# Inverse Rendering for Computer Graphics

My Ph.D. thesis is available as a 2.6M PDF file (two-sided format, 163 pages) that includes all the images at 75 dpi. If you don't already have it, you will need Adobe Acrobat Reader in order to read the PDF file. If you are going to print it out and you want to save half the paper, I have also prepared a 2.4M PDF file that has two pages per side (prints on 41 pieces of paper).

You can also download the full 9.1M gzipped PostScript file, which has all the images at around 150 dpi.

## Abstract

Creating realistic images has been a major focus in the study of computer graphics for much of its history. This effort has led to mathematical models and algorithms that can compute predictive, or physically realistic, images from known camera positions and scene descriptions that include the geometry of objects, the reflectance of surfaces, and the lighting used to illuminate the scene. These images accurately describe the physical quantities that would be measured from a real scene. Because these algorithms can predict real images, they can also be used in inverse problems to work backward from photographs to attributes of the scene.

Work on three such inverse rendering problems is described. The first, inverse lighting, assumes knowledge of geometry, reflectance, and the recorded photograph and solves for the lighting in the scene. A technique using a linear least-squares system is proposed and demonstrated. Also demonstrated is an application of inverse lighting, called re-lighting, which modifies lighting in photographs.

The second two inverse rendering problems solve for unknown reflectance, given images with known geometry, lighting, and camera positions. Photographic texture measurement concentrates on capturing the spatial variation in an object's reflectance. The resulting system begins with scanned 3D models of real objects and uses photographs to construct accurate, high-resolution textures suitable for physically realistic rendering. The system is demonstrated on two complex natural objects with detailed surface textures.

Image-based BRDF measurement takes the opposite approach to reflectance measurement, capturing the directional characteristics of a surface's reflectance by measuring the bidirectional reflectance distribution function, or BRDF. Using photographs of an object with spatially uniform reflectance, the BRDFs of paints and papers are measured with completeness and accuracy that rival that of measurements obtained using specialized devices. The image-based approach and novel light source positioning technique require only general-purpose equipment, so the cost of the apparatus is low compared to conventional approaches. In addition, very densely sampled data can be measured very quickly, when the wavelength spectrum of the BRDF does not need to be measured in detail.

## Contents

• Introduction
• Background
• Mathematical Preliminaries
• The Bidirectional Reflectance Distribution Function
• Rendering
• Inverse Lighting
• Problem Statement
• Prior Work
• Basic Least-squares Solution
• Regularized Solution
• Re-lighting
• A Test with a Synthetic Photograph
• A Test with a Rigid Object
• Tests on Human Faces
• Conclusion
• Photographic Texture Measurement
• Prior Work
• Texture Representation
• Estimating Reflectance
• A Synthetic Example
• Measurement Setup
• Results
• Future Work
• Conclusion
• Image-based BRDF Measurement
• Overview of Method
• Prior Work
• Apparatus
• Data Processing
• Results
• Mapping the BRDF Domain to 3-space
• BRDF Resampling
• Conclusion
• Conclusion
• Appendices
• Camera Calibration