Oscar E. Ruiz

Interactive visualization of volumetric data with WebGL in real-time

This article presents and discusses the implementation of a direct volume rendering system for the Web, which articulates a large portion of the rendering task in the client machine. By placing the rendering emphasis in the local client, our system takes advantage of its power, while at the same time eliminates processing from unreliable bottlenecks (e.g. network). The system developed articulates in efficient manner the capabilities of the recently released WebGL standard, which makes available the accelerated graphic pipeline (formerly unusable). The dependency on specially customized hardware is eliminated, and yet efficient rendering rates are achieved. The Web increasingly competes against desktop applications in many scenarios, but the graphical demands of some of the applications (e.g. interactive scientific visualization by volume rendering), have impeded their successful settlement in Web scenarios. Performance, scalability, accuracy, security are some of the many challenges that must be solved before visual Web applications popularize. In this publication we discuss both performance and scalability of the volume rendering by WebGL ray-casting in two different but challenging application domains: medical imaging and radar meteorology.

Realtime Dense Stereo Matching with Dynamic Programming in CUDA

Real-time depth extraction from stereo images is an important process in computer vision. This paper proposes a new implementation of the dynamic programming algorithm to calculate dense depth maps using the CUDA architecture achieving real-time performance with consumer graphics cards. We compare the running time of the algorithm against CPU implementation and demonstrate the scalability property of the algorithm by testing it on different graphics cards.

Algebraic geometry and group theory in geometric constraint satisfaction for computer-aided design and assembly planning

Mechanical design and assembly planning inherently involve geometric constraint satisfaction or scene feasibility (GCS/SF) problems. Such problems imply the satisfaction of proposed relations placed between undefined geometric entities in a given scenario. If the degrees of freedom remaining in the scene are compatible with the proposed relations or constraints, a set of entities is produced that populate the scenario satisfying the relations. Otherwise, a diagnostic of inconsistency of the problem is emitted. This problem appears in various forms in assembly planning (assembly model generation), process planning, constraint driven design, computer vision, etc. Previous attempts at solution using separate numerical, symbolic or procedural approaches suffer serious shortcomings in characterizing the solution space, in dealing simultaneously with geometric (dimensional) and topological (relational) inconsistencies, and in completely covering the possible physical variations of the problem. This investigatio...

Upper Limb Posture Estimation in Robotic and Virtual Reality-Based Rehabilitation

New motor rehabilitation therapies include virtual reality (VR) and robotic technologies. In limb rehabilitation, limb posture is required to (1) provide a limb realistic representation in VR games and (2) assess the patient improvement. When exoskeleton devices are used in the therapy, the measurements of their joint angles cannot be directly used to represent the posture of the patient limb, since the human and exoskeleton kinematic models differ. In response to this shortcoming, we propose a method to estimate the posture of the human limb attached to the exoskeleton. We use the exoskeleton joint angles measurements and the constraints of the exoskeleton on the limb to estimate the human limb joints angles. This paper presents (a) the mathematical formulation and solution to the problem, (b) the implementation of the proposed solution on a commercial exoskeleton system for the upper limb rehabilitation, (c) its integration into a rehabilitation VR game platform, and (d) the quantitative assessment of the method during elbow and wrist analytic training. Results show that this method properly estimates the limb posture to (i) animate avatars that represent the patient in VR games and (ii) obtain kinematic data for the patient assessment during elbow and wrist analytic rehabilitation.

FIXED GRID FINITE ELEMENT ANALYSIS FOR 3D STRUCTURAL PROBLEMS

Fixed Grid (FG) methodology was first introduced by Garcia and Steven as an engine for numerical estimation of two-dimensional elasticity problems. The advantages of using FG are simplicity and speed at a permissible level of accuracy. Two-dimensional FG has been proved effective in approximating the strain and stress field with low requirements of time and computational resources. Moreover, FG has been used as the analytical kernel for different structural optimization methods as Evolutionary Structural Optimization, Genetic Algorithms (GA), and Evolutionary Strategies. FG consists of dividing the bounding box of the topology of an object into a set of equally sized cubic elements. Elements are assessed to be inside (I), outside (O) or neither inside nor outside (NIO) of the object. Different material properties assigned to the inside and outside medium transform the problem into a multi-material elasticity problem. As a result of the subdivision NIO elements have non-continuous properties. They can be approximated in different ways which range from simple setting of NIO elements as O to complex non-continuous domain integration. If homogeneously averaged material properties are used to approximate the NIO element, the element stiffness matrix can be computed as a factor of a standard stiffness matrix thus reducing the computational cost of creating the global stiffness matrix. An additional advantage of FG is found when accomplishing re-analysis, since there is no need to recompute the whole stiffness matrix when the geometry changes. This article presents CAD to FG conversion and the stiffness matrix computation based on non-continuous elements. In addition inclusion/exclusion of O elements in the global stiffness matrix is studied. Preliminary results shown that non-continuous NIO elements improve the accuracy of the results with considerable savings in time. Numerical examples are presented to illustrate the possibilities of the method.

Technical Section: 2D shape similarity as a complement for Voronoi-Delone methods in shape reconstruction

In surface reconstruction from planar cross sections it is necessary to build surfaces between 2D contours in consecutive cross sections. This problem has been traditionally attacked by (i) direct reconstruction based on local geometric proximity between the contours, and (ii) classification of topological events between the cross sections. These approaches have been separately applied with limited success. In case (i), the resulting surfaces may have overstretched or unnatural branches. These arise from local contour proximity which does not reflect global similarity between the contours. In case (ii), the topological events are identified but are not translated into the actual construction of a surface. This article presents an integration of the approaches (i) and (ii). Similarity between the composite 2D regions bounded by the contours in consecutive cross sections is used to: (a) decide whether a surface should actually relate two composite 2D regions, (b) identify the type and location of topological transitions between cross sections and (c) drive the surface construction for the regions found to be related in step (a). The implemented method avoids overstretched or unnatural branches, rendering a surface which is both geometrically intuitive and topologically faithful to the cross sections of the original object. The presented method is a good alternative in cases in which correct reproduction of the topology of the surface (e.g. simulation of flow in conduits) is more important than its geometry (e.g. assessment of tumor mass in radiation planning).

Real-time depth map generation architecture for 3D videoconferencing

In this paper we present a reliable depth estimation system which works in real-time with commodity hardware. The system is specially intended for 3D visualization using autostereoscopic displays. The core of this work is an implementation of a modified version of the adaptive support-weight algorithm that includes highly optimized algorithms for GPU, allowing accurate and stable depth map generation. Our approach overcomes typical problems of live depth estimation systems such as depth noise and flickering. Proposed approach is integrated within the versatile GStreamer multimedia software platform. Accurate depth map estimation together with real-time performance make proposed approach suitable for 3D videoconferencing.

Principal component and Voronoi skeleton alternatives for curve reconstruction from noisy point sets

Surface reconstruction from noisy point samples must take into consideration the stochastic nature of the sample. In other words, geometric algorithms reconstructing the surface or curve should not insist on matching each sampled point precisely. Instead, they must interpret the sample as a “point cloud” and try to build the surface as passing through the best possible (in the statistical sense) geometric locus that represents the sample. This work presents two new methods to find a piecewise linear approximation from a Nyquist-compliant stochastic sampling of a quasi-planar C 1 curve C(u):R → R 3, whose velocity vector never vanishes. One of the methods combines principal component analysis (PCA) (statistical) and Voronoi-Delaunay (deterministic) approaches in an entirely new way. It uses these two methods to calculate the best possible tape-shaped polygon covering the flattened point set, and then approximates the manifold using the medial axis of such a polygon. The other method applies PCA to find a direct piecewise linear approximation of C(u). A complexity comparison of these two methods is presented, along with a qualitative comparison with previously developed ones. The results show that the method solely based on PCA is both simpler and more robust for non-self-intersecting curves. For self-intersecting curves, the Voronoi-Delaunay based medial axis approach is more robust, at the price of higher computational complexity. An application is presented in the integration of meshes created from range images of a sculpture to form a complete unified mesh.

Analytical method for the kinetostatic analysis of the second-class RRR Assur group allowing for friction in the kinematic pairs

The calculation of forces in the kinematic pairs of mechanisms by inverse dynamics is usually performed without friction considerations. In practice, when examination of articulated mechanisms takes into account friction, the solution of the inverse dynamics results in a complex procedure. If a modular approach for the inverse dynamics is used, then exact solutions are available, but not necessarily are practical. For example, the analytical solution for a second-class first-type Assur group is a 16th degree equation. Previous researches proposed an approximated but practical (graphical) method to calculate the forces on the kinematic pairs taking into account the friction forces. In this article, an analytical interpretation of the Artobolevski approximated method is developed for the second-class Assur group with three rotational pairs. The final results for the reactions calculated with the implemented method present a good approximation with respect to the graphical solution. Future work should consider friction forces not only in second-class groups with rotational joints, but also in second-class groups with prismatic joints and high-class Assur groups.

Computational Geometry in the Preprocessing of Point Clouds for Surface Modeling

In Computer Aided Geometric Design (CAGD) the automated fitting of surfaces to massive series of data points presents several difficulties: (i) even the formal definition of the problem is ambiguous because the mathematical characteristics (continuity, for example) of the surface fit are dependent on non-geometric considerations, (ii) the data has an stochastic sampling component that cannot be taken as literal, and, (iii) digitization characteristics, such as sampling interval and directions are not constant, etc. In response, this investigation presents a set of computational tools to reduce, organize and re-sample the data set to fit the surface. The routines have been implemented to be portable across modeling or CAD servers. A case study is presented from the footwear industry, successfully allowing the preparation of a foreign, neutral laser digitization of a last for fitting a B-spline surface to it. Such a result was in the past attainable only by using proprietary software, produced by the same maker of the digitizing hardware.