Wavelet-based numerical methods for the solution of the Nonuniform Multiconductor Transmission Lines

This work presents a new Time-Domain Space Expansion (TDSE) method for the numerical solution of the Nonuniform Multiconductor Transmission Lines (NMTL). This method is based on a weak formulation of the NMTL equations, which leads to a class of numerical schemes of different approximation order according to the particular choice of some trial and test functions. The core of this work is devoted to the definition of trial and test functions that can be used to produce accurate representations of the solution by keeping the computational effort as small as possible. It is shown that bases of wavelets are a good choice

Exploiting Spatio-Temporal Coherence for Video Object Detection in Robotics

This paper proposes a method to enhance video object detection for indoor environments in robotics. Concretely, it exploits knowledge about the camera motion between frames to propagate previously detected objects to successive frames. The proposal is rooted in the concepts of planar homography to propose regions of interest where to find objects, and recursive Bayesian filtering to integrate observations over time. The proposal is evaluated on six virtual, indoor environments, accounting for the detection of nine object classes over a total of ∼ 7k frames. Results show that our proposal improves the recall and the F1-score by a factor of 1.41 and 1.27, respectively, as well as it achieves a significant reduction of the object categorization entropy (58.8%) when compared to a two-stage video object detection method used as baseline, at the cost of small time overheads (120 ms) and precision loss (0.92).</p

Multiresolutions Numerically from Subdivisions

In previous work we introduced a construction to produce multiresolutions from given subdivisions. A portion of that construction required solving bilinear equations using a symbolic algebra system. Here we replace the bilinear equations with a pair of linear equation systems, resulting in a completely numerical construction. Diagrammatic tools provide assistance in carrying this out. The construction is shown for an example of univariate subdivision. The results for a bivariate subdivision are given to illustrate the construction's ability to handle multivariate meshes, as well as special points, without requiring any modi cation of approach. The construction usually results in analysis and reconstruction lters that are nite, since it seeks each lter locally for the neighborhood of the mesh to which it applies. The use of a set of lters constructed in this way is compared with lters based on spline wavelets for image compression to show that the construction can yield satisfactory results.N