A neural approach for obstacle detection with a linear stereoscopic sensor

A neural implementation for achieving real-time obstacle detection in front of a moving vehicle using a linear stereoscopic sensor is presented. The key problem is the so-called “correspondence problem” which consists in matching features in two stereo images that are projections of the same physical entity in the three-dimensional world. In our approach, the set of edge points extracted from each linear image is first split into two classes. Within each of these classes, the matching problem is turned into an optimization task where an energy function, which represents the constraints on the solution, is to be minimized. The optimization problem is then performed thanks to an analog Hopfield neural network. The preliminary discrimination of the edge points allows us to implement the matching process as two networks running in parallel. Experimental results are presented to demonstrate the effectiveness of the approach for 3-D reconstruction in real traffic conditions.     

Rough fuzzy set based scale space transforms and their use in image analysis

In this paper we present a multi-scale method based on the hybrid notion of rough fuzzy sets, coming from the combination of two models of uncertainty like vagueness by handling rough sets and coarseness by handling fuzzy sets. Marrying both notions lead to consider, as instance, approximation of sets by means of similarity relations or fuzzy partitions. The most important features are extracted from the scale spaces by unsupervised cluster analysis, to successfully tackle image processing tasks. Here, we report some results achieved by applying the method to multi-class image segmentation and edge detection, but it can be shown to be successfully applied to texture discrimination problem too.     

Edge detection based on fractional order differentiation and its application to railway track images

Edge detection is one of the most fundamental necessities in image processing. Usally, edge detection algorithms are based on integer order differentiation operators. In many applications it is essential to perform a robust edge detection also to noisy input image data with low SNR as well. Thereby, integer based differentiation operators are often not leading to sufficient detection results. For this purpose an edge detector based on fractional order differentiation is introduced, which can significantly improve the detection performance to noisy images. Furthermore, a real application scenario of fractional order based edge detection is given within a modular railway track measurement system. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Using Conventional Edge Detectors and Postsmoothing for Segmentation of Spotted Microarray Images

Segmentation of spotted microarray images is important in generating gene expression data. It aims to distinguish foreground pixels from background pixels for a given spot of a microarray image. Edge detection in the image processing literature is a closely related research area, because spot boundary curves separating foregrounds from backgrounds in a microarray image can be treated as edges. However, for generating gene expression data, segmentation methods for handling spotted microarray images are required to classify each pixel as either a foreground or a background pixel; most conventional edge detectors in the image processing literature do not have this classification property, because their detected edge pixels are often scattered in the whole design space and consequently the foreground or background pixels are not defined. In this article, we propose a general postsmoothing procedure for estimating spot boundary curves from the detected edge pixels of conventional edge detectors, such that these conventional edge detectors together with the proposed postsmoothing procedure can be used for segmentation of spotted microarray images. Numerical studies show that this proposal works well in applications.

Datasets and computer code are available in the online supplements.     

Edge detection of noisy images based on cellular neural networks

This paper studies a technique employing both cellular neural networks (CNNs) and linear matrix inequality (LMI) for edge detection of noisy images. Our main work focuses on training templates of noise reduction and edge detection CNNs. Based on the Lyapunov stability theorem, we derive a criterion for global asymptotical stability of a unique equilibrium of the noise reduction CNN. Then we design an approach to train edge detection templates, and this approach can detect the edge precisely and efficiently, i.e., by only one iteration. Finally, we illustrate performance of the proposed methodology from the aspect of peak signal to noise ratio (PSNR) through computer simulations. Moreover, some comparisons are also given to prove that our method outperforms classical operators in gray image edge detection.     

Iterative adaptive RBF methods for detection of edges in two-dimensional functions

Radial basis functions have gained popularity for many applications including numerical solution of partial differential equations, image processing, and machine learning. For these applications it is useful to have an algorithm which detects edges or sharp gradients and is based on the underlying basis functions. In our previous research, we proposed an iterative adaptive multiquadric radial basis function method for the detection of local jump discontinuities in one-dimensional problems. The iterative edge detection method is based on the observation that the absolute values of the expansion coefficients of multiquadric radial basis function approximation grow exponentially in the presence of a local jump discontinuity with fixed shape parameters but grow only linearly with vanishing shape parameters. The different growth rate allows us to accurately detect edges in the radial basis function approximation. In this work, we extend the one-dimensional iterative edge detection method to two-dimensional problems. We consider two approaches: the dimension-by-dimension technique and the global extension approach. In both cases, we use a rescaling method to avoid ill-conditioning of the interpolation matrix. The global extension approach is less efficient than the dimension-by-dimension approach, but is applicable to truly scattered two-dimensional points, whereas the dimension-by-dimension approach requires tensor product grids. Numerical examples using both approaches demonstrate that the two-dimensional iterative adaptive radial basis function method yields accurate results.     

Nonlinear separation approach for the augmented Lagrangian in nonlinear semidefinite programming

This paper aims at showing that the class of augmented Lagrangian functions for nonlinear semidefinite programming problems can be derived, as a particular case, from a nonlinear separation scheme in the image space associated with the given problem. By means of the image space analysis, a global saddle point condition for the augmented Lagrangian function is investigated. It is shown that the existence of a saddle point is equivalent to a regular nonlinear separation of two suitable subsets of the image space. Without requiring the strict complementarity, it is proved that, under second order sufficiency conditions, the augmented Lagrangian function admits a local saddle point. The existence of global saddle points is then obtained under additional assumptions that do not require the compactness of the feasible set. Motivated by the result on global saddle points, we propose two modified primal-dual methods based on the augmented Lagrangian using different strategies and prove their convergence to a global solution and the optimal value of the original problem without requiring the boundedness condition of the multiplier sequence.     

基于方向信息测度的图像边缘检测

边缘检测是图像处理中—个重要的研究课题．针对传统图像边缘检测算法对噪声敏感的问题,本文在分析图像像素灰度信息的基础上,建立了—个改进的确定方向信息测度的方法,并利用震动滤波对边缘检测图像进行增强,该方法在滤除噪声的同时,能有效地保留图像的基本目标信息,正确提取图像的边缘．     

Identification of objects in an acoustic wave guide inversion II: Robin–Dirichlet conditions

In this paper we investigate the unknown body problem in a wave guide where one boundary has a pressure release condition and the other an impedance condition. The method used in the paper for solving the unknown body inverse problem is the intersection canonical body approximation (ICBA). The ICBA is based on the Rayleigh conjecture, which states that every point on an illuminated body radiates sound from that point as if the point lies on its tangent sphere. The ICBA method requires that an analytical solution be known exterior to a canonical body in the wave guide. We use the sphere of arbitrary centre and radius in the wave guide as our canonical body. We are lead then to analytically computing the exterior solution for a sphere between two parallel plates. We use the ICBA to construct solutions at points ranging over the suspected surface of the unknown object to reconstruct the unknown object using a least‐squares matching of computed, acoustic field against the measured, scattered field. Copyright © 2005 John Wiley & Sons, Ltd.     

Relaxed two points projection method for solving the multiple-sets split equality problem

The multiple-sets split equality problem, a generalization and extension of the split feasibility problem, has a variety of specific applications in real world, such as medical care, image reconstruction, and signal processing. It can be a model for many inverse problems where constraints are imposed on the solutions in the domains of two linear operators as well as in the operators’ ranges simultaneously. Although, for the split equality problem, there exist many algorithms, there are but few algorithms for the multiple-sets split equality problem. Hence, in this paper, we present a relaxed two points projection method to solve the problem; under some suitable conditions, we show the weak convergence and give a remark for the strong convergence method in the Hilbert space. The interest of our algorithm is that we transfer the problem to an optimization problem, then, based on the model, we present a modified gradient projection algorithm by selecting two different initial points in different sets for the problem (we call the algorithm as two points algorithm). During the process of iteration, we employ subgradient projections, not use the orthogonal projection, which makes the method implementable. Numerical experiments manifest the algorithm is efficient.     

Multiobjective improved spatial fuzzy c-means clustering for image segmentation combining Pareto-optimal clusters

In this paper, we propose a grayscale image segmentation method based on a multiobjective optimization approach that optimizes two complementary criteria (region and edge based). The region-based fitness used is the improved spatial fuzzy c-means clustering measure that is shown performing better than the standard fuzzy c-means (FCM) measure. The edge-based fitness used is based on the contour statistics and the number of connected components in the image segmentation result. The optimization algorithm used is the multiobjective particle swarm optimization (MOPSO), which is well suited to handle continuous variables problems, the case of FCM clustering. In our case, each particle of the swarm codes the centers of clusters. The result of the multiobjective optimization technique is a set of Pareto-optimal solutions, where each solution represents a segmentation result. Instead of selecting one solution from the Pareto front, we propose a method that combines all solutions to get a better segmentation. The combination method takes place in two steps. The first step is the detection of high-confidence points by exploiting the similarity between the results and the membership degrees. The second step is the classification of the remaining points by using the high-confidence extracted points. The proposed method was evaluated on three types of images: synthetic images, simulated MRI brain images and real-world MRI brain images. This method was compared to the most widely used FCM-based algorithms of the literature. The results demonstrate the effectiveness of the proposed technique.     

A DC optimization-based clustering technique for edge detection

We introduce a method for edge detection which is based on clustering the pixels representing any given digital image into two sets (the edge pixels and the non-edge ones). The process is based on associating to each pixel an appropriate vector representing the differences in brightness w.r.t. the surrounding pixels. Clustering is driven by the norms of such vectors, thus it takes place in \(\mathbb {R}\), which allows us to use a (simple) DC (Difference of Convex) optimization algorithm to get the clusters. A novel thinning technique, based on calculation of the edge phase angles, refines the classification obtained by the clustering algorithm. The results of some numerical experiments are also provided.     

Margin maximization in spherical separation

We face the problem of strictly separating two sets of points by means of a sphere, considering the two cases where the center of the sphere is fixed or free, respectively. In particular, for the former we present a fast and simple solution algorithm, whereas for the latter one we use the DC-Algorithm based on a DC decomposition of the error function. Numerical results for both the cases are presented on several classical binary datasets drawn from the literature.     

The Method of Virtual Experts in Mathematical Diagnostics

Mathematical Diagnostics (MD) deals with identification problems arising in different practical areas. Some of these problems can be described by mathematical models where it is required to identify points belonging to two or more sets of points. Most of the existing tools provide some identification rule (a classifier) by means of which a given point is assigned (attributed) to one of the given sets. Each classifier can be viewed as a virtual expert. If there exist several classifiers (experts), the problem of evaluation of experts’ conclusions arises. In the paper for the case of supervised classification the method of virtual experts (the VE-method) is described. Based on this method, a generalized VE method is proposed where each of the classifiers can be chosen from a given family of classifiers. As a result, a new optimization problem with a discontinuous functional is stated. Examples illustrating the proposed approach are provided. The work of the second author was supported by the Russian Foundation for Fundamental Studies (RFFI) under Grant No 03-01-00668.     

A lower bound on the performance of the quadratic discriminant function

The quadratic discriminant function is often used to separate two classes of points in a multidimensional space. When the two classes are normally distributed, this results in the optimum separation. In some cases however, the assumption of normality is a poor one and the classification error is increased. The current paper derives an upper bound for the classification error due to a quadratic decision surface. The bound is strict when the class means and covariances and the quadratic discriminant surface satisfy certain specified symmetry conditions.     

Reference free structure determination through eigenvectors of center of mass operators

Recovering the three-dimensional structure of molecules is important for understanding their functionality. We describe a spectral graph algorithm for reconstructing the three-dimensional structure of molecules from their cryo-electron microscopy images taken at random unknown orientations.We first identify a one-to-one correspondence between radial lines in three-dimensional Fourier space of the molecule and points on the unit sphere. The problem is then reduced to determining the coordinates of points on the sphere given a subset of their pairwise geodesic distances. To recover those coordinates, we exploit the special geometry of the problem, as rendered by the Fourier projection–slice theorem, to construct a weighted graph whose vertices are the radial Fourier lines and whose edges are linked using the common line property. The graph organizes the radial lines on the sphere in a global manner that reveals the acquisition direction of each image. This organization is derived from a global computation of a few eigenvectors of the graph's sparse adjacency matrix. Once the directions are obtained, the molecule can be reconstructed using classical tomography methods.The presented algorithm is direct (as opposed to iterative refinement schemes), does not require any prior model for the reconstructed object, and is shown to have favorable computational and numerical properties. Moreover, the algorithm does not impose any assumption on the distribution of the projection orientations. Physically, this means that the algorithm is applicable to molecules that have unknown spatial preference.     

A fixed-center spherical separation algorithm with kernel transformations for classification problems

We consider a special case of the optimal separation, via a sphere, of two discrete point sets in a finite dimensional Euclidean space. In fact we assume that the center of the sphere is fixed. In this case the problem reduces to the minimization of a convex and nonsmooth function of just one variable, which can be solved by means of an “ad hoc” method in O(p log p) time, where p is the dataset size. The approach is suitable for use in connection with kernel transformations of the type adopted in the support vector machine (SVM) approach. Despite of its simplicity the method has provided interesting results on several standard test problems drawn from the binary classification literature. This research has been partially supported by the Italian “Ministero dell’Istruzione, dell’Università e della Ricerca Scientifica”, under PRIN project Numerical Methods for Global Optimization and for some classes of Nonsmooth Optimization Problems (2005017083.002).     

Combining landmark and intensity driven registrations

One of the challenging tasks in today image processing is image registration. Image registration is inevitable whenever images taken for example at different times or from different perspectives need to be compared or to be integrated. Typically, the location of corresponding points in the different views of one object or even of different objects is distorted. For example, motion or different properties of the underlying optical systems (MR, CT) are responsible for the distortion. Thus, a basic problem is to find a meaningful spatial transformation of a given image, such that the transformed image becomes similar to a given second one. Typically, the transformation is computed by minimizing a suitable similarity measure. For many applications it is also desirable to guide the registration by additional information, like the locations of outstanding points. In this note, be present a general variational based approach for image registration which allows the choice of a user supplied similarity measure and a user supplied regularizer as well as the integration of external knowledge, like, for example, the location of outstanding points.     

Matching interdiction

We introduce two interdiction problems involving matchings, one dealing with edge removals and the other dealing with vertex removals. Given is an undirected graph G with positive weights on its edges. In the edge interdiction problem, every edge of G has a positive cost and the task is to remove a subset of the edges constrained to a given budget, such that the weight of a maximum matching in the resulting graph is minimized. The vertex interdiction problem is analogous to the edge interdiction problem, with the difference that vertices instead of edges are removed. Hardness results are presented for both problems under various restrictions on the weights, interdiction costs and graph classes. Furthermore, we study the approximability of the edge and vertex interdiction problem on different graph classes. Several approximation-hardness results are presented as well as two constant-factor approximations, one of them based on iterative rounding. A pseudo-polynomial algorithm for solving the edge interdiction problem on graphs with bounded treewidth is proposed which can easily be adapted to the vertex interdiction problem. The algorithm presents a general framework to apply dynamic programming for solving a large class of problems in graphs with bounded treewidth. Additionally, we present a method to transform pseudo-polynomial algorithms for the edge interdiction problem into fully polynomial approximation schemes, using a scaling and rounding technique.     

Checking oriented matroid isomorphism by means of canonical labeling

In this paper a method for establishing the structural equivalence of sets of planar geometric features composed by points and lines is presented. It is based on oriented matroid theory, a setting in which the combinatorial structural properties of these geometric features, such as incidence, order, partitioning, separation, and convexity, can be represented and analyzed in a coordinate-free manner. Projective transformations in computer vision keep in general the convexity property which implies an invariant oriented matroid representation of the planar geometric features under this class of transformations. As long as points and lines are in general position, the oriented matroid representation is also insensitive to small changes in the geometric image features. However the oriented matroid representation depends on the labeling of its elements. Checking the structural equivalence of the above mentioned geometric features represented by means of oriented matroids implies establishing whether two oriented matroid representations are equivalent up to relabeling of their elements. This is the oriented matroid isomorphism problem which is solved in this paper by means of a canonical labeling of the elements.