Fast calculation of soft shadow textures using convolution
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Eigen-Texture Method: Appearance Compression and Synthesis Based on a 3D Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image-based 3D photography using opacity hulls
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Light field mapping: efficient representation and hardware rendering of surface light fields
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Interactive Design of Complex Time-Dependent Lighting
IEEE Computer Graphics and Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
All-frequency shadows using non-linear wavelet lighting approximation
ACM SIGGRAPH 2003 Papers
Clustered principal components for precomputed radiance transfer
ACM SIGGRAPH 2003 Papers
ACM Transactions on Graphics (TOG)
A signal-processing framework for reflection
ACM Transactions on Graphics (TOG)
A Fourier Theory for Cast Shadows
IEEE Transactions on Pattern Analysis and Machine Intelligence
A frequency analysis of light transport
ACM SIGGRAPH 2005 Papers
Clustered Blockwise PCA for Representing Visual Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-Negative Lighting and Specular Object Recognition
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
All-frequency relighting of glossy objects
ACM Transactions on Graphics (TOG)
Inverse shade trees for non-parametric material representation and editing
ACM SIGGRAPH 2006 Papers
Toeplitz and circulant matrices: a review
Communications and Information Theory
All-frequency precomputed radiance transfer for glossy objects
EGSR'04 Proceedings of the Fifteenth Eurographics conference on Rendering Techniques
Symmetric photography: exploiting data-sparseness in reflectance fields
EGSR'06 Proceedings of the 17th Eurographics conference on Rendering Techniques
A framework for precomputed and captured light transport
ACM Transactions on Graphics (TOG)
Eigentransport for efficient and accurate all-frequency relighting
Proceedings of the 5th international conference on Computer graphics and interactive techniques in Australia and Southeast Asia
Kernel Nyström method for light transport
ACM SIGGRAPH 2009 papers
Frequency analysis and sheared reconstruction for rendering motion blur
ACM SIGGRAPH 2009 papers
Precomputation-Based Rendering
Foundations and Trends® in Computer Graphics and Vision
Optical computing for fast light transport analysis
ACM SIGGRAPH Asia 2010 papers
LightSlice: matrix slice sampling for the many-lights problem
Proceedings of the 2011 SIGGRAPH Asia Conference
An analysis of the in-out BRDF factorization for view-dependent relighting
EGSR'08 Proceedings of the Nineteenth Eurographics conference on Rendering
Sparsely precomputing the light transport matrix for real-time rendering
EGSR'10 Proceedings of the 21st Eurographics conference on Rendering
On the effective dimension of light transport
EGSR'10 Proceedings of the 21st Eurographics conference on Rendering
5D Covariance tracing for efficient defocus and motion blur
ACM Transactions on Graphics (TOG)
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Blockwise or Clustered Principal Component Analysis (CPCA) is commonly used to achieve real-time rendering of shadows and glossy reflections with precomputed radiance transfer (PRT). The vertices or pixels are partitioned into smaller coherent regions, and light transport in each region is approximated by a locally low-dimensional subspace using PCA. Many earlier techniques such as surface light field and reflectance field compression use a similar paradigm. However, there has been no clear theoretical understanding of how light transport dimensionality increases with local patch size, nor of the optimal block size or number of clusters. In this paper, we develop a theory of locally low dimensional light transport, by using Szego's eigenvalue theorem to analytically derive the eigenvalues of the covariance matrix for canonical cases. We show mathematically that for symmetric patches of area A, the number of basis functions for glossy reflections increases linearly with A, while for simple cast shadows, it often increases as √A. These results are confirmed numerically on a number of test scenes. Next, we carry out an analysis of the cost of rendering, trading off local dimensionality and the number of patches, deriving an optimal block size. Based on this analysis, we provide useful practical insights for setting parameters in CPCA and also derive a new adaptive subdivision algorithm. Moreover, we show that rendering time scales sub-linearly with the resolution of the image, allowing for interactive all-frequency relighting of 1024 x 1024 images.