A local Gaussian filter and adaptive morphology as tools for completing partially discontinuous curves

This paper presents a method for extraction and analysis of curve--type structures which consist of disconnected components. Such structures are found in electron--microscopy (EM) images of metal nanograins, which are widely used in the field of nanosensor technology. The topography of metal nanograins in compound nanomaterials is crucial to nanosensor characteristics. The method of completing such templates consists of three steps. In the first step, a local Gaussian filter is used with different weights for each neighborhood. In the second step, an adaptive morphology operation is applied to detect the endpoints of curve segments and connect them. In the last step, pruning is employed to extract a curve which optimally fits the template

On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Image segmentation and pattern classification using support vector machines

Image segmentation and pattern classification have long been important topics in computer science research. Image segmentation is one of the basic and challenging lower-level image processing tasks. Feature extraction, feature reduction, and classifier design based on selected features are the three essential issues for the pattern classification problem. In this dissertation, an automatic Seeded Region Growing (SRG) algorithm for color image segmentation is developed. In the SRG algorithm, the initial seeds are automatically determined. An adaptive morphological edge-linking algorithm to fill in the gaps between edge segments is designed. Broken edges are extended along their slope directions by using the adaptive dilation operation with suitably sized elliptical structuring elements. The size and orientation of the structuring element are adjusted according to local properties. For feature reduction, an improved feature reduction method in input and feature spaces using Support Vector Machines (SVMs) is developed. In the input space, a subset of input features is selected by the ranking of their contributions to the decision function. In the feature space, features are ranked according to the weighted support vectors in each dimension. For object detection, a fast face detection system using SVMs is designed. Twoeye patterns are first detected using a linear SVM, so that most of the background can be eliminated quickly. Two-layer 2nd-degree polynomial SVMs are trained for further face verification. The detection process is implemented directly in feature space, which leads to a faster SVM. By training a two-layer SVM, higher classification rates can be achieved. For active learning, an improved incremental training algorithm for SVMs is developed. Instead of selecting training samples randomly, the k-mean clustering algorithm is applied to collect the initial set of training samples. In active query, a weight is assigned to each sample according to its distance to the current separating hyperplane and the confidence factor. The confidence factor, calculated from the upper bounds of SVM errors, is used to indicate the degree of closeness of the current separating hyperplane to the optimal solution

Image morphological processing

Mathematical Morphology with applications in image processing and analysis has been becoming increasingly important in today\u27s technology. Mathematical Morphological operations, which are based on set theory, can extract object features by suitably shaped structuring elements. Mathematical Morphological filters are combinations of morphological operations that transform an image into a quantitative description of its geometrical structure based on structuring elements. Important applications of morphological operations are shape description, shape recognition, nonlinear filtering, industrial parts inspection, and medical image processing. In this dissertation, basic morphological operations, properties and fuzzy morphology are reviewed. Existing techniques for solving corner and edge detection are presented. A new approach to solve corner detection using regulated mathematical morphology is presented and is shown that it is more efficient in binary images than the existing mathematical morphology based asymmetric closing for corner detection. A new class of morphological operations called sweep mathematical morphological operations is developed. The theoretical framework for representation, computation and analysis of sweep morphology is presented. The basic sweep morphological operations, sweep dilation and sweep erosion, are defined and their properties are studied. It is shown that considering only the boundaries and performing operations on the boundaries can substantially reduce the computation. Various applications of this new class of morphological operations are discussed, including the blending of swept surfaces with deformations, image enhancement, edge linking and shortest path planning for rotating objects. Sweep mathematical morphology is an efficient tool for geometric modeling and representation. The sweep dilation/erosion provides a natural representation of sweep motion in the manufacturing processes. A set of grammatical rules that govern the generation of objects belonging to the same group are defined. Earley\u27s parser serves in the screening process to determine whether a pattern is a part of the language. Finally, summary and future research of this dissertation are provided

Measuring cellular traction forces on non-planar substrates

Animal cells use traction forces to sense the mechanics and geometry of their environment. Measuring these traction forces requires a workflow combining cell experiments, image processing and force reconstruction based on elasticity theory. Such procedures have been established before mainly for planar substrates, in which case one can use the Green's function formalism. Here we introduce a worksflow to measure traction forces of cardiac myofibroblasts on non-planar elastic substrates. Soft elastic substrates with a wave-like topology were micromolded from polydimethylsiloxane (PDMS) and fluorescent marker beads were distributed homogeneously in the substrate. Using feature vector based tracking of these marker beads, we first constructed a hexahedral mesh for the substrate. We then solved the direct elastic boundary volume problem on this mesh using the finite element method (FEM). Using data simulations, we show that the traction forces can be reconstructed from the substrate deformations by solving the corresponding inverse problem with a L1-norm for the residue and a L2-norm for 0th order Tikhonov regularization. Applying this procedure to the experimental data, we find that cardiac myofibroblast cells tend to align both their shapes and their forces with the long axis of the deformable wavy substrate.Comment: 34 pages, 9 figure

A Cosmic Watershed: the WVF Void Detection Technique

On megaparsec scales the Universe is permeated by an intricate filigree of clusters, filaments, sheets and voids, the Cosmic Web. For the understanding of its dynamical and hierarchical history it is crucial to identify objectively its complex morphological components. One of the most characteristic aspects is that of the dominant underdense Voids, the product of a hierarchical process driven by the collapse of minor voids in addition to the merging of large ones. In this study we present an objective void finder technique which involves a minimum of assumptions about the scale, structure and shape of voids. Our void finding method, the Watershed Void Finder (WVF), is based upon the Watershed Transform, a well-known technique for the segmentation of images. Importantly, the technique has the potential to trace the existing manifestations of a void hierarchy. The basic watershed transform is augmented by a variety of correction procedures to remove spurious structure resulting from sampling noise. This study contains a detailed description of the WVF. We demonstrate how it is able to trace and identify, relatively parameter free, voids and their surrounding (filamentary and planar) boundaries. We test the technique on a set of Kinematic Voronoi models, heuristic spatial models for a cellular distribution of matter. Comparison of the WVF segmentations of low noise and high noise Voronoi models with the quantitatively known spatial characteristics of the intrinsic Voronoi tessellation shows that the size and shape of the voids are succesfully retrieved. WVF manages to even reproduce the full void size distribution function.Comment: 24 pages, 15 figures, MNRAS accepted, for full resolution, see http://www.astro.rug.nl/~weygaert/tim1publication/watershed.pd