8 resultados para Analytical geometry
em Massachusetts Institute of Technology
Resumo:
The interpretation and recognition of noisy contours, such as silhouettes, have proven to be difficult. One obstacle to the solution of these problems has been the lack of a robust representation for contours. The contour is represented by a set of pairwise tangent circular arcs. The advantage of such an approach is that mathematical properties such as orientation and curvature are explicityly represented. We introduce a smoothing criterion for the contour tht optimizes the tradeoff between the complexity of the contour and proximity of the data points. The complexity measure is the number of extrema of curvature present in the contour. The smoothing criterion leads us to a true scale-space for contours. We describe the computation of the contour representation as well as the computation of relevant properties of the contour. We consider the potential application of the representation, the smoothing paradigm, and the scale-space to contour interpretation and recognition.
Resumo:
We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call "relative affine structure". Via a number of corollaries of our main results we show that our framework unifies previous work --- including Euclidean, projective and affine --- in a natural and simple way, and introduces new, extremely simple, algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications.
Resumo:
Three-dimensional models which contain both geometry and texture have numerous applications such as urban planning, physical simulation, and virtual environments. A major focus of computer vision (and recently graphics) research is the automatic recovery of three-dimensional models from two-dimensional images. After many years of research this goal is yet to be achieved. Most practical modeling systems require substantial human input and unlike automatic systems are not scalable. This thesis presents a novel method for automatically recovering dense surface patches using large sets (1000's) of calibrated images taken from arbitrary positions within the scene. Physical instruments, such as Global Positioning System (GPS), inertial sensors, and inclinometers, are used to estimate the position and orientation of each image. Essentially, the problem is to find corresponding points in each of the images. Once a correspondence has been established, calculating its three-dimensional position is simply a matter of geometry. Long baseline images improve the accuracy. Short baseline images and the large number of images greatly simplifies the correspondence problem. The initial stage of the algorithm is completely local and scales linearly with the number of images. Subsequent stages are global in nature, exploit geometric constraints, and scale quadratically with the complexity of the underlying scene. We describe techniques for: 1) detecting and localizing surface patches; 2) refining camera calibration estimates and rejecting false positive surfels; and 3) grouping surface patches into surfaces and growing the surface along a two-dimensional manifold. We also discuss a method for producing high quality, textured three-dimensional models from these surfaces. Some of the most important characteristics of this approach are that it: 1) uses and refines noisy calibration estimates; 2) compensates for large variations in illumination; 3) tolerates significant soft occlusion (e.g. tree branches); and 4) associates, at a fundamental level, an estimated normal (i.e. no frontal-planar assumption) and texture with each surface patch.
Resumo:
The report addresses the problem of visual recognition under two sources of variability: geometric and photometric. The geometric deals with the relation between 3D objects and their views under orthographic and perspective projection. The photometric deals with the relation between 3D matte objects and their images under changing illumination conditions. Taken together, an alignment-based method is presented for recognizing objects viewed from arbitrary viewing positions and illuminated by arbitrary settings of light sources.
Resumo:
Biological systems exhibit rich and complex behavior through the orchestrated interplay of a large array of components. It is hypothesized that separable subsystems with some degree of functional autonomy exist; deciphering their independent behavior and functionality would greatly facilitate understanding the system as a whole. Discovering and analyzing such subsystems are hence pivotal problems in the quest to gain a quantitative understanding of complex biological systems. In this work, using approaches from machine learning, physics and graph theory, methods for the identification and analysis of such subsystems were developed. A novel methodology, based on a recent machine learning algorithm known as non-negative matrix factorization (NMF), was developed to discover such subsystems in a set of large-scale gene expression data. This set of subsystems was then used to predict functional relationships between genes, and this approach was shown to score significantly higher than conventional methods when benchmarking them against existing databases. Moreover, a mathematical treatment was developed to treat simple network subsystems based only on their topology (independent of particular parameter values). Application to a problem of experimental interest demonstrated the need for extentions to the conventional model to fully explain the experimental data. Finally, the notion of a subsystem was evaluated from a topological perspective. A number of different protein networks were examined to analyze their topological properties with respect to separability, seeking to find separable subsystems. These networks were shown to exhibit separability in a nonintuitive fashion, while the separable subsystems were of strong biological significance. It was demonstrated that the separability property found was not due to incomplete or biased data, but is likely to reflect biological structure.
Resumo:
Caches are known to consume up to half of all system power in embedded processors. Co-optimizing performance and power of the cache subsystems is therefore an important step in the design of embedded systems, especially those employing application specific instruction processors. In this project, we propose an analytical cache model that succinctly captures the miss performance of an application over the entire cache parameter space. Unlike exhaustive trace driven simulation, our model requires that the program be simulated once so that a few key characteristics can be obtained. Using these application-dependent characteristics, the model can span the entire cache parameter space consisting of cache sizes, associativity and cache block sizes. In our unified model, we are able to cater for direct-mapped, set and fully associative instruction, data and unified caches. Validation against full trace-driven simulations shows that our model has a high degree of fidelity. Finally, we show how the model can be coupled with a power model for caches such that one can very quickly decide on pareto-optimal performance-power design points for rapid design space exploration.
Resumo:
The present success in the manufacture of multi-layer interconnects in ultra-large-scale integration is largely due to the acceptable planarization capabilities of the chemical-mechanical polishing (CMP) process. In the past decade, copper has emerged as the preferred interconnect material. The greatest challenge in Cu CMP at present is the control of wafer surface non-uniformity at various scales. As the size of a wafer has increased to 300 mm, the wafer-level non-uniformity has assumed critical importance. Moreover, the pattern geometry in each die has become quite complex due to a wide range of feature sizes and multi-level structures. Therefore, it is important to develop a non-uniformity model that integrates wafer-, die- and feature-level variations into a unified, multi-scale dielectric erosion and Cu dishing model. In this paper, a systematic way of characterizing and modeling dishing in the single-step Cu CMP process is presented. The possible causes of dishing at each scale are identified in terms of several geometric and process parameters. The feature-scale pressure calculation based on the step-height at each polishing stage is introduced. The dishing model is based on pad elastic deformation and the evolving pattern geometry, and is integrated with the wafer- and die-level variations. Experimental and analytical means of determining the model parameters are outlined and the model is validated by polishing experiments on patterned wafers. Finally, practical approaches for minimizing Cu dishing are suggested.
Resumo:
The present success in the manufacture of multi-layer interconnects in ultra-large-scale integration is largely due to the acceptable planarization capabilities of the chemical-mechanical polishing (CMP) process. In the past decade, copper has emerged as the preferred interconnect material. The greatest challenge in Cu CMP at present is the control of wafer surface non-uniformity at various scales. As the size of a wafer has increased to 300 mm, the wafer-level non-uniformity has assumed critical importance. Moreover, the pattern geometry in each die has become quite complex due to a wide range of feature sizes and multi-level structures. Therefore, it is important to develop a non-uniformity model that integrates wafer-, die- and feature-level variations into a unified, multi-scale dielectric erosion and Cu dishing model. In this paper, a systematic way of characterizing and modeling dishing in the single-step Cu CMP process is presented. The possible causes of dishing at each scale are identified in terms of several geometric and process parameters. The feature-scale pressure calculation based on the step-height at each polishing stage is introduced. The dishing model is based on pad elastic deformation and the evolving pattern geometry, and is integrated with the wafer- and die-level variations. Experimental and analytical means of determining the model parameters are outlined and the model is validated by polishing experiments on patterned wafers. Finally, practical approaches for minimizing Cu dishing are suggested.