Structuring element

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

Adaptive grayscale morphological filters for image noise smoothing

Abstract: The authors find an optimal solution for designing a gray-scale morphological filter. An adaptive algorithm is developed for determining, from a given class of gray-scale morphological filters, a filter which minimizes the mean square error between its output and a desired process. The adaptation using the conventional least mean square algorithm optimizes the gray-scale structuring element in a given search area. The noise removal performance is compared to that of another class of nonlinear filters, i.e., adaptive and nonadaptive stack-based filters. >

Smooth Surface Reconstruction Using Tensor Fields as Structuring Elements

Abstract: We propose a new strategy to estimate surface normal information from highly noisy sparse data. Our approach is based on a tensor field morphologically adapted to infer normals. It acts as a three-dimensional structuring element of smooth surfaces. Robust orientation inference for all input elements is performed by morphological operations using the tensor field. A general normal estimator is defined by combining the inferred normals, their confidences and the tensor field. This estimator can be used to directly reconstruct the surface or give input normals to other reconstruction methods. We present qualitative and quantitative results to show the behavior of the original methods and ours. A comparative discussion of these results shows the efficiency of our propositions.

An adaptive soft-morphological-gradient-filter-for-edge-detection

Abstract: In this paper, a novel adaptive soft morphological gradient (ASMG) filter is proposed, based on a combination of the idea of the soft morphological filtering and the adaptive technique ASMG filtering is an efficient nonlinear sharpening method, which can be applied for edge detection By employing four directional structuring elements, ASMG filtering has the capability of selecting the directional structuring element with the maximum response, whose direction varies depending on the change of directional edges In addition, by comparing the variance of the moving structuring window with the base variance, the ASMG filter provides an adaptive algorithm for morphological operations The experimental results show that the ASMG filter is better than the traditional operators in edge detection and noise suppression

Efficient convolution based algorithms for erosion and dilation.

Abstract: Morphological operations based on primitives such as dilation and erosion are slow to compute in practice especially for large structuring elements. For direct implementation of these primitives, the computing time grows exponentially with the size of the structuring element used. The latter renders these implementations impractical for large structuring elements due to a rapid increase in computation time. There have been attempts in the literature to develop fast algorithms for implementation of morphological primitive operations. These are mainly restricted to convex and often symmetric structuring element shapes. We have developed a fast convolution-based approach for implementing morphological erosion and dilation and other operations such as opening and closing based on these primitives. The major advantages of this approach are: (i) it can use any structuring element shape including non-convex cases and (ii) it is very fast. This paper briefly introduces the approach and presents timing results for dilation and erosion using three different implementations of the approach. These results are also compared against a direct (brute force) implementation of the primitives.

Logical structural filters

Abstract: Binary granulometric filters are formed from unions of parameterized openings, a point passing the filter if and only if a translate of at least one structuring element fits in the image and contains the point. A granulometry induces a reconstructive granulometry by passing any image component not eliminated by the granulometry. As historically studied in the context of Matheron's granulometric theory, reconstructive granulometries appear as unions of reconstructive parameterized openings. The theory is extended to a much wider class of filters: a logical structural filter (LSF) is formed as a union of intersections of both reconstructive and complementary reconstructive openings. A reconstructive opening passes a component if and only if at least one translate of the structuring element fits inside; a complementary reconstructive opening passes a component if and only if no translate of the structuring element fits inside. The original reconstructive granulometries form the special class of disjunctive LSFs. Complement-free LSFsform granulometries in a slightly more general sense; LSFs containing complements are not increasing and therefore not openings. Along with the relevant algebraic representations for LSFs, the theories of optimal and adaptive granulometric filters are extended to LSFs, a systematic formulation of adaptive transitions is given, transition probabilities for adaptation are found, and two applications to biological imaging are presented.