexity, combined with an easiness for describing the element form. The algorithm is exemplified with granulometry. Quantum dots are segmented using a multiscale morphologic decomposition. Our new algorithm is particularly well suited for this type of morphological treatments, as they use structuring elements with both a large size and a form fitting the object to extract, that is to say depending on the application.

Software implementation of 2D gray-level dilation using SKIPSM

Abstract: The earlier papers on SKIPSM (separated-kernel image processing using finite state machines) concentrated mainly on implementations using pipelined hardware. Because of the potential for significant speed increases, the technique has even more to offer for software implementations. However, the gigantic structuring elements (e.g., 51 by 51 in one pass) readily available in binary morphology using SKIPSM are not practical in gray-level morphology. Nevertheless, useful structuring element sizes can be achieved. This paper describes two such applications: dilation with a 7 by 7 square and a 7 by 7 octagon. Previous 2-D SKIPSM implementations had one row machine and one column machine. Two of the implementations described here follow this pattern, but the other has four machines: row, column, and the two 45-degree diagonals. In operation, all of these are one-pass algorithms: The next pixel is 'fetched' from the input device, the two (or four) machines are updated in turn, and the resulting output pixel is written to the output device. All neighborhood information needed for processing is encoded in the state vectors of the finite-state machines. Therefore, no intermediate image stores are needed. Furthermore, even the input and output image stores can be eliminated if the image processor can keep up with the input pixel rate. Comparisons are provided between these finite-state-machine implementations and conventional implementation of the 2-step and 4-step decompositions, all based on the same structuring elements.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Signal restoration by statistical soft morphology

Abstract: A new set of non-linear signal and image processing operators is presented. Their definition is based on the introduction of the statistical properties of Bayesian reconstruction in soft morphological operators. Statistical soft operators represent a trade-off between the noise cleaning properties of statistical morphology and the shape preservation properties of soft morphology. The main characteristic of these operators is the individualization of two parts within each structuring element (SE) according to soft morphology (i.e. "hard" and "soft" SEs), and to define on this basis a probabilistic estimation model which is a generalization of the statistical morphology model. Results are presented to show that the statistical soft morphological operators can be considered robust to structured noise, i.e. noise showing both statistical (e.g. additive Gaussian noise) and morphological (e.g. noise with a particular shape) structure.

Experiments on the Decomposition of Arbitrarily Shaped Binary Morphological Structuring Elements

Abstract: The decomposition of binary structuring elements is a key problem in morphological image processing. So far only the decomposition of convex structuring elements and of specific subsets of non-convex ones have been proposed in the literature. This work presents the results of a new approach, based on a Genetic Algorithm, in which no constraints are imposed on the shape of the initial structuring element, nor assumptions are made on the elementary factors, which are chosen from a given set.

A directional morphological operation and its application to immunological image processing

Abstract: A directional morphological operation can be performed by utilizing a rotational structuring element with a directional information, and its associated processing methods for overlapping and enclosing are proposed. As an example of the overlapping method, derived from the directional morphological operation, a distribution of high/low atmospheric pressures is obtained from the wind direction of a weather report. The enclosing method obtained from the directional morphological operation is applied to a shape recognition system utilizing multi-ultrasonic sensors. This method is also applied to immunological image processing which utilizes the function of self or non-self discrimination in the immune system of a living body. From simulation and experimental results, it has been shown that these methods are effective for extracting mutual relationships among data including directional information, and that object categories are discriminated by applying directional morphological operation for immunological discrimination.

Using mature point to speed up binary morphological algorithms

Abstract: In this paper, mature point, which is either 0 or 1 depending on erosion or dilation operation for binary images, is used to speed up binary morphological algorithms. Whenever the mature point of a particular searching area at coordinates (i,j) has been reached, the morphological operation performed on that area is stopped and moved forward to new coordinates. Two algorithms are tested. They are the bitmap representation algorithm proposed by Boomgaard and Balen [1992] and the overlapping search algorithm recently proposed by Lam and Li [to be published]. Experiment shows that significant computation saving can be realized with the use of mature point even for a small structuring element and small percentage of mature points in the image.

Recursive binary dilation using digital line-structuring elements in arbitrary orientations

Abstract: Performing morphological operations such as dilation and erosion of binary images, using very long line structuring elements is computationally expensive when performed brute- force following the definitions. In this paper, we present a two-pass algorithm that runs at constant time for obtaining dilations, irrespective of the lengths and orientations of the line structuring elements. We use the concept of orientation error between the continuous line and its discrete counterpart in generating the basic digital line structuring element used in obtaining what we call the dilation transform. To obtain any dilation, we just threshold the dilation transform with a value that is the length of the desired line structuring element. We implemented the algorithm in general image processing system environment on a sun sparc station 10, and tested them on a set of 240 X 250 sized salt and pepper noise images with probability of a pixel being a 1-pixel set to 0.25, for orientations (theta) (epsilon) [ (pi) /2, 3(pi) /2 ] of the normals of the continuous lines, of which the digital line structuring elements are a discretization, and their lengths in the range 5 to 145 pixels. We achieved a speed up of about 50 over the conventional methods when the structuring elements had lengths of 145 pixels. The algorithm ran at a constant time of 200ms. We required only one minimum operation per result pixel.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Optimized optical morphological object classification

Abstract: Morphological transformation provides a powerful, nonlinear means of quantitatively analyzing data sets such as images. This technique has traditionally been applied to feature location or feature removal, as in noise removal. However, the technique holds some promise for fast object classification. By viewing the transformation as a neural network, proven training techniques may be applied to optimize the performance. The critical step in applying morphology is the design of the structuring element or shape of the filter. By casting the problem as that of object classification and by properly defining error functions, neural network training techniques may be used to optimize performance. In addition, this view of the procedure as a neural network allows the generalization of the technique to include sequences of filters, which correspond to multiple layer neural networks. an optical architecture is being considered to implement a sequence of morphological transformations, taking into account known principles and limitations of the optics and of neural networks, in order to perform a complex object classification task. Then the corresponding morphological filter parameter will be optimized using neural network training techniques.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A new morphological approach for removing speckle noise and emphasizing defect features in ultrasonic images

Abstract: Ultrasonic NDE images are often contaminated with speckle noise. The degradation caused by the presence of speckle noise makes it difficult to identify features of interest that are typically thin or small in nature. A variety of techniques have been proposed to date for reducing such noise. As an example, lowpass filters can be employed to reduce speckle noise. However, they tend to blur thin features and edges. Median filters are also used widely to remove impulse type noise while preserving edges in images [1]. Unfortunately, such filters perform poorly when the spatial density of the noise is high [3,6]. As an alternative, gray-scale morphological approaches involving such operations as opening, closing or combinations thereof can be applied to reduce noise in gray-scale images [1–5]. Even in this case, features that are thin or small tend to be filtered out along with the noise [6]. Prior attempts to remedy the problem have relied on the use of multi-resolution (or multi-scale) morphological filters using an array of structuring element sizes. Such algorithms tend to be overly complex and computationally expensive to implement [6].

Multivariate granulometric filters

Abstract: As introduced by Matheron, granulometries depend on a single sizing parameter for each structuring element. The concept of granulometry has recently been extended in such a way that each structuring element has its own sizing parameter resulting in a filter (Psi) t depending on the vector parameter t equals (t1..., tn). The present paper generalizes the concept of a parameterized reconstructive (tau) -opening to the multivariate setting, where the reconstructive filter (Lambda) t fully passes any connected component not fully eliminated by (Psi) t. The problem of minimizing the MAE between the filtered and ideal image processes becomes one of vector optimization in an n- dimensional search space. Unlike the univariate case, the MAE achieved by the optimum filter (Lambda) t is global in the sense that it is independent of the relative sizes of structuring elements in the filter basis. As a consequence, multivariate granulometries provide a natural environment to study optimality of the choice of structuring elements. If the shapes of the structuring elements are themselves parameterized, the expected error is a deterministic function of the shape and size parameters and its minimization yields the optimal MAE filter.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Shift-Invariant Fuzzy-Morphology Neural Network for Occluded Target Recognition

Abstract: This paper describes an architectural extension of the shared-weight neural network (SWNN) that performs shift-invariant filtering using fuzzy-morphological operations for feature extraction. The nodes in this stage employ the generalized-mean operator to implement fuzzymorphological operations. The network parameters, weights, morphological structuring element and fuzziness, are optimized through error back-propagation(EBP) training method.

A fast binary morphological algorithm by overlapping and mature point

Abstract: One of the most efficient binary morphological algorithms was proposed by Boomgaard and van Balen (1992). Their method exploited the potential of the present 32-bit and 64-bit computer architecture by encoding the image in bitmap format and performed the operation in a 32-bit or 64-bit parallel fashion. In addition, the logarithmic decomposition of the structuring element is also employed to achieve high efficiency for the method. Nevertheless, this fast morphological algorithm can be further improved by including two proposed techniques, they are the technique of using overlap among processing areas of neighbouring pixels and the technique of mature point respectively.