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In this paper, a new formulation based on bidirectional composition on Lie groups (BCL) for parametric gradient-based image alignment is presented. Contrary to the conventional approaches, the BCL method takes advantage of the gradients of both template and current image without combining them a priori. Based on this bidirectional formulation, two methods are proposed and their relationship with state-of-the-art gradient based approaches is fully discussed. The first one, i.e., the BCL method, relies on the compositional framework to provide the minimization of the compensated error with respect to an augmented parameter vector. The second one, the projected BCL (PBCL), corresponds to a close approximation of the BCL approach. A comparative study is carried out dealing with computational complexity, convergence rate and frequence of convergence. Numerical experiments using a conventional benchmark show the performance improvement especially for asymmetric levels of noise, which is also discussed from a theoretical point of view. [ABSTRACT FROM AUTHOR]

In this paper, we present a new parametric modeling of three-dimensional homogeneous volumes of textured images (3-D texture) based on 3-D Wold decomposition for discrete processes. This decomposition additively separates any 3-D discrete homogeneous process into three mutually orthogonal components: a purely indeterministic, a "remote past"—type deterministic and an evanescent component. The evanescent component can be further decomposed into two orthogonal components called type 1 evanescent and type 2 evanescent. Assuming that the 3-D image volume is a finite realization of a discrete homogeneous stochastic process, the 3-D texture field can be uniquely represented as a sum of four mutually orthogonal components with different spectral properties. The aim of this paper is to present new parametric models able to describe both the spectral support and spatial characteristics of each component. A spectral decomposition algorithm to separate a 3-D texture into structured and unstructured parts is also proposed. [ABSTRACT FROM AUTHOR]

In the framework of the electrocardiography (ECG) signals, this paper describes an original approach to identify heartbeat morphologies and to detect R-wave events. The proposed approach is based on a "geometrical matching" rule evaluated using a decision function in a local moving-window procedure. The decision function is a normalized measurement of a similarity criterion comparing the windowed input signal with the reference beat-pattern into a nonlinear-curve space. A polynomial expansion model describes the reference pattern. For the curve space, an algebraic-fitting distance is built according to the canonical equation of the unit circle. The geometrical matching approach operates in two stages, i.e., training and detection ones. In the first stage, a learning-method based on genetic algorithms allows us estimating the decision function from training beat-pattern. In the second stage, a level-detection algorithm evaluates the decision function to establish the threshold of similarity between the reference pattern and the input signal. Finally, the findings for the MIT-BIH Arrhythmia Database present about 98% of sensitivity and 99% of positive predictivity for the R-waves detection, using low-order polynomial models. [ABSTRACT FROM AUTHOR]

Time-domain analysis is a powerful tool for testing A/D converters (ADCs), particularly by incoherent sampling. This sampling is encountered for instance in real application and systems where the clock is generated by an on-board crystal oscillator. In the case of the sine-wave model for ADC output samples, fitting a sine-wave function to the data record is nonlinear with respect to the frequency. To overcome the convergence problem, the authors propose some alternative methods based on frequency estimation by means of fast Fourier transform and eigenanalysis of the autocorrelation matrix. This leads to a simple linear problem. The effectiveness of these methods is proven on both simulation and experimental results. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of three-dimensional autoregressive (3-D AR) model order estimation. We show that the information for the 3-D AR model order is implicitly contained in an appropriate matrix rank built from the autocorrelation function (ACF) of the underlying 3-D Gaussian process. Exploiting this property, we develop an algorithm to estimate the order (p1, p2, p3) corresponding to the quarter-space (QS) region of support. The proposed method is based upon a rank test procedure (RTP) using singular value decomposition (SVD) and solving nonlinear system equations. Numerical simulations are presented to illustrate the performances of the proposed algorithm. [ABSTRACT FROM AUTHOR]