A robust high-sensitivity algorithm for automated detection of proteins in two-dimensional electrophoresis gels

The automated interpretation of two-dimensional gel electrophoresis images used in protein separation and analysis presents a formidable problem in the detection and characterization of ill-defined spatial objects. We describe in this paper a hierarchical algorithm that provides a robust, high-sensitivity solution to this problem, which can be easily adapted to a variety of experimental situations. The software implementation of this algorithm functions as part of a complete package designed for general protein gel analysis applications

Edge and Line Feature Extraction Based on Covariance Models

age segmentation based on contour extraction usually involves three stages of image operations: feature extraction, edge detection and edge linking. This paper is devoted to the first stage: a method to design feature extractors used to detect edges from noisy and/or blurred images. The method relies on a model that describes the existence of image discontinuities (e.g. edges) in terms of covariance functions. The feature extractor transforms the input image into a “log-likelihood ratio” image. Such an image is a good starting point of the edge detection stage since it represents a balanced trade-off between signal-to-noise ratio and the ability to resolve detailed structures. For 1-D signals, the performance of the edge detector based on this feature extractor is quantitatively assessed by the so called “average risk measure”. The results are compared with the performances of 1-D edge detectors known from literature. Generalizations to 2-D operators are given. Applications on real world images are presented showing the capability of the covariance model to build edge and line feature extractors. Finally it is shown that the covariance model can be coupled to a MRF-model of edge configurations so as to arrive at a maximum a posteriori estimate of the edges or lines in the image

The polytope of non-crossing graphs on a planar point set

For any finite set \A of $n$ points in $\R^2$, we define a $(3n-3)$-dimensional simple polyhedron whose face poset is isomorphic to the poset of ``non-crossing marked graphs'' with vertex set \A, where a marked graph is defined as a geometric graph together with a subset of its vertices. The poset of non-crossing graphs on \A appears as the complement of the star of a face in that polyhedron. The polyhedron has a unique maximal bounded face, of dimension $2n_i +n -3$ where $n_i$ is the number of points of \A in the interior of \conv(\A). The vertices of this polytope are all the pseudo-triangulations of \A, and the edges are flips of two types: the traditional diagonal flips (in pseudo-triangulations) and the removal or insertion of a single edge. As a by-product of our construction we prove that all pseudo-triangulations are infinitesimally rigid graphs.Comment: 28 pages, 16 figures. Main change from v1 and v2: Introduction has been reshape

Geometrical-based algorithm for variational segmentation and smoothing of vector-valued images

An optimisation method based on a nonlinear functional is considered for segmentation and smoothing of vector-valued images. An edge-based approach is proposed to initially segment the image using geometrical properties such as metric tensor of the linearly smoothed image. The nonlinear functional is then minimised for each segmented region to yield the smoothed image. The functional is characterised with a unique solution in contrast with the Mumford–Shah functional for vector-valued images. An operator for edge detection is introduced as a result of this unique solution. This operator is analytically calculated and its detection performance and localisation are then compared with those of the DroGoperator. The implementations are applied on colour images as examples of vector-valued images, and the results demonstrate robust performance in noisy environments

Feature Lines for Illustrating Medical Surface Models: Mathematical Background and Survey

This paper provides a tutorial and survey for a specific kind of illustrative visualization technique: feature lines. We examine different feature line methods. For this, we provide the differential geometry behind these concepts and adapt this mathematical field to the discrete differential geometry. All discrete differential geometry terms are explained for triangulated surface meshes. These utilities serve as basis for the feature line methods. We provide the reader with all knowledge to re-implement every feature line method. Furthermore, we summarize the methods and suggest a guideline for which kind of surface which feature line algorithm is best suited. Our work is motivated by, but not restricted to, medical and biological surface models.Comment: 33 page

Performing edge detection by difference of Gaussians using q-Gaussian kernels

In image processing, edge detection is a valuable tool to perform the extraction of features from an image. This detection reduces the amount of information to be processed, since the redundant information (considered less relevant) can be unconsidered. The technique of edge detection consists of determining the points of a digital image whose intensity changes sharply. This changes are due to the discontinuities of the orientation on a surface for example. A well known method of edge detection is the Difference of Gaussians (DoG). The method consists of subtracting two Gaussians, where a kernel has a standard deviation smaller than the previous one. The convolution between the subtraction of kernels and the input image results in the edge detection of this image. This paper introduces a method of extracting edges using DoG with kernels based on the q-Gaussian probability distribution, derived from the q-statistic proposed by Constantino Tsallis. To demonstrate the method's potential, we compare the introduced method with the traditional DoG using Gaussians kernels. The results showed that the proposed method can extract edges with more accurate details.Comment: 5 pages, 5 figures, IC-MSQUARE 201

Disorder-free localization around the conduction band edge of crossing and kinked silicon nanowires

We explore ballistic regime quantum transport characteristics of oxide-embedded crossing and kinked silicon nanowires (NWs) within a large-scale empirical pseudopotential electronic structure framework, coupled to the Kubo-Greenwood transport analysis. A real-space wave function study is undertaken and the outcomes are interpreted together with the findings of ballistic transport calculations. This reveals that ballistic transport edge lies tens to hundreds of millielectron volts above the lowest unoccupied molecular orbital, with a substantial number of localized states appearing in between, as well as above the former. We show that these localized states are not due to the oxide interface, but rather core silicon-derived. They manifest the wave nature of electrons brought to foreground by the reflections originating from NW junctions and bends. Hence, we show that the crossings and kinks of even ultraclean Si NWs possess a conduction band tail without a recourse to atomistic disorder.Comment: Published version, 7 pages, 9 figure