THREE-DIMENSIONAL RECONSTRUCTION OF THE HUMAN MOTION BASED ON IMAGES FROM A SINGLE CAMERA

It is widely accepted that the photograms of two or more cameras are required for the spatial reconstruction of the human motion. Each projection of the spatial coordinates of a given anatomical point of the human body is described by two equations. Consequently, two or more cameras are necessary for at least three independent linear equations required to obtain the original three coordinates of the point from its projected positions. If n cameras are used in the reconstruction process 2n equations are available for that purpose. In this case more equations than unknowns are available, and the solution for the reconstruction must minimize the error in those equations. Regardless of the number of cameras available, no information of the biomechanical model is generally used during the reconstruction process. In this work, a biomechanical model of 16 segments is used to support the motion reconstruction. The kinematic equations that characterize the dependency between the Cartesian coordinates of the points describing each component of the biomechanical model are used together with the two equations describing their projection in each frame. The single triangle describing the lower torso is defined by three points corresponding to nine spatial coordinates. For a given frame of a single camera six independent linear equations are defined. The remaining three equations needed to the spatial reconstruction of the triangle are the kinematic constraint equations ensuring that the distance between each two points remains constant throughout the motion. The system of nonlinear equations defined in this form has multiple solutions. For each subsequent camera frame the same process is followed to obtain the multiple solutions of the triangle reconstruction. The motion of the triangle representing the lower torso is selected as the combination of the solutions of the independent frames that minimizes a given function, defined as a measure of the smoothness of the triangle motion, variation of its angular orientation or increment of its distance between frames. Only the two solutions for the motion corresponding to the lower values of the functional, evaluated during four frames, are kept. Assuming that the motion for both solutions is feasible for the remaining frames, the method proceeds with the reconstruction of the segments adjacent to the lower torso, followed by the segments adjacent to the first set and so forth. A branch of solutions is eliminated if it cannot proceed from one frame to the next, either because no solution is possible or because the reconstructed motion develops behind the camera. Finally the reconstruction of the full motion is obtained in an automatic form. The methodology is applied to a case of complex human body motion demonstrating that it is feasible to reconstruct the three dimensional human motion using the photograms of a single stationary camera and a consistent biomechanical model

Usando sensores magnéticos em um trilho de ar

Neste trabalho propomos um sistema de medida e coleta de dados para trilhos de ar baseado em sensores magnéticos ligados à porta de jogos de um PC. A leitura dos dados na porta é feita por um pequeno programa escrito em Logo. O sistema foi testado com excelentes resultados em um estudo dos movimentos uniforme e uniformemente variado sobre o trilho

Duality Theorems in Ergodic Transport

We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class of problems is the following: suppose $\sigma$ is the shift acting on Bernoulli space $X=\{0,1\}^\mathbb{N}$, and, consider a fixed continuous cost function $c:X \times X\to \mathbb{R}$. Denote by $\Pi$ the set of all Borel probabilities $\pi$ on $X\times X$, such that, both its $x$ and $y$ marginal are $\sigma$-invariant probabilities. We are interested in the optimal plan $\pi$ which minimizes $\int c d \pi$ among the probabilities on $\Pi$. We show, among other things, the analogous Kantorovich Duality Theorem. We also analyze uniqueness of the optimal plan under generic assumptions on $c$. We investigate the existence of a dual pair of Lipschitz functions which realizes the present dual Kantorovich problem under the assumption that the cost is Lipschitz continuous. For continuous costs $c$ the corresponding results in the Classical Transport Theory and in Ergodic Transport Theory can be, eventually, different. We also consider the problem of approximating the optimal plan $\pi$ by convex combinations of plans such that the support projects in periodic orbits

Chaperone-mediated native folding of a β-scorpion toxin in the periplasm of E.coli

Background: Animal neurotoxin peptides are valuable probes for investigating ion channel structure/function relationships and represent lead compounds for novel therapeutics and insecticides. However, misfolding and aggregation are common outcomes when toxins containing multiple disulfides are expressed in bacteria. Methods: The ß-scorpion peptide toxin Bj-xtrIT from Hottentotta judaica and four chaperone enzymes (DsbA, DsbC, SurA and FkpA) were co-secreted into the oxidizing environment of the E.coli periplasm. Expressed Bj-xtrIT was purified and analyzed by HPLC and FPLC chromatography. Its thermostability was assessed using synchrotron radiation circular dichroism spectroscopy and its crystal structure was determined. Results: Western blot analysis showed that robust expression was only achieved when cells co-expressed the chaperones. The purified samples were homogenous and monodisperse and the protein was thermostable. The crystal structure of the recombinant toxin confirmed that it adopts the native disulfide connectivity and fold. Conclusions: The chaperones enabled correct folding of the four-disulfide-bridged Bj-xtrIT toxin. There was no apparent sub-population of misfolded Bj-xtrIT, which attests to the effectiveness of this expression method. General Significance: We report the first example of a disulfide-linked scorpion toxin natively folded during bacterial expression. This method eliminates downstream processing steps such as oxidative refolding or cleavage of a fusion-carrier and therefore enables efficient production of insecticidal Bj-xtrIT. Periplasmic chaperone activity may produce native folding of other extensively disulfide-reticulated proteins including animal neurotoxins. This work is therefore relevant to venomics and studies of a wide range of channels and receptors

Entropy production in Gaussian thermostats

We show that an arbitrary Anosov Gaussian thermostat on a surface is dissipative unless the external field has a global potential