Registration using Graphics Processor Unit

Data point set registration is an important operation in coordinate metrology. Registration is the operation by which sampled point clouds are aligned with a CAD model by a 4X4 homogeneous transformation (e.g., rotation and translation). This alignment permits validation of the produced artifact\u27s geometry. State-of-the-art metrology systems are now capable of generating thousands, if not millions, of data points during an inspection operation, resulting in increased computational power to fully utilize these larger data sets. The registration process is an iterative nonlinear optimization operation having an execution time directly related to the number of points processed and CAD model complexity. The objective function to be minimized by this optimization is the sum of the square distances between each point in the point cloud and the closest surface in the CAD model. A brute force approach to registration, which is often used, is to compute the minimum distance between each point and each surface in the CAD model. As point cloud sizes and CAD model complexity increase, this approach becomes intractable and inefficient. Highly efficient numerical and analytical gradient based algorithms exist and their goal is to convergence to an optimal solution in minimum time. This thesis presents a new approach to efficiently perform the registration process by employing readily available computer hardware, the graphical processor unit (GPU). The data point set registration time for the GPU shows a significant improvement (around 15-20 times) over typical CPU performance. Efficient GPU programming decreases the complexity of the steps and improves the rate of convergence of the existing algorithms. The experimental setup reveals the exponential increasing nature of the CPU and the linear performance of the GPU in various aspects of an algorithm. The importance of CPU in the GPU programming is highlighted. The future implementations disclose the possible extensions of a GPU for higher order and complex coordinate metrology algorithms

Least Squares Fitting of Analytic Primitives on a GPU

Metrology systems take coordinate information directly from the surface of a manufactured part and generate millions of (X, Y, Z) data points. The inspection process often involves fitting analytic primitives such as sphere, cone, torus, cylinder and plane to these points which represent an object with the corresponding shape. Typically, a least squares fit of the parameters of the shape to the point set is performed. The least squares fit attempts to minimize the sum of the squares of the distances between the points and the primitive. The objective function however, cannot be solved in the closed form and numerical minimization techniques are required to obtain the solution. These techniques as applied to primitive fitting entail iteratively solving large systems of linear equations generally involving large floating point numbers until the solution has converged. The current problem in-process metrology faces is the large computational times for the analysis of these millions of streaming data points. This research addresses the bottleneck using the Graphical Processing Unit (GPU), primarily developed by the computer gaming industry, to optimize operations. The explosive growth in the programming capabilities and raw processing power of Graphical Processing Units has opened up new avenues for their use in non-graphic applications. The combination of large stream of data and the need for 3D vector operations make the primitive shape fit algorithms excellent candidates for processing via a GPU. The work presented in this research investigates the use of the parallel processing capabilities of the GPU in expediting specific computations involved in the fitting procedure. The least squares fit algorithms for the circle, sphere, cylinder, plane, cone and torus have been implemented on the GPU using NVIDIA\u27s Compute Unified Device Architecture (CUDA). The implementations are benchmarked against those on a CPU which are carried out using C++. The Gauss Newton minimization algorithm is used to obtain the best fit parameters for each of the aforementioned primitives. The computation times for the two implementations are compared. It is demonstrated that the GPU is about 3-4 times faster than the CPU for a relatively simple geometry such as the circle while the factor scales to about 14 for a torus which is more complex

Nonlinear optimization framework for image-based modeling on programmable graphics hardware

Graphics hardware is undergoing a change from fixed-function pipelines to more programmable organizations that resemble general-purpose stream processors. In this paper, we show that certain general algorithms, not normally associated with computer graphics, can be mapped to such designs. Specifically, we cast nonlinear optimization as a data streaming process that is well matched to modern graphics processors. Our framework is particularly well suited for solving image-based modeling problems since it can be used to represent a large and diverse class of these problems using a common formulation. We successfully apply this approach to two distinct image-based modeling problems: light field mapping approximation and fitting the Lafortune model to spatial bidirectional reflectance distribution functions. Comparing the performance of the graphics hardware implementation to a CPU implementation, we show more than 5-fold improvement

Aceleración de métodos de reducción de modelos dispersos en arquitecturas multi mani-core

El estudio de sistemas dinámicos es un componente fundamental de varias áreas de la ingeniería así como también de otras disciplinas, como por ejemplo en Teoría de Control, Procesamiento de Señnales, Análisis Estructural o Economía. En algunos casos, el estudio se aborda mediante un enfoque empírico basado en la manipulación de las entradas de dicho sistema y la posterior medición de los resultados con el fin de realizar ajustes [30]. Sin embargo, por lo general, estos sistemas son demasiado complejos, o su construcción muy costosa o peligrosa, por lo que es necesario emplear otro tipo de técnicas. Es por esto que dichos sistemas suelen describirse mediante modelos físicos, y luego, aplicando distintas leyes de la Física, es posible desarrollar sistemas de ecuaciones matemáticas que describan su comportamiento. Estas ecuaciones matemáticas pueden ser de distinta índole, dependiendo del problema que se intente describir. Cuando estas ecuaciones son lineales se habla de un sistema dinámico lineal