Two-dimensional Fourier transform of scaled Dirac delta curves

We obtain a Fourier transform scaling relation to find analytically, numerically, or experimentally the spectrum of an arbitrary scaled two-dimensional Dirac delta curve from the spectrum of the nonscaled curve. An amplitude factor is derived and given explicitly in terms of the scaling factors and the angle of the forward tangent at each point of the curve about the positive x axis. With the scaling relation we determine the spectrum of an elliptic curve by a circular geometry instead of an elliptical one. The generalization to N-dimensional Dirac delta curves is also included.     

CPM: a deformable model for shape recovery and segmentation based on charged particles

A novel, physically motivated deformable model for shape recovery and segmentation is presented. The model, referred to as the charged-particle model (CPM), is inspired by classical electrodynamics and is based on a simulation of charged particles moving in an electrostatic field. The charges are attracted towards the contours of the objects of interest by an electrostatic field, whose sources are computed based on the gradient-magnitude image. The electric field plays the same role as the potential forces in the snake model, while internal interactions are modeled by repulsive Coulomb forces. We demonstrate the flexibility and potential of the model in a wide variety of settings: shape recovery using manual initialization, automatic segmentation, and skeleton computation. We perform a comparative analysis of the proposed model with the active contour model and show that specific problems of the latter are surmounted by our model. The model is easily extendable to 3D and copes well with noisy images.     

Formal verification of a generic framework to synthesize SAT-provers

We present in this paper an application of the ACL2 system to generate and reason about propositional satisfiability provers. For that purpose, we develop a framework in which we define a generic S AT-prover based on transformation rules, and we formalize this generic framework in the ACL2 logic, carrying out a formal proof of its termination, soundness, and completeness. This generic framework can be instantiated to obtain a number of verified and executable SAT-provers in ACL2, and this instantiation can be done in an automated way. Three instantiations of the generic framework are considered: semantic tableaux, sequent calculus, and Davis-Putnam-Logeman-Loveland methods.     

Minimax mutual information approach for independent component analysis

Minimum output mutual information is regarded as a natural criterion for independent component analysis (ICA) and is used as the performance measure in many ICA algorithms. Two common approaches in information-theoretic ICA algorithms are minimum mutual information and maximum output entropy approaches. In the former approach, we substitute some form of probability density function (pdf) estimate into the mutual information expression, and in the latter we incorporate the source pdf assumption in the algorithm through the use of nonlinearities matched to the corresponding cumulative density functions (cdf). Alternative solutions to ICA use higher-order cumulant-based optimization criteria, which are related to either one of these approaches through truncated series approximations for densities. In this article, we propose a new ICA algorithm motivated by the maximum entropy principle (for estimating signal distributions). The optimality criterion is the minimum output mutual information, where the estimated pdfs are from the exponential family and are approximate solutions to a constrained entropy maximization problem. This approach yields an upper bound for the actual mutual information of the output signals - hence, the name minimax mutual information ICA algorithm. In addition, we demonstrate that for a specific selection of the constraint functions in the maximum entropy density estimation procedure, the algorithm relates strongly to ICA methods using higher-order cumulants.     

Estimating the entropy rate of spike trains via Lempel-Ziv complexity

Normalized Lempel-Ziv complexity, which measures the generation rate of new patterns along a digital sequence, is closely related to such important source properties as entropy and compression ratio, but, in contrast to these, it is a property of individual sequences. In this article, we propose to exploit this concept to estimate (or, at least, to bound from below) the entropy of neural discharges (spike trains). The main advantages of this method include fast convergence of the estimator (as supported by numerical simulation) and the fact that there is no need to know the probability law of the process generating the signal. Furthermore, we present numerical and experimental comparisons of the new method against the standard method based on word frequencies, providing evidence that this new approach is an alternative entropy estimator for binned spike trains.     

Line Extraction in 2D Range Images for Mobile Robotics

This paper presents a geometrical feature detection framework for use with conventional 2D laser rangefinders. This framework is composed of three main procedures: data pre-processing, breakpoint detection and line extraction. In data pre-processing, low-level data organization and processing are discussed, with emphasis to sensor bias compensation. Breakpoint detection allows to determine sequences of measurements which are not interrupted by scanning surface changing. Two breakpoint detectors are investigated, one based on adaptive thresholding, and the other on Kalman filtering. Implementation and tuning of both detectors are also investigated. Line extraction is performed to each continuous scan sequence in a range image by applying line kernels. We have investigated two classic kernels, commonly used in mobile robots, and our Split-and-Merge Fuzzy (SMF) line extractor. SMF employs fuzzy clustering in a split-and-merge framework without the need to guess the number of clusters. Qualitative and quantitative comparisons using simulated and real images illustrate the main characteristics of the framework when using different methods for breakpoint and line detection. These comparisons illustrate the characteristics of each estimator, which can be exploited according to the platform computing power and the application accuracy requirements.     

Treatment of saline wastewater contaminated with hydrocarbons by the photo-Fenton process

The application of the photo-Fenton process to the treatment of saline wastewater contaminated with hydrocarbons is investigated. Aqueous saline solutions containing raw gasoline were used as a model oil-field-produced water. The dependence on concentrations of the following reagents has been appropriately evaluated: hydrogen peroxide (100-200 mM), iron ions (0.5-1 mM), and sodium chloride (200-2000 ppm). The reactions were monitored by measurement of the absorption spectra and total organic carbon (TOC). Experimental results demonstrate that the photo-Fenton process is feasible for the treatment of wastewaters containing hydrocarbons, even in the presence of high concentrations of salt. The effect of the salt in this process is described through a series of reactions. A simple feedforward neural network model was found to correlate well the observed data for the degradation process.     

Performance index for quality response of dynamical systems

The use of performance indices to measure the quality response of dynamical systems is studied in this paper. A definition of a general performance index is proposed which is easy to compute, easy to interpret, and flexible enough to account for different cases commonly presented in practice. The index is tested over several dynamical responses obtained from different systems obtaining good results, in the sense that it is able to rank the behaviors from best to worse, compared with a pattern response.