Structuring element

About: Structuring element is a research topic. Over the lifetime, 997 publications have been published within this topic receiving 26839 citations.

Optimal mean-square N -observation digital morphological filters: i. optimal binary filters

Abstract: The present paper places binary morphological filtering into the framework of statistical estimation, the intent being to develop the theory of mean-square (MS) optimization. Classical binary morphological operations are interpreted as numerical functionals on binary N-vectors, so that in the random setting they can be treated as estimators dependent on N binary observation random variables. For single-erosion filters, optimization is achieved by finding the structuring element that minimizes MS error. Using the Matheron representation as a guide, we generalize the analysis to morphological filters given by unions of multiple erosions and optimize by minimizing MS error over all collections of erosions, or over a prefixed number of erosions. In all cases, MS error is relative to the estimation of an unobserved variable by a morphological function of observed variables. A key element in the method is use of the basis form of the Matheron expansion to reduce significantly the structuring-element search. The technique is adapted to special morphological filters by constraining the basis representation in accordance with the class of interest. It is demonstrated that optimization in terms of erosions is equivalent to optimization in terms of dilations.

Semi-automatic segmentation of vascular network images using a rotating structuring element (ROSE) with mathematical morphology and dual feature thresholding

Abstract: A method for measuring the spatial concentration of specific categories of vessels in a vascular network consisting of vessels of several diameters, lengths, and orientations is demonstrated. It is shown that a combination of the mathematical morphology operation, opening, with a linear rotating structuring element (ROSE) and dual feature thresholding can semi-automatically segment categories of vessels in a vascular network. Capillaries and larger vessels (arterioles and venules) are segmented here in order to assess their spatial concentrations. The ROSE algorithm generates the initial segmentation, and dual feature thresholding provides a means of eliminating the nonedge artifact pixels. The subsequent gray-scale histogram of only the edge pixels yields the correct segmentation threshold value. This image processing strategy is demonstrated on micrographs of vascular casts. By adjusting the structuring element and rotation angles, it could be applied to other network structures where a segmentation by network component categories is advantageous, but where the objects can have any orientation. >

A Euclidean distance transform using grayscale morphology decomposition

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

Detecting Defects in Fabric with Laser-Based Morphological Image Processing

Abstract: Morphological operations such as erosion and opening are applied to both direct and spatially filtered images of test fabrics to identify defects. Detecting defects morpholog ically on spatially filtered images of fabrics produces better results, particularly when the fabric is fine and contains defects of small size. The diffraction pattern of the test fabric is obtained optically by illuminating it with a collimated laser beam. A spatial filter is placed at the Fourier plane to remove the periodic grating structure of the fabric from the image. Morphological operations with a critically selected structuring element are then applied to the image after suitable pre-processing.