Irregular Z-buffer

Abstract: The classical Z-buffer visibility algorithm samples a scene at regularly spaced points on an image plane. Previously, we introduced an extension of this algorithm called the irregular Z-buffer that permits sampling of the scene from arbitrary points on the image plane. These sample points are stored in a two-dimensional spatial data structure. Here we present a set of architectural enhancements to the classical Z-buffer acceleration hardware which supports efficient execution of the irregular Z-buffer. These enhancements enable efficient parallel construction and query of certain irregular data structures, including the grid of linked lists used by our algorithm. The enhancements include flexible atomic read-modify-write units located near the memory controller, an internal routing network between these units and the fragment processors, and a MIMD fragment processor design. We simulate the performance of this new architecture and demonstrate that it can be used to render high-quality shadows in geometrically complex scenes at interactive frame rates. We also discuss other uses of the irregular Z-buffer algorithm and the implications of our architectural changes in the design of chip-multiprocessors.

Abstract: We develop algorithms for the construction of irregular cell (block) models for parameterization of tomographic inverse problems. The forward problem is defined on a regular basic grid of non-overlapping cells. The basic cells are used as building blocks for construction of non-overlapping irregular cells. The construction algorithms are not computationally intensive and not particularly complex, and, in general, allow for grid optimization where cell size is determined from scalar functions, e.g., measures of model sampling or a priori estimates of model resolution. The link between a particular cell j in the regular basic grid and its host cell k in the irregular grid is provided by a pointer array which implicitly defines the irregular cell model. The complex geometrical aspects of irregular cell models are not needed in the forward or in the inverse problem. The matrix system of tomographic equations is computed once on the regular basic cell model. After grid construction, the basic matrix equation is mapped using the pointer array on a new matrix equation in which the model vector relates directly to cells in the irregular model. Next, the mapped system can be solved on the irregular grid. This approach avoids forward computation on the complex geometry of irregular grids. Generally, grid optimization can aim at reducing the number of model parameters in volumes poorly sampled by the data while elsewhere retaining the power to resolve the smallest scales warranted by the data. Unnecessary overparameterization of the model space can be avoided and grid construction can aim at improving the conditioning of the inverse problem. We present simple theory and optimization algorithms in the context of seismic tomography and apply the methods to Rayleigh-wave group velocity inversion and global travel-time tomography.

Abstract: The invention provides an image-based visibility measurement solution in which an image is used to calculate a visibility (visual range). In one embodiment, a lighting condition for the image is determined and the visibility calculation is adjusted based on the lighting condition. Further, the invention can obtain image data for a set of portions of the image and estimate a visual range based on each portion. The estimated visual ranges can be combined to calculate the visibility for the image. Still further, multiple metrics can be calculated, each of which is used to estimate a visual range. Subsequently, the visual ranges can be used to calculate the visibility for the image. Even further, configuration data that is based on a set of training images can be used to calculate the visibility for a new image. To this extent, the invention can incorporate the lighting condition, portions of the image having differing features, multiple metrics, and/or feedback through training images to accurately measure visibility based on an image.