Showing papers on "Structuring element published in 1988"

The digital morphological sampling theorem

Abstract: There are potential industrial applications for any methodology which inherently reduces processing time and cost and yet produces results sufficiently close to the result of full processing. It is for this reason that a morphological sampling theorem is important. The morphological sampling theorem described by the authors states: (1) how a digital image must be morphologically filtered before sampling to preserve the relevant information after sampling; (2) to what precision an appropriately morphologically filtered image can be reconstructed after sampling; and (3) the relationship between morphologically operating before sampling and the more computationally efficient scheme of morphologically operating on the sampled image with a sampled structuring element. The digital sampling theorem is developed for the case of binary morphology. >

Automated image segmentation by mathematical morphology and fractal geometry

Abstract: SUMMARY A new method for automated image segmentation is presented. It makes use of a combination of principles derived from mathematical morphology and fractal geometry. The method consists of searching for regions in which the grey-tone function defining the black-and-white image can be represented, inside a certain range of resolutions, by a fractal surface with a given fractal dimension. The probability for a planar, circular structuring element, randomly positioned on a grey-level plane inside a region of the digitized image, to intersect the surface which represents the grey-tone function, is derived by two methods, fractal geometry and mathematical morphology. A fundamental equation is finally derived, relating, in a fractal region of the grey-tone surface, the sum of discrete (pixel) grey-level differences between the images obtained by ***multi-grey-level dilation and erosion of the original image, respectively, to the size of the structuring element and the fractal dimension. This equation represents the basis of the method. The automated image analysis program, written for the IBAS (Kontron), works on several memorized images, each produced by a subtraction between the images obtained by dilation and erosion of the original image, using several sizes for the structuring element. Although minimal computations are made, the algorithms are too slow for practical applications and will require massive parallel processing for future use. The method relies on the assumption that regions of an image having a particular structure will usually produce a fractal grey-tone surface, with a particular value of the fractal dimension. The feasibility of such an approach is demonstrated with segmentations obtaining the isolation of various objects on different biological images. The natural structures we have studied indeed show a fractal grey-tone surface, at least within a certain range of (low) resolutions. Our studies also allow us to consider whether human vision uses a combination of image transformations and principles of self-similarity to segment images.

An algorithm for a generalized distance transformation based on Minkowski operations

Abstract: A generalized distance transformation of binary images based on successive Minkowski operations is discussed. This distance transformation is obtained by using a two-scan algorithm. A related medial axis for image compression is defined. As an example of the transformation's application, a fast algorithm for elementary morphological operations with an arbitrary structuring element is given. >

Automated fast recognition and location of arbitrarily shaped objects by image morphology

Abstract: Morphological operations are used for segmentation, feature generation and location extraction. A recursive adaptive thresholding algorithm transforms a gray-level image into a set of multiple level regions of objects. A distance transformation algorithm then is used to transform a binary image into the minimum distance from each object point to the object's boundary. This algorithm uses a morphological erosion with a large structuring element which may correspond to Euclidean, city-block, or chessboard distance measures. A shape library database with hierarchical features is automatically generated. The features extracted are the shape number and the skeletal local-maximum points radii and coordinates. Object recognition is achieved by comparing the shape number and the hierarchical radii. Object location is detected by a hierarchical morphological bandpass filter. >

Industrial parts recognition and inspection by image morphology

Abstract: Application algorithms for industrial parts and tool recognition and inspection by image morphology techniques are discussed. A recursive adaptive thresholding algorithm transforms a gray-level image into a set of multiple-level regions of objects. This algorithm uses a morphological erosion with a large symmetrical concave structuring element. A distance-transformation algorithm transforms these binary image regions into the minimum distance from each object point to the boundary of the object. This algorithm also uses a morphological erosion. From the distance transform, it is possible to compute a shape number and extract the skeleton, which is useful for generic pattern recognition and feature extraction. Corner angles and the radii of circular holes can be located, identified, and estimated by using morphological openings and erosions. The algorithms allow robust tool and part recognition and inspection. >

Morphological Operator Distributions Based On Monotonicity And The Problem Posed By Digital Disk-Shaped Structuring Elements

Abstract: A sequence of structuring elements S = {S1,...,SN} is said to be increasing if it has the property that for each i, Si+i ⊃ Si. In general, such sequences are made up of elements with similar shapes but different sizes; e. g., lines, squares, octagons, and disks. A morphological operation ψ is said to be monotonic with respect to an Increasing structuring element sequence S, if, for any set X, either: (X 'F Si+1) 2 (X 'F Si), Vi (Monotonic increasing) Or (X AIF Si) 3 (X III Si+1), Vi (Monotonic decreasing) Dilation is monotonic increasing while erosion is monotonic decreasing. These properties make it possible to unambiguously classify every pixel in a binary image by associating each with one of the elements in the sequence S. Morphological openings and closings are also monotonic, but only if an additional property holds for the sequence 5, namely, that for each i, there exists a structuring element T such that Si+1 = (Si ⊕ T), or in other words, Si and Si+1 must be similar in shape up to a dilation. In the digital world, squares, hexagons, and octagons are similar but digital approximations to disks are not. This poses problems for trying to generate morphological shape and size distributions based on very accurate digital disks. This paper proves the monotonicity properties for erosions, dilations, openings, and closings, and shows how pixel distributions or classifications based on shape can be generated from these properties. It also discusses the problem posed by digital disks, and describes one method of circumventing it.© (1988) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Skeletonization And Distance Transformation By Greyscale Morphology

Abstract: Mathematical morphology applied to image processing which deals directly with shape is a more direct and faster approach to feature measurements than traditional techniques. It has grown to include many applications and architectures in image analysis. Binary morphology has been successfully extended to greyscale morphology which allows a new set of applications. In this paper, the distance transformation, skeletonization, and reconstruction algorithms using the greyscale morphology approach are described and proven to be remarkably simple. The distance transformation of an object is the minimum distance from inner points to the background of an object. The algorithm is a recursive greyscale erosion of the image with a small size structuring element. The distance can be Euclidean, chessboard, or city-block distance which depends on the selection of its structuring element. The skeleton extracted is the Medial Axis Transformation (MAT) which is produced from the result of the distance transformation. The values of the distance transform along the skeleton are maintained to represent distance to the closest boundary. We can easily reconstruct the distance transform from the skeleton by iterative greyscale dilations with the same struc-turing element. In order for this method to be useful for grey level images, a simple adaptive threshold algorithm using greyscale ero-sion with a non-linear structuring element has been developed.21 A decomposition technique which reduces the large size non-linear structuring element into a recursive operation with a small window allows real-time implementation.

Feature-Size Dependent Selective Edge Enhancement Of X-Ray Images

Abstract: Morphological filters are nonlinear signal transformations that operate on a picture directly in the space domain. Such filters are based on the theory of mathematical morphology as formulated by Matheron [1] and Serra [2,3]. Sternberg [4,5] generalized earlier results to include graytone images. He also introduced the "rolling ball" morphological operator and pointed out that it can be used for edge enhancement. This paper reports on an variation of the rolling ball algorithm. An introduction to some of the concepts used here was given by Herman [6]. The filter being presented here features a "mask" operator (called a "structuring element" in some of the literature) which is a function of the two spatial coordinates x and y. The two basic mathematical operations are called "masked erosion" and "masked dilation". In the case of masked erosion the mask is passed over the input image in a raster pattern. At each position of the mask, the pixel values under the mask are multiplied by the mask pixel values. Then the output pixel value, located at the center position of the mask, is set equal to the minimum of the product of the mask and input values. Similarly, for masked dilation, the output pixel value is the maximum of the product of the input and the mask pixel values. The two basic processes of dilation and erosion can be used to construct the next level of operations the "positive sieve" [4] (also called "open-ing") and the "negative sieve" ("closing"). The positive sieve modifies the peaks in the image, whereas the negative sieve works on image valleys. The positive sieve is implemented by passing the output of the masked erosion step through the masked dilation function. The negative sieve reverses this procedure, using a dilation followed by an erosion. Each such sifting operator is characterized by a "hole size". If one considers a two dimensional image as a three dimensional function or surface over the two coordinates x and y, then a positive sieve will eliminate all peaks of this surface which have a cross section parallel to the x-y plane which is smaller than the hole size. Conversely, a negative sieve will clip all valleys smaller than the hole size. The hole size of a masked sifting operator in any given direction is equal to the size of the mask minus one pixel in that direction. It will be shown that the choice of hole size will select the range of pixel detail sizes which are to be enhanced. The shape of the mask will govern the shape of the enhancement. Finally positive sifting is used to enhance positive-going (peak) features, whereas negative sifting enhances the negative-going (valley) landmarks.

Textured images segmentation by morphological partition filters

Abstract: This paper presents a new segmentation procedure for textured images, using morphological partition filters. These filters are c haracaterized by a controllable selectivity of action with respect to b oth directivity and spatial frequency. They are thus able to homogenize regions whose structure corresponds to t heir characteristics, while leaving o thers untouched. Automatic adjustment of their structuring element is obtained through computation of the image covariograms, during the various stages of the procedure. This segmentation procedure appears to perform well in cases of highly structured textures.

Morphological image analysis for studying Alzheimer's disease

Abstract: One of the hallmarks of Alzheimer's disease is the presence of a brain lesion known as a senile plaque (SP), which appears as a circular cluster of small objects when viewed through the microscope. To quantitatively study their number and distribution, the author has developed an image analysis system that will automatically detect and count these lesions. The morphological operation of closing can group a cluster of small objects into a singular one, and thus allow detection of the SP. Since the optimal structuring element size for grouping the SP is different in each image, the Bayesian decision-making method is used to dynamically determine the size. A study comparing computer and human detection of SP was performed by evaluating 50 images from five different patients. The results of this comparison demonstrate that the computer counts correlate well with the neuropathologists counts (correlation coefficient=0.81). >

The Digital Morphological Sampling Theorem

Abstract: There are potential industrial applications for any methodology which inherently reduces processing time and cost and yet produces results sufficiently close to the result of full processing It is for this reason that a morphological sampling theorem is important The morphological sampling theorem described in this paper states: (1) how a digital image must be morphologically filtered before sampling in order to preserve the relevant information after sampling; (2) to what precision an appropriately morphologically filtered image can be reconstructed after sampling; and (3) the relationship between morphologically operating before sampling and the more computationally efficient scheme of morphologically operating on the sampled image with a sampled structuring element The digital sampling theorem is developed first for the case of binary morphology and then it is extended to gray scale morphology through the use of the umbra homomorphism theorems

Morphological image analysis for studying alzheimer's disease

Abstract: One of the hallmarks of Alzhimer's diAease is the presence of a brain lesion known as a senile plaque (SP), which appears as a drcu­ lar cluster of small objects when viewed through the microscope. In order to quantitatively study their number and dildribution, we have developed an imlLge anftlysis system that will automatically detect and count these lesions. The morphological operation of closing can group a cluster of small objects into a. singular one, and thus allow detection of the SP. Since the optimal structuring element size for grouping the SP is different in each image, the Baysian decision making method is used to dynamically determine the size. A study comparing computer and human detection of SP was performed by evaluating 50 images from 5 di:ff erent patients. The results of this comparison demonstrate that the computer counts correlate well with the neuropathologist 's counts (correlation coefficie nt = .81).