Motion Cooperation: Smooth Piece-Wise Rigid Scene Flow from RGB-D Images

We propose a novel joint registration and segmentation approach to estimate scene flow from RGB-D images. Instead of assuming the scene to be composed of a number of independent rigidly-moving parts, we use non-binary labels to capture non-rigid deformations at transitions between the rigid parts of the scene. Thus, the velocity of any point can be computed as a linear combination (interpolation) of the estimated rigid motions, which provides better results than traditional sharp piecewise segmentations. Within a variational framework, the smooth segments of the scene and their corresponding rigid velocities are alternately refined until convergence. A K-means-based segmentation is employed as an initialization, and the number of regions is subsequently adapted during the optimization process to capture any arbitrary number of independently moving objects. We evaluate our approach with both synthetic and real RGB-D images that contain varied and large motions. The experiments show that our method estimates the scene flow more accurately than the most recent works in the field, and at the same time provides a meaningful segmentation of the scene based on 3D motion.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Spanish Government under the grant programs FPI-MICINN 2012 and DPI2014- 55826-R (co-founded by the European Regional Development Fund), as well as by the EU ERC grant Convex Vision (grant agreement no. 240168)

Fundamental Limits of Wideband Localization - Part II: Cooperative Networks

The availability of positional information is of great importance in many commercial, governmental, and military applications. Localization is commonly accomplished through the use of radio communication between mobile devices (agents) and fixed infrastructure (anchors). However, precise determination of agent positions is a challenging task, especially in harsh environments due to radio blockage or limited anchor deployment. In these situations, cooperation among agents can significantly improve localization accuracy and reduce localization outage probabilities. A general framework of analyzing the fundamental limits of wideband localization has been developed in Part I of the paper. Here, we build on this framework and establish the fundamental limits of wideband cooperative location-aware networks. Our analysis is based on the waveforms received at the nodes, in conjunction with Fisher information inequality. We provide a geometrical interpretation of equivalent Fisher information for cooperative networks. This approach allows us to succinctly derive fundamental performance limits and their scaling behaviors, and to treat anchors and agents in a unified way from the perspective of localization accuracy. Our results yield important insights into how and when cooperation is beneficial.Comment: To appear in IEEE Transactions on Information Theor

Finsler and Lagrange Geometries in Einstein and String Gravity

We review the current status of Finsler-Lagrange geometry and generalizations. The goal is to aid non-experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to understand the crucial importance of such geometric methods for applications in modern physics. We also would like to orient mathematicians working in generalized Finsler and Kahler geometry and geometric mechanics how they could perform their results in order to be accepted by the community of ''orthodox'' physicists. Although the bulk of former models of Finsler-Lagrange spaces where elaborated on tangent bundles, the surprising result advocated in our works is that such locally anisotropic structures can be modelled equivalently on Riemann-Cartan spaces, even as exact solutions in Einstein and/or string gravity, if nonholonomic distributions and moving frames of references are introduced into consideration. We also propose a canonical scheme when geometrical objects on a (pseudo) Riemannian space are nonholonomically deformed into generalized Lagrange, or Finsler, configurations on the same manifold. Such canonical transforms are defined by the coefficients of a prime metric and generate target spaces as Lagrange structures, their models of almost Hermitian/ Kahler, or nonholonomic Riemann spaces. Finally, we consider some classes of exact solutions in string and Einstein gravity modelling Lagrange-Finsler structures with solitonic pp-waves and speculate on their physical meaning.Comment: latex 2e, 11pt, 44 pages; accepted to IJGMMP (2008) as a short variant of arXiv:0707.1524v3, on 86 page

Gait Recognition from Motion Capture Data

Gait recognition from motion capture data, as a pattern classification discipline, can be improved by the use of machine learning. This paper contributes to the state-of-the-art with a statistical approach for extracting robust gait features directly from raw data by a modification of Linear Discriminant Analysis with Maximum Margin Criterion. Experiments on the CMU MoCap database show that the suggested method outperforms thirteen relevant methods based on geometric features and a method to learn the features by a combination of Principal Component Analysis and Linear Discriminant Analysis. The methods are evaluated in terms of the distribution of biometric templates in respective feature spaces expressed in a number of class separability coefficients and classification metrics. Results also indicate a high portability of learned features, that means, we can learn what aspects of walk people generally differ in and extract those as general gait features. Recognizing people without needing group-specific features is convenient as particular people might not always provide annotated learning data. As a contribution to reproducible research, our evaluation framework and database have been made publicly available. This research makes motion capture technology directly applicable for human recognition.Comment: Preprint. Full paper accepted at the ACM Transactions on Multimedia Computing, Communications, and Applications (TOMM), special issue on Representation, Analysis and Recognition of 3D Humans. 18 pages. arXiv admin note: substantial text overlap with arXiv:1701.00995, arXiv:1609.04392, arXiv:1609.0693

Mean Curvature Flow on Ricci Solitons

We study monotonic quantities in the context of combined geometric flows. In particular, focusing on Ricci solitons as the ambient space, we consider solutions of the heat type equation integrated over embedded submanifolds evolving by mean curvature flow and we study their monotonicity properties. This is part of an ongoing project with Magni and Mantegazzawhich will treat the case of non-solitonic backgrounds \cite{a_14}.Comment: 19 page