Structuring element

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

Narrow branch preservation in morphological reconstruction

Abstract: We present a morphological approach to the reconstruction of fine branching structures in three dimensional data, developed from the basic procedures of reconstruction by dilation. We address a number of closely related questions arising from this reconstruction goal, including issues of structuring element size and shape, noise propagation, iterated approaches, and the relationship between geodesic and conditional dilation. We investigate and assess the effect and importance of these considerations in the context of the overall reconstruction process, and examine the effectiveness of the approach in addressing the task of reconstructing narrow branch features in noisy data.

Graph-based representation for 2-D shape using decomposition scheme

Abstract: In this paper, to represent 2-D shape as a relational structure, i.e. graph, we propose a new shape decomposition scheme composed of two stages: first, a given shape is decomposed into meaningful parts by using the constrained morphological decomposition (CMD) in a recursive manner. More specifically, the CMD adopts the use of the opening operation with the ball-shaped structuring element and the weighted convexity to select the optimal decomposition. Second, the iterative merging stage provides a compact graph-based representation based on the weighted convexity difference. From the experimental results for various and modified 2-D shapes, it is believed that the graph-based representation for 2-D shape coincides with that based on human insight, and also provides robustness to scaling, rotation, noise, shape deformation and occlusion.

A Study of Morphological Edge Detector by Multidirectional Structuring Element

Abstract: In this paper we present a morphologic edge detector using multidirectional structuring element approach for detecting edges of complex images under noisy condition. The experimental results show that the proposed edge detector has the desirable properties that a good edge detector should have. Comparative study reveals its detection performance exceeds conventional edge detectors and other morphologic edge detectors.

Quadtree decomposition of binary structuring elements

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.

The symbolic representation, analysis, and manipulation of morphological algorithms

Abstract: Mathematical morphology has become increasingly important in machine vision and image analysis applications. To aid the design of efficient morphological transforms, this thesis explores some of the issues involved in developing an environment that can automatically analyze and manipulate morphological algorithms. This thesis presents representations of signals and systems and definitions of computational costs associated with producing signals from morphological systems. These representations are illustrated with the scMETAMORPH environment, an algorithm analysis system that operates at the symbolic level of the expression and permits expression rewriting such as simplifications, generation of equivalent forms, and expression analysis such as the determination of signal and system properties. The class of algorithms that may be analyzed include all transformations represented by compositions of the elemental operations of morphology. The symbolic manipulation of morphological expressions eliminates redundancies and exploits signal properties to minimize the computational cost of evaluating the expressions. The generation of equivalent forms for expressions uncovers alternate, and novel, implementations as shown by the automatic generation of efficient morphological skeletonization and reconstruction algorithms. The development of computational cost descriptors allows the relative complexity of algorithms to be compared and the implementation most suited to a particular architecture selected. To facilitate the system property analysis of compound expressions, a framework is presented that abstracts and unifies signal and system property analysis. Finally, addressing the limits of computational reduction of morphological algorithms, a lower bound on the number of points needed for a Minkowski addition decomposition of an arbitrary N-point structuring element has been found and is given by $\lceil 3{{\rm ln}N\over\rm ln3}\rceil$ points. Because there are fewer points in the decomposed kernel than the original structuring element, decomposing structuring elements permits more efficient implementations of the morphological operators. A technique for optimally decomposing (in terms of the number of unions or signal accesses required) the class of connected line structuring elements has been developed.