Spatial transformations are mappings between locations of a $d$-dimensional space and are commonly used in computer vision and image analysis. Many of the spatial transformation sets have a group structure and can be represented by matrix groups. In the computer vision and image analysis fields there is a recent and growing interest in performing analyses on spatial transformations data. Differential and Riemannian geometry have been used as a framework to endow the set of spatial transformations with a metric space structure, allowing the extension of the standard analysis techniques defined on vector spaces. This paper presents a review of the concepts and an overview of approaches to computing Riemannian geodesics on spatial transformation groups. The paper is aimed at providing a bridge for researchers from computer vision and image analysis fields to fill in the gap between differential geometry and computer vision and imaging disciplines. Some application examples are shown to illustrate the use of invariant Riemannian geodesics, such as interpolation of spatial transformations and filtering of matrix-valued images.

Computational Anatomy aims for the study of the statistical variability in anatomical structures. Variability is encoded by the transformations existing among populations of anatomical images. These transformations are usually computed from diffeomorphic registration based on the large deformation paradigm. In this framework diffeomorphisms are usually computed as end points of paths on the Riemannian manifold of diffeomorphisms parameterized by non-stationary vector fields. Recently, an alternative parameterization based on stationary vector fields has been developed. In this article we propose to use this stationary parameterization for diffeomorphic registration. We formulate the variational problem related to this registration scenario and derive the associated Euler-Lagrange equations. We evaluate the performance of the non-stationary vs the stationary parameterizations in real and synthetic 3D-MRI datasets. Compared to the non-stationary parameterization, our proposal provides similar accuracy in terms of image matching and deformation smoothness while drastically reducing memory and time requirements.

A new real-time compression method for electrocardiogram (ECG) signals has been developed based on the wavelet transform approach. The method is specifically adaptable for packetized telecardiology applications. The signal is segmented into beats and a beat template is subtracted from them, producing a residual signal. Beat templates and residual signals are coded with a wavelet expansion. Compression is achieved by selecting a subset of wavelet coefficients. The number of selected coefficients depends on a threshold which has different definitions depending on the operational mode of the coder. Compression performance has been tested using a subset of ECG records from MIT-BIH Arrhythmia database. This method has been designed for real-time packetized telecardiology scenarios both in wired and wireless environments.

In this paper, we present the development of a remote server that provides a user-friendly access to advanced electrocardiographic (ECG) signal processing techniques. The prototype supplies telemedicine facilities to doctors for clinical indexes remote computation to support diagnosis through the Internet. The user-friendly interface is based on the selection of the desired ECG signal processing tools on a Web browser window. The centralized structure of the system permits unique and user-independent update and management of the software and, therefore, is especially suitable for remote or rural regions to have access to the new ECG information techniques.

In this work we show that orthogonal expansions of recurrent signals like electrocardiograms with a reduced number of coefficients can be considered as a periodic time-variant filter. Instantaneous impulse and frequency responses are analyzed for two cases: estimation of the coefficients with inner product and adaptive estimation with LMS algorithm.