Accuracy of Spherical Harmonic Approximations for Images of Lambertian Objects under Far and Near Lighting 1st edition by Darya Frolova, Denis Simakov, Ronen Basri ISBN 3540219842 9783540219842
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Authors:Darya Frolova, Denis Simakov; Ronen Basri , Tags:Computer Vision – ECCV 2004 , Author sort:Darya Frolova, Denis Simakov & Basri, Ronen , Languages:Languages:eng , Published:Published:Mar 2004
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ISBN 10: 3540219842
ISBN 13: 978-3540219842
Author: Darya Frolova, Denis Simakov, Ronen Basri
Various problems in Computer Vision become difficult due to a strong influence of lighting on the images of an object. Recent work showed analytically that the set of all images of a convex, Lambertian object can be accurately approximated by the low-dimensional linear subspace constructed using spherical harmonic functions. In this paper we present two major contributions: first, we extend previous analysis of spherical harmonic approximation to the case of arbitrary objects; second, we analyze its applicability for near light. We begin by showing that under distant lighting, with uniform distribution of light sources, the average accuracy of spherical harmonic representation can be bound from below. This bound holds for objects of arbitrary geometry and color, and for general illuminations (consisting of any number of light sources). We further examine the case when light is coming from above and provide an analytic expression for the accuracy obtained in this case. Finally, we show that low-dimensional representations using spherical harmonics provide an accurate approximation also for fairly near light. Our analysis assumes Lambertian reflectance and accounts for attached, but not for cast shadows. We support this analysis by simulations and real experiments, including an example of a 3D shape reconstruction by photometric stereo under very close, unknown lighting.
Accuracy of Spherical Harmonic Approximations for Images of Lambertian Objects under Far and Near Lighting 1st Table of contents:
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Introduction
- 1.1 Background and Motivation
- 1.2 The Role of Spherical Harmonics in Lighting and Image Representation
- 1.3 Lambertian Surfaces and Their Significance in Computer Vision
- 1.4 Objectives of the Study
- 1.5 Structure of the Paper
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Fundamentals of Spherical Harmonics
- 2.1 Definition and Mathematical Properties of Spherical Harmonics
- 2.2 Spherical Harmonics in the Context of Light and Imaging
- 2.3 Approximation of Functions Using Spherical Harmonics
- 2.4 Higher-Order and Low-Order Approximations in Spherical Harmonics
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Lambertian Reflectance Model
- 3.1 Understanding Lambertian Reflectance
- 3.2 Lambertian Model for Surface Reflection
- 3.3 Surface Normals and Their Impact on Image Intensity
- 3.4 Lambertian Assumptions in Computer Vision and Image Processing
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Lighting Models: Far-Field vs. Near-Field
- 4.1 Characteristics of Far-Field Lighting
- 4.2 Characteristics of Near-Field Lighting
- 4.3 The Impact of Lighting Conditions on Image Formation
- 4.4 Far-Field vs. Near-Field Lighting: Theoretical Differences
- 4.5 Modeling Lighting Effects in Image Formation
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Spherical Harmonics for Image Representation
- 5.1 Using Spherical Harmonics to Approximate Lighting Conditions
- 5.2 Image Representation in Terms of Spherical Harmonics
- 5.3 Challenges in Applying Spherical Harmonics to Real-World Images
- 5.4 Efficiency and Accuracy of Spherical Harmonic Approximations
- 5.5 Practical Considerations for Implementing Spherical Harmonics in Imaging
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Accuracy of Spherical Harmonic Approximations
- 6.1 Measuring the Accuracy of Approximations for Lambertian Objects
- 6.2 Comparison of Different Approximation Orders (Low vs. High)
- 6.3 Error Metrics for Spherical Harmonic Approximations
- 6.4 Impact of Lighting Conditions on Accuracy
- 6.5 Case Studies: Accuracy in Far-Field Lighting
- 6.6 Case Studies: Accuracy in Near-Field Lighting
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Experimental Setup and Methodology
- 7.1 Description of Experimental Setup
- 7.2 Image Data Collection: Lambertian Objects and Lighting Conditions
- 7.3 Evaluation Metrics for Model Performance
- 7.4 Approach for Estimating Spherical Harmonics Coefficients
- 7.5 Data Analysis Techniques
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Results and Analysis
- 8.1 Results from Far-Field Lighting Conditions
- 8.2 Results from Near-Field Lighting Conditions
- 8.3 Comparison of Approximation Accuracy Across Different Lighting Models
- 8.4 Analysis of Errors in Spherical Harmonic Approximations
- 8.5 Sensitivity of Accuracy to Higher-Order Terms
- 8.6 Impact of Noise and Imperfections in Real-World Images
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Applications and Implications
- 9.1 Applications in Computer Vision and 3D Object Recognition
- 9.2 Use of Spherical Harmonics in Lighting Estimation and Rendering
- 9.3 Implications for Image-based Rendering Techniques
- 9.4 Real-Time Processing and Practical Use in Vision Systems
- 9.5 Extending the Model for Non-Lambertian Surfaces
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Challenges and Open Problems
- 10.1 Handling Complex Lighting Conditions in Real Environments
- 10.2 Improving the Accuracy of Spherical Harmonic Approximations for Non-Ideal Surfaces
- 10.3 Scalability and Efficiency Issues in High-Resolution Images
- 10.4 Future Directions in Spherical Harmonic Approximations for Computer Vision
- 10.5 Exploring New Lighting Models and Reflectance Properties
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Conclusion
- 11.1 Summary of Findings
- 11.2 Contributions of the Study to the Field of Web and Image Processing
- 11.3 Practical Implications for Image Processing and Computer Vision
- 11.4 Future Research Directions
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