## Date of Award

Spring 2015

## Degree Type

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Department

Computer Science

## First Advisor

Voicu Popescu

## Committee Chair

Voicu Popescu

## Committee Member 1

Elisha Sacks

## Committee Member 2

Christoph Hoffmann

## Committee Member 3

Xavier Tricoche

## Committee Member 4

Daniel Aliaga

## Abstract

This dissertation introduces the image generalization paradigm for computing visibility. The paradigm is based on the observation that an image is a powerful tool for computing visibility. An image can be rendered efficiently with the support of graphics hardware and each of the millions of pixels in the image reports a visible geometric primitive. However, the visibility solution computed by a conventional image is far from complete. A conventional image has a uniform sampling rate which can miss visible geometric primitives with a small screen footprint. A conventional image can only find geometric primitives to which there is direct line of sight from the center of projection (i.e. the eye) of the image; therefore, a conventional image cannot compute the set of geometric primitives that become visible as the viewpoint translates, or as time changes in a dynamic dataset. Finally, like any sample-based representation, a conventional image can only confirm that a geometric primitive is visible, but it cannot confirm that a geometric primitive is hidden, as that would require an infinite number of samples to confirm that the primitive is hidden at all of its points. ^ The image generalization paradigm overcomes the visibility computation limitations of conventional images. The paradigm has three elements. (1) Sampling pattern generalization entails adding sampling locations to the image plane where needed to find visible geometric primitives with a small footprint. (2) Visibility sample generalization entails replacing the conventional scalar visibility sample with a higher dimensional sample that records all geometric primitives visible at a sampling location as the viewpoint translates or as time changes in a dynamic dataset; the higher-dimensional visibility sample is computed exactly, by solving visibility event equations, and not through sampling. Another form of visibility sample generalization is to enhance a sample with its trajectory as the geometric primitive it samples moves in a dynamic dataset. (3) Ray geometry generalization redefines a camera ray as the set of 3D points that project at a given image location; this generalization supports rays that are not straight lines, and enables designing cameras with non-linear rays that circumvent occluders to gather samples not visible from a reference viewpoint. ^ The image generalization paradigm has been used to develop visibility algorithms for a variety of datasets, of visibility parameter domains, and of performance-accuracy tradeoff requirements. These include an aggressive from-point visibility algorithm that guarantees finding all geometric primitives with a visible fragment, no matter how small primitive's image footprint, an efficient and robust exact from-point visibility algorithm that iterates between a sample-based and a continuous visibility analysis of the image plane to quickly converge to the exact solution, a from-rectangle visibility algorithm that uses 2D visibility samples to compute a visible set that is exact under viewpoint translation, a flexible pinhole camera that enables local modulations of the sampling rate over the image plane according to an input importance map, an animated depth image that not only stores color and depth per pixel but also a compact representation of pixel sample trajectories, and a curved ray camera that integrates seamlessly multiple viewpoints into a multiperspective image without the viewpoint transition distortion artifacts of prior art methods.

## Recommended Citation

Cui, Jian, "Visibility computation through image generalization" (2015). *Open Access Dissertations*. 445.

https://docs.lib.purdue.edu/open_access_dissertations/445