Structuring element

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

Two 3D Morphological Filtering Methods Based on Sphere Structuring Element

Abstract: D morphological filtering based on mathematical morphology can become very time-consuming when using a large-scale structuring element involving the operation; however, if the structuring element is sphere, the Euclidean distance transform (EDT) could be used to perform basic mor- phological operations instead. Taking some geologic body as a case study, the comparison analysis results show that two filtering methods based on sphere structuring element have the same effects, whereas, the method based on EDT is more effective and applicable for large-scale structuring element involved.

Morphological decomposition of arbitrarily shaped images

Abstract: Decomposition of images is a very important issue in pattern analysis and recognition. Especially, for image processing systems that can not handle large size of images, image decomposition is the only way to overcome this difficulty. The technique presented in this paper is based on mathematical morphology and decomposes a binary structuring element into dilations of smaller size of images (factors). Park and Chin (1995) proposed a method of morphological decomposition of simply connected images into 3/spl times/3 size factors. We extend their theorem to make it possible for any n/spl times/n size factors. A method for optimal decomposition is also discussed. Based on this method, users can therefore select their favorable shape of structuring elements to process images efficiently.

Optimal and adaptive design of reconstructive granulometric filters

Abstract: The present paper provides a brief overview of the optimization and adaptive theories of reconstructive binary granulometric filters. When the generating sets of a Euclidean granulometry are compact and convex, the granulometry represents a parameterized family of-openings, each being a union of openings with structuring elements scalar multiplied by t > 0. The concept is generalized to a multivariate granulometry by allowing each structuring element to be parameterized by a vector, thereby generating a family of-openings parameterized by the vectors. Each such multivariate granulometry induces a reconstructive multivariate granulometry defined by passing each connected component of an image that is not eliminated by the original granulometry and not passing each connected component that is fully eliminated. Given ideal and observed (corrupted) random sets, the optimization problem for image restoration by multivariate reconstructive gran-ulometries is find to a value of the parameter vector that minimizes the expected error (expected symmetric-difference area) between the ideal and the filtered observation. The corresponding adaptive filter problem is to allow the parameter vector to transition during a scanning process in such a way as to produce desired results and to study the steady-state properties of the multi-dimensional Markov chain defined by the state space of the now random parameter vector. A second approach to granulometric filtering is to decompose an image by means of the spectral components produced by the granulometry and then pass some subfamily of the spectral components. Given ideal and observed image processes, the optimization for these bandpass filters is to pass spectral components in a manner that minimizes restoration error. One can also proceed adaptively by allowing the parameters defining the passbands to adapt, thereby producing a multi-dimensional state space for a Markov chain whose steady-state properties characterize adaptivity. These four optimization and adaptation problems are discussed in the present paper, with emphasis how they yield filters for restoration in the signal-union-noise model.

Hybrid bipixel structuring element decomposition and Euclidean morphological transforms

Abstract: Hybrid bipixel structuring element decomposition can be accomplished if the decomposed primary components of astructuring element are either line segments or parallelograms, since both have optimal bipixel decomposition. The proposed method is used for the decomposition of digital disks and can be extended to arbitrary structuring elements. Using the decomposed digital disks, Euclidean morphological dilation and erosion can be performed with linear computational corn-plexity. 1. INTRODUCTION Basic morphological transforms can be efficiently performed by a variety of parallel image processing architectures,such as the Cytocomputer' , the image flow computer2, and the pipeline systolic array3. Those architectures usually have res-trictions on the applicable size of structuring elements. On the Cytocomputer, for example, each pipeline stage supports astructuring element whose domain is either a subset of 3x3 neighborhoods or 7-pixel hexagonal neighborhoods. The imageflow computer is suitable for any structuring element consisting of two pixels. When a structuring element with a domainsize larger than the limit set by a specific architecture, it must be decomposed into smaller components in order to be per-