Showing papers on "Structuring element published in 1991"
TL;DR: A versatile algorithm for computing dilations and erosions of digital binary pictures with structuring elements of arbitrary size and shape that turns out to be extremely fast whatever the utilized elements.
85 citations
31 Oct 1991
TL;DR: The authors have applied mathematical morphology for fractal analysis on bone X-ray images to demonstrate that the fractal dimension using mathematical morphology gives a robust texture measure of trabecular bone structures.
Abstract: The authors have applied mathematical morphology for fractal analysis on bone X-ray images. The digitized gray level image is treated as a three-dimensional surface whose fractal dimension is calculated by performing a series of dilations on this surface and plotting the area of the resulting set of surfaces against the size of the structuring element. This approach has the added advantage of encoding structural information via the use of a structuring element. The algorithm has been applied to several bone radiographs, and the results demonstrate that the fractal dimension using mathematical morphology gives a robust texture measure of trabecular bone structures. >
78 citations
TL;DR: The method of calculating the fractal signature on image acquisition and digitization parameters is described and the difference between the two resulting signatures in individual knees is shown to be a measure of the change in texture seen in osteoarthritis.
Abstract: In osteoarthritis of the knee, horizontal trabeculae in the tibia thicken, leading to the appearance of horizontal striations on radiographs. Any attempt to understand and monitor the disease process must examine these changes. We have previously described a method of analysing the texture in these images that uses the mathematical morphology operations of dilation and erosion to calculate how image fractal dimension varies with resolution. This variation with resolution is the fractal signature. Calculation of fractal dimension should be independent of linear transformations in image values, and it is shown that careful choice of morphological structuring element is required for this. In this paper we describe the dependence of our method of calculating the fractal signature on image acquisition and digitization parameters. Errors due to variations in pixel size, X-ray exposure, and patient repositioning are small compared to the changes seen in the signature due to osteoarthritic change. Using pairs of ...
62 citations
TL;DR: Techniques for decomposing big grayscale morphological structuring elements into combined structures of segmented small components will allow full freedom for users to design any kind and any size of gray-scale morphologicalStructuring element.
59 citations
TL;DR: In this article, a method for decomposing any grey-scale structuring element into the sum of a separable and a totally inseparable template is described, and the theory behind the decomposition and algorithms for computing them are both presented.
Abstract: Decomposition of templates is a useful technique for increasing the computational efficiency of image processing operations, either by decreasing the number of operations required or by reorganizing computations into forms more compatible with specialized image processing architectures. There are numerous examples of useful decompositions including FFTs, decomposition of Laplacians of Gaussian masks, and decompositions of separable, convex greyscale structuring elements in mathematical morphology. In this paper, a method for decomposing any grey-scale structuring element into the sum of a separable and a totally inseparable template is described. Simple methods for decomposing the resulting separable template, or any separable template, into separable factors with respect to dilation are also described. The theory behind the decompositions and algorithms for computing them are both presented. If the original template is separable, then the method yields a separable decomposition. If the original template is not separable, the method yields the closest separable template to the original in the mean square sense.
32 citations
TL;DR: It is shown that the decomposition of an arbitrary N-point structuring element will require at least (3 ln N/ln 3)points.
Abstract: A theoretical lower bound on the number of points required in the decomposition of morphological structuring elements is described. It is shown that the decomposition of an arbitrary N-point structuring element will require at least (3 ln N/ln 3)points. Using this lower bound it is possible to find the optimal decompositions (in terms of the minimum number of unions or the minimum number of points) for all one-dimensional connected line segments. L-dimensional rectangles may be decomposed by optimally decomposing the L one-dimensional line segments that describe the rectangle. >
22 citations
TL;DR: An algorithm for multiscale description of binary digital regions that satisfies meaningful algebraic properties and converges to a final result in a bounded number of steps and allows an economical representation of shape in terms of structuring elements, and so it can be applied in binary image coding.
19 citations
TL;DR: The present paper is mainly concerned with the development of structuring-element libraries to which the basis search can be confined, and focuses on the expert-library approach: various subl libraries are formed, each of which corresponds to certain key filters, and a suboptimal filter is derived from image-noise statistics in conjunction with a basis search restricted to relevant sublibraries.
Abstract: For both the binary and gray scales, mean-square optimal digital morphological filters have been fully characterized previously in terms of the Matheron erosion representation for increasing, translation-invariant mappings. Included in the characterization is the minimal search strategy for the optimal filter basis; nonetheless, in the absence of prior statistical information or an adequate image-noise model, even in the binary setting design is computationally intractable for moderately sized observation windows.The computational burden can be mitigated by imposing constraints on the filter. The present paper is mainly concerned with the development of structuring-element libraries to which the basis search can be confined. More specifically, the authors focus on the expert-library approach: various sublibraries are formed, each of which corresponds to certain key filters, the overall library is formed as the union of the sublibraries, and a suboptimal filter is derived from image-noise statistics in conjunction with a basis search restricted to relevant sublibraries.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
15 citations
TL;DR: A class of shift-variant reduction operations is introduced, that is useful for performing efficient and controllable shape and texture transformations between resolution levels, and some general properties of the cycle are derived.
Abstract: A class of shift-variant reduction operations is introduce d, that is useful for performing efficient and controllable shape and texture transformations between resolution levels. In their most general form, the operations proceed in three steps: (a) convolve a binary image with a kernel of arbitrary size; (b) threshold the result; (c) subsample to produce the reduced image. Taking a binary structuring element for the kernel, the threshold convolution on a binary image is equivalent to a rank order filter, and the full reduction operation is a threshold reduction. Threshold reductions that use convolution filters and subs ample tiles of equal size are optimized by combining the three operations, using only logical raster operations and producing threshold convolution values only at the sampling points. For 2x reduction, the four possible threshold values (1, 2, 3, and 4) refer to the minimum number of ON pixels within each 2x2 tile for which a pixel in the reduced image will be ON. Algorithms for boolean raster operations are given for 2x, 3x, and 4x threshold reduction, and lookup tables that effici ently implement column raster operations are provided. Threshold reduction rates of 2.5x pixel/second can be achieved with a Sun SparcStation2 . A mask-forming image analysis cycle of threshold reduction, augmented by morphology and followed by replicative expansion to full resolution, is described, an d some general properties of the cycle are derived. A simple application of threshold reduction to document image analysis, the extraction of halftone regions from scanned images that also contain text and line graphics, is illustrated. A sequence of 2x reductions with first low and then high thresholds is used to create a redu ced image consisting of a mask over the halftone regions. In this way, the extraction occurs as a nat ural consequence of the reductions.
12 citations
11 Jun 1991
TL;DR: A new VLSI architecture for morphological filtering is proposed that reduces the need of arithmetic addition and subtraction by a simple logical candidate selection and fast real-time implementation is feasible through these concise architectures.
Abstract: The authors propose a new VLSI architecture for morphological filtering. It reduces the need of arithmetic addition and subtraction by a simple logical candidate selection. Hardware complexity is simplified with pipeline operations. The word-parallel bit-pipeline architecture is suitable for high-speed processing while the bit-serial architecture is suitable for large structuring element. A bit-level systolic design is also demonstrated. This architecture can be applied to distance transformation. Fast real-time implementation is feasible through these concise architectures. >
10 citations
14 Apr 1991
TL;DR: A class of nonlinear filters called rank order based filters, including, as special cases, rank order and morphological (with flat structuring element) filters, are dealt with, and the necessity of a special processing stage dedicated to shape preservation is shown.
Abstract: A class of nonlinear filters called rank order based filters, including, as special cases, rank order and morphological (with flat structuring element) filters, are dealt with. How they achieve size-sensitive multiresolution decompositions is described. The necessity of a special processing stage dedicated to shape preservation is shown, and a solution is proposed. The problem of filter mask (or structuring element) optimization to minimize a statistical criterion is also studied. The proposed algorithms are very simple, and their derivation is performed by using an implicit formulation of the filtering process. Both techniques are applied to a practical defect detection problem. >
14 Apr 1991
TL;DR: A morphological hit-or-miss algorithm is presented which can distinguish a distorted shape from among others and locate it and it is shown that the boundary of the complement of the shape, delta A/sup c/, can be used as a structuring element on the completeness of the image.
Abstract: A morphological hit-or-miss algorithm is presented which can distinguish a distorted shape from among others and locate it. Shape recognition is presented in noisy environments as a problem of recognizing imperfect shapes. The method employs only one hit-or-miss operation. The resultant shape location is presented by a small cluster of points within a known set. The role of window W in the hit-or-miss transformation is discussed, and it is shown that the boundary of the complement of the shape, delta A/sup c/, can be used as a structuring element on the complement of the image, I/sup c/, with the result of the hit-or-miss transformation being the same as that when a window is used in the transformation. Without a window restriction, the hit-or-miss transformation is more practical in shape recognition. >
31 Oct 1991
TL;DR: An algorithm for enhancement of angiogra hic images using morphological opening filter which can significantly improve the processing speed, and yet gives excellent enliancement for the angiographic images.
Abstract: In this paper we present an algorithm for enhancement of angiogra hic images using morphological opening filter. Opening ora gray-scale image by a gray-scale structuring element(SE) can generate a background image. To remove the background image , we can subtract it from the original image. Usually, there are a large number of computations involved in gray-scale opening operation. We present a skipped SE algorithm which can significantly improve the processing speed, and yet gives excellent enliancement for the angiographic images.
TL;DR: An automaton of the MP-class whose objective is to establish the medial axis by the displacement of discs of maximum size included in the object, has been built and has been applied to the determination of an integrated density profile and the straightening of a chromosome image.
16 Jun 1991
TL;DR: In this article, two morphological operators with multiple structuring elements, namely multistage erosion (ME) and multi-stage dilation (MD), are proposed. And a new morphological-based filter is proposed, which embodies the new morphologically operators, called multi-age morphological (MM) filter, which can remove noise effectively and preserve more geometrical features and details than a simple morphological filter.
Abstract: Many applications of mathematical morphology use only a single structuring element. In some cases, this may not produce the best result. Combination of morphological operators with other operations as well as the utilization of multiple structuring elements can improve the performance of morphological-based filters. This paper defines two new morphological operators with multiple structuring elements-multistage erosion (ME) and multistage dilation (MD). The properties of the ME and the MD are presented. Then a new morphological-based filter, which embodies the new morphological operators, called multistage morphological (MM) filter is proposed. The MM filter can remove noise effectively and preserve more geometrical features and details than a simple morphological filter, or other nonlinear filtering algorithms. >
TL;DR: This paper will concetrate on a technique for unsupervised learning of hidden layers of structuring elements where a training image is inspected with very little input as to what will be done with the image.
Abstract: A very robust form of pattern recognition results from using mathematical morphology on binary images that have been segmented into various edge directions. These edge direction images are then transformed by a set of structuring elements to derive a set of feature images. Morphological transformations on the feature images by a final set of structuring elements result in the location or classification of the desired objects. Thus, there are two types of structuring element sets. The training of the final set of structuring elements can be provided by a method similar to supervised Hebbian learning used in neural networks, where the goal is to unambiguously locate specified objects. The first set of structuring elements is similar to a hidden layer in neural networks and is more difficult to train. A technique of unsupervised competitive learning is used. The definition of orthogonality, or uniqueness within the set of features defined by the first layer of erosions is crucial to successful training. These features must be independent and span the space of possible features; otherwise, information that may be critical to the final layer of erosions will be lost. This paper will concetrate on a technique for unsupervised learning of hidden layers of structuring elements where a training image is inspected with very little input as to what will be done with the image.
14 Apr 1991
TL;DR: A new algorithm for exact reconstruction of an original image from its morphological skeleton and edge structure is presented, which results in improved computational performance and reduced memory storage requirements.
Abstract: A new algorithm for exact reconstruction of an original image from its morphological skeleton and edge structure is presented. The new technique results in improved computational performance and reduced memory storage requirements. The algorithm is also shown to have better performance characteristics than two previous algorithms in terms of data storage, data transmission rate, and computational complexity. If the size of the maximal element of a skeleton point is larger than the size of a unit structuring element, the algorithm will result in at least a 25% computational savings. The computational savings increases nonlinearly as the size of the maximal element increases. >
TL;DR: The authors consider the case when a finite image is part of a pixel display which changes ate discrete times, and develop two important algorithms for computing the dilation and erosion of such images in o(n2) less time then with brute force.
Abstract: Two of the most important basic morphological operations used in image filtering are erosion and dilation. In this paper the authors consider the case when a finite image is part of a pixel display which changes ate discrete times. Taking advantage of the fact that not all pixels will change from time t to time t + 1, they develop two important algorithms for computing the dilation and erosion of such images in o(n2) less time then with brute force. These results hold also for translation and rotation and can be extended to opening and closing of images by structuring elements. These results are also extended to images which contain multi-uncertain values, that is, the extended fuzzy pointing set. The advantages of these fast operations are obvious in on-the-fly image processing schemes such as real-time filtering of images.
03 Jun 1991
TL;DR: A fast and exact Euclidean distance transformation using grayscale mathematical morphology is presented and the large structuring element required for this operation is decomposed into iterative applications of simple 3*3 windows.
Abstract: A fast and exact Euclidean distance transformation using grayscale mathematical morphology is presented. The large structuring element required for this operation is decomposed into iterative applications of simple 3*3 windows. This is possible because the square of the Euclidean distance matrix is easily decomposable. Non-square pixels can also be used in this application. >
01 Apr 1991
TL;DR: It will be shown how an image transformed by a sequence of hit-and-miss, order statistic, matrices of structuring elements is isomorphic to a multiple layer translation invariant neural network that has excitatory and inhibitory connections with unit weights.
Abstract: A number of binary images derived from a segmentation process can be represented with a matrix indexing. Morphological operators can be similarly denoted. A formalism is described, where erosions and dilations operate on matrices of images. Matrix erosions and dilations can be extended to binary order statistic filters and hit- and-miss transforms. It will be shown how an image transformed by a sequence of hit-and-miss, order statistic, matrices of structuring elements is isomorphic to a multiple layer translation invariant neural network that has excitatory and inhibitory connections with unit weights. Network connections are equivalent to points in a structuring element. A form of supervised Hebbian learning can be applied to these morphological networks as follows. All weights are initially zero. A number of training cycles are performed by showing many images to the system. The weight of the connection that would provide the largest number of correct responses over the training set is chanced from zero to +1, or, the connection that would lead to the largest number of incorrect responses is changed from zero to -1 to provide an inhibitory connection. The best connection is determined, and then added to the network, and the cycles are repeated to build up enough connections to give low error rates.
01 Jun 1991
TL;DR: The separable ellipsoid is obtained, obtained by dilating two one-dimensional elliptical SEs aligned in the row and column directions, which gives comparable results to those of the ellipseid and allows a significant reduction in the computational time.
Abstract: Morphological image processing (MORPH) is a useful technique for angiogram enhancement. We compare the technique with digital subtraction angiography (DSA) by viewing the filtering operation as the approximation of the mask image in DSA processing. Viewing the enhancement process in this manner allows us to judge the performance of the filter by measuring the RMS error between the DSA and MORPH images. By computing the error for a wide variety of structuring element (SE) shapes and sizes, we are able to pick the optimal SE as the one with minimum error. Two shapes of SEs are under investigation: ellipsoidal and an approximation to this, called the separable ellipsoid, obtained by dilating two one-dimensional elliptical SEs aligned in the row and column directions. The separable ellipsoid gives comparable results to those of the ellipsoid and allows a significant reduction in the computational time.
01 Jul 1991
TL;DR: Experiments have shown that the overall computational complexity of the proposed adaptive morphological filter is comparable to that of the nonadaptive one combining four 1-D structuring elements of the same size.
Abstract: A new opening operation (NOP) and a new closing operation (NCP) are introduced and the algorithms to effectively compute the NOP and the NCP are developed. Based on the NOP and the NCP algorithms, an adaptive morphological filter is constructed. The filter adapts to the change of the image features in a way that it finds the optimal shape of the local structuring element of the filter according to the local features of the image. The shape can be any connected shape of a given size, which is considered the best to preserve the local details of the image. In that way, the filter can preserve any details larger or equal to the given mask size and remove those of smaller size. The local computational complexity of the filter changes according to the complexity of the local features of the image. Experiments have shown that the overall computational complexity of the proposed adaptive morphological filter is comparable to that of the nonadaptive one combining four 1-D structuring elements of the same size.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: It is shown that by a suitable choice of the structuring element, selective crease and roof edges can be extracted, and by using multiple structuring elements oriented in different directions, directional sensitivity to edge detection can be incorporated.
Abstract: Range images provide an explicit encoding of the shape and the geometric structure of the objects in the image from the point of view of the sensor. Morphological operators are ideally suited for analysis of range images due to their inherently geometric nature. Most morphological edge operators meant for intensity images are concerned only with jump and ramp edges and not with crease and roof edges. Since roof and crease edges do not correspond to depth discontinuity, such operators cannot be used to detect these edges in range images. In this paper, edge detection schemes for range images based on morphological operations are presented. It is shown that by a suitable choice of the structuring element, selective crease and roof edges can be extracted, and by using multiple structuring elements oriented in different directions, directional sensitivity to edge detection can be incorporated. Several examples of morphological edge detection in range images are presented.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
01 Apr 1991
TL;DR: In this paper, a direct approach algorithm has been developed to map size values for all pore pixels without iterative steps, and the result is a size map and the histogram of this size map represents the pore size distribution.
Abstract: Characterizing highly irregular 2D pore images requires special image analysis methods. An opening operation with a small circular structuring element has been used to remove small pores and small features of large pores from an image. Through a series of openings with increasingly larger structuring elements, all pore pixels are gradually removed according to the sizes of associated features. A pore size distribution is obtained as a result of this process. However, the conventional opening algorithm is very slow in performing this size analysis due to its iterative character. A direct approach algorithm has been developed to map size values for all pore pixels without iterative steps. There are three major steps in this algorithm. First, a distance map is constructed in which each pixel has a value equal to the distance between the pixel and the nearest pore boundary. Second, local maxima on the distance map are found. Finally, for each local maximum, a circular area is scanned around the pixel with a radius equal to the pixel value and all pixels within the circle are assigned the same value (as the local maximum). One pixel may be assigned several values from different local maxima; in such a case, the largest value should be chosen. The result is a size map and the histogram of this size map represents the pore size distribution. This analysis can be applied to any binary image.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
01 Apr 1991
TL;DR: An algorithm for quadtree decomposition is described, and experimental results of this decomposition for some structuring elements are shown.
Abstract: In order to efficiently perform morphological binary operations by relatively large structuring elements, we propose to decompose each structuring element into squares with 2 X 2 pixels by the quadtree approach. There are two types of decomposition--the dilation decomposition and the union decomposition. The first type decomposition is very efficient, but it is not necessarily always possible. The decomposition of second type is available for any structuring element, but the time cost of computation is proportional to the area of the structuring element. The quadtree decomposition proposed here is the combination of these two types of decomposition, and exists for any structuring element. When the Minkowski addition A (direct sum) B or the Minkowski subtraction A - B is computed, the number of times of the union/intersection of translations of the binary image is about the number of leaves of the quadtree representation of the structuring element B, which is roughly proportional to the square root of the area of B. In this paper, an algorithm for quadtree decomposition is described, and experimental results of this decomposition for some structuring elements are shown.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
08 Dec 1991
TL;DR: Deconvolution and morphological filters in tandem are applied in tandem in order to improve resolution and SNR and the performance of these algorithms and the design of the deconvolution kernel and structuring element as well as Morphological filters are evaluated using experimental results.
Abstract: Resolution of ultrasonic B-scans for NDE is limited by the bandwidth of the transducer and the presence of noise. An improvement in signal-to-noise ratio (SNR) can be obtained, to some extent, by performing ensemble averaging of numerous measurements. This method is impractical and can not eliminate interfering echoes resulting from stationary scatterers. Contrary to averaging, morphological filters, a class of nonlinear filters, are capable of eliminating impulse noise, moderately reducing grain echoes and improving the overall image quality while selectively preserving certain image features. The authors have applied deconvolution and morphological filters in tandem (i.e., deconvolution before or after morphological operations) in order to improve resolution and SNR. In particular, the performance of these algorithms and the design of the deconvolution kernel and structuring element as well as morphological filters are evaluated using experimental results. >
TL;DR: In this paper, a template decomposition technique based on the factorization of max-polynomials is presented and a sufficient condition for decomposing a one-dimensional morphological template into a set of two-point templates is established.
Abstract: Template decomposition plays an important role in image processing algorithm optimization andparallel image processing. In this paper, a template decomposition technique based on the factorizationof max-polynomials is presented. A morphological template may be represented by a max-polynomial,a notation used in combinatorial optimization. The problem of decomposition of a morphological tem-plate is thus reduced to the problem of factorization of the corresponding max-polynomial. A sufficientcondition for decomposing a one-dimensional morphological template into a set of two-point templates is established. Once the condition is satisfied, the construction of the decomposition is straight for- ward. A general procedure is also given for testing whether such a decomposition exists for an arbitraryone-dimensional morphological template. 1 Introduction Template decomposition plays an important role in image processing algorithm optimization and parallelimage processing. A linear or morphological filter used in image processing is usually implemented as aconvolution between a given image and a template, which is also referred to as convolution mask in linearfilter and structuring element in morphological filter. For a large template, the computation cost resultingfrom the direct convolution can be prohibitive. However, in many instances, this cost can be significantlyreduced by decomposing the template into a set of smaller templates and convolving the image with thesesmaller templates sequentially. In addition, such decompositions may be constructed for specialized imageprocessing architectures and, thus, resulting in optimal computational efficiency.The problem of template decomposition has been investigated by several researchers. Ritter and Gader[ 5] presented some efficient methods for decomposing discrete Fourier transform (DFT) templates. Wiejakand Buxton [3J proposed a method to decompose a two-dimensional (or higher dimensional) Marr-Hildrethconvolution operator into one-dimensional convolution operators ,
14 Apr 1991
TL;DR: The authors provide a morphologically realizable representation and decomposition for the general gray-scale structuring function and show recursive algorithms which are pipelineable for efficiently performinggray-scale morphological operations.
Abstract: Two major structuring element decomposition techniques are compared, and the superiority of the two pixel decomposition techniques over the cellular decomposition technique is shown in terms of the number of pipeline stages. As for the general structuring function decomposition, to the authors' knowledge, there is no efficient algorithm that has been found. The difficulty can be overcome by using an adequate representation of the general gray-scale structuring function. Representing a gray-scale image as a specific 3-D set, i.e. an umbra, makes it easier to shift all morphological theorems from the binary domain to the gray-scale domain; however, a direct umbra representation is not appropriate for the general gray-scale structuring function decomposition. The authors also provide a morphologically realizable representation and decomposition for the general gray-scale structuring function and show recursive algorithms which are pipelineable for efficiently performing gray-scale morphological operations. >
01 Jan 1991
TL;DR: A method for residue normalization considering the fundamental morphological operation, erosion, is presented and an optimal structuring element can be determined at the selected pyramid level on the basis of minimal residues, providing as complete a representation of the image as possible.
Abstract: The problem of selecting the pyramid level for optimal morphological processing of an image with a selected structuring element is considered. Each level in the image pyramid is eroded by a structuring element and the residue computed. The residues for all pyramid levels are normalized and compared in order to determine the optimal image pyramid level. A method for residue normalization considering the fundamental morphological operation, erosion, is presented. An optimal structuring element can be determined at the selected pyramid level on the basis of minimal residues, providing as complete a representation of the image as possible. >
05 Mar 1991
TL;DR: The image is processed by an error-diffusion technique to reduce the number of bit-planes without significant quality degradation and converted to Gray code and represented by a modified morphological skeleton which uses an increasing size structuring element.
Abstract: The image is processed by an error-diffusion technique to reduce the number of bit-planes without significant quality degradation. The bit-planes of the resulting image are converted to Gray code and represented by a modified morphological skeleton which uses an increasing size structuring element. Redundancy in this representation is reduced with an algorithm motivated by a geometric sampling theorem. These reduced modified morphological skeletons are coded with an entropy coding scheme devised particularly for efficient skeleton coding. A post-processing operation. as well as the possibility of geometric progressive transmission, are also discussed. >