A Novel Self-Intersection Penalty Term for Statistical Body Shape Models and Its Applications in 3D Pose Estimation

Statistical body shape models are widely used in 3D pose estimation due to their low-dimensional parameters representation. However, it is difficult to avoid self-intersection between body parts accurately. Motivated by this fact, we proposed a novel self-intersection penalty term for statistical body shape models applied in 3D pose estimation. To avoid the trouble of computing self-intersection for complex surfaces like the body meshes, the gradient of our proposed self-intersection penalty term is manually derived from the perspective of geometry. First, the self-intersection penalty term is defined as the volume of the self-intersection region. To calculate the partial derivatives with respect to the coordinates of the vertices, we employed detection rays to divide vertices of statistical body shape models into different groups depending on whether the vertex is in the region of self-intersection. Second, the partial derivatives could be easily derived by the normal vectors of neighboring triangles of the vertices. Finally, this penalty term could be applied in gradient-based optimization algorithms to remove the self-intersection of triangular meshes without using any approximation. Qualitative and quantitative evaluations were conducted to demonstrate the effectiveness and generality of our proposed method compared with previous approaches. The experimental results show that our proposed penalty term can avoid self-intersection to exclude unreasonable predictions and improves the accuracy of 3D pose estimation indirectly. Further more, the proposed method could be employed universally in triangular mesh based 3D reconstruction

MATEX: A Distributed Framework for Transient Simulation of Power Distribution Networks

We proposed MATEX, a distributed framework for transient simulation of power distribution networks (PDNs). MATEX utilizes matrix exponential kernel with Krylov subspace approximations to solve differential equations of linear circuit. First, the whole simulation task is divided into subtasks based on decompositions of current sources, in order to reduce the computational overheads. Then these subtasks are distributed to different computing nodes and processed in parallel. Within each node, after the matrix factorization at the beginning of simulation, the adaptive time stepping solver is performed without extra matrix re-factorizations. MATEX overcomes the stiff-ness hinder of previous matrix exponential-based circuit simulator by rational Krylov subspace method, which leads to larger step sizes with smaller dimensions of Krylov subspace bases and highly accelerates the whole computation. MATEX outperforms both traditional fixed and adaptive time stepping methods, e.g., achieving around 13X over the trapezoidal framework with fixed time step for the IBM power grid benchmarks.Comment: ACM/IEEE DAC 2014. arXiv admin note: substantial text overlap with arXiv:1505.0669

Complexity Analysis of Balloon Drawing for Rooted Trees

In a balloon drawing of a tree, all the children under the same parent are placed on the circumference of the circle centered at their parent, and the radius of the circle centered at each node along any path from the root reflects the number of descendants associated with the node. Among various styles of tree drawings reported in the literature, the balloon drawing enjoys a desirable feature of displaying tree structures in a rather balanced fashion. For each internal node in a balloon drawing, the ray from the node to each of its children divides the wedge accommodating the subtree rooted at the child into two sub-wedges. Depending on whether the two sub-wedge angles are required to be identical or not, a balloon drawing can further be divided into two types: even sub-wedge and uneven sub-wedge types. In the most general case, for any internal node in the tree there are two dimensions of freedom that affect the quality of a balloon drawing: (1) altering the order in which the children of the node appear in the drawing, and (2) for the subtree rooted at each child of the node, flipping the two sub-wedges of the subtree. In this paper, we give a comprehensive complexity analysis for optimizing balloon drawings of rooted trees with respect to angular resolution, aspect ratio and standard deviation of angles under various drawing cases depending on whether the tree is of even or uneven sub-wedge type and whether (1) and (2) above are allowed. It turns out that some are NP-complete while others can be solved in polynomial time. We also derive approximation algorithms for those that are intractable in general

Kants transzendentale Erkenntnistheorie und der Ichbegriff

Kants transzendentale Erkenntnistheorie in der Kritik der reinen Vernunft ist bekannt für ihre kopernikanische Wende, weil sie nicht mehr durch das erkannte Objekt selbst, sondern umgekehrt durch das erkennende Subjekt und seine transzendentalen Vermögen (die transzendentale Subjektivität) die Objektivität der menschlichen Erkenntnis erklärt. Dabei spielt der Ichbegriff eine unentbehrliche, aber zugleich strittige Rolle. Das Kernproblem besteht darin, dass die Vorstellung des denkenden Ichs in der transzendentalen Deduktion einerseits die höchste Bedingung der Erkenntnis ist und objektive Gültigkeit haben soll, andererseits ihm seine Realität und Objektivität gemäß der Lehre der transzendentalen Paralogismen gänzlich entzogen werden müssen. Diese Spannung entsteht aus einer noch fundamentaleren Ursache, dass Kant in seiner Erkenntnistheorie keine explizite und komplette Angabe des Status des Ichs aufstellt. Um diese Problematik zu behandeln, analysiere ich in dieser Dissertation die positiven Funktionen und die negativen Wirkungen des Ichbegriffs zunächst in Bezug auf den Ansatz (Einleitung) und den allgemeinen Rahmen (Kap. 1) der transzendentalen Erkenntnistheorie Kants, dann auf die relevanten konkreten Texte, inklusive der transzendentalen Deduktion (Kap. 2), und der transzendentalen Paralogismen (Kap. 3). Nach der Aufklärung der Notwendigkeit und der Schwierigkeit des Ichbegriffs in Kants System rekonstruiere und bewerte ich die möglichen Ichlehren Kants jeweils nach drei Richtungen (Intellektualismus, Sensualismus und Logismus) (Kap. 4). Daraus ziehe ich die Schlussfolgerung, dass nur der abgeschwächte Logismus eine selbstkonsistente und zugleich mit Kants Erkenntnistheorie vereinbare Ichlehre darstellen kann (Schluss)

The Ambiguity of Kant's Concept of the Highest Good: Finding the Correct Interpretation

The aim of this paper is to resolve the tension between Kant's doctrine of the highest good and his entire philosophical system. The concept of the highest good is the first major ambiguity of the doctrine. There are three pairs of ambiguities: immanent‐transcendent; justice‐perfection; and individual‐community. They are able to form eight combinations. Corresponding to the various combinations and conceptions of the highest good, interpreters also conceive different reasons for the necessity of the doctrine as well as various conditions of its applicability. For example, some emphasize its religious dimension, whereas others understand it in the political sense. In this paper, I adopt a different approach in understanding the highest good's systematic meaning as the moral confirmation, and suggest that only a transcendent, perfect and communal concept of the highest good can provide the most consistent doctrine. Additionally, it explains the importance of the different branches (such as philosophies of religion and of politics) of Kant's system

Development of a coupling algorithm for fluid-structure interaction analysis of submerged aquaculture nets

A coupling algorithm between two open-source numerical toolboxes, i.e., OpenFOAM and Code_Aster, is implemented for fluid-structure interaction analysis of submerged nets. This algorithm is developed to handle the wake effects of thin, flexible and highly permeable structures with complex geometries. Compared to previous approaches, the present algorithm simplifies the procedures of the model preparation by removing additional data-fitting processes for porous coefficients, and improves the accuracy of structural responses by employing a fluid solver to calculate the flow field and a superior Screen model to calculate the hydrodynamic forces. The coupling algorithm is comprehensively described and validated with published experiments for both fixed and flexible nets. Different solidities, inflow angles, incoming velocities and dimensions of nets are also considered. The comparisons of flow velocity in the wake, deformation of flexible nets and drag force on the full-scale fish cage show that the numerical results obtained from the present coupling algorithm are in good agreement with published experimental data.publishedVersio

WATER ENTRY HYDROELASTICITY ANALYSIS OF LATTICE SANDWICH PANEL WITH IMPERFECTION: SIMULATION AND ENGINEERING MODEL

In the present work, the three dimensional (3D) hydroelasticity characteristics of imperfect lattice sandwich panel (ILSP) subjected to water entry via analytical prediction and numerical simulations are proposed. Firstly, numerical investigations are performed on water entry characteristics based on Arbitrary Eulerian-Lagrange (ALE) coupling method for modeling fluid-structure interaction (FSI) at an impact velocity of 5.0m/s. The results show the impact pressure on total FSI surface of ILSP is generally lower than that of the perfect lattice sandwich panel. Then a novel semi-analytical method to calculate the elastic constants of ILSP is introduced. Based on this approach, an engineering computational model is developed to predict the deformation of ILSP, in which the total deformation is separated into two parts; local field deformation and global field deformation. Good agreement between the numerical and analytical results is achieved. And the effects of geometric parameters such as the thickness of face sheet, height of ILSP and relative density of core are discussed