Stochastic sampling in computer graphics
ACM Transactions on Graphics (TOG)
Filters for common resampling tasks
Graphics gems
Design of accurate and smooth filters for function and derivative reconstruction
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Reconstruction filters in computer-graphics
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
An evaluation of reconstruction filters for volume rendering
VIS '94 Proceedings of the conference on Visualization '94
Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice
IEEE Transactions on Visualization and Computer Graphics
Box Spline Reconstruction On The Face-Centered Cubic Lattice
IEEE Transactions on Visualization and Computer Graphics
Compressed sensing of analog signals in shift-invariant spaces
IEEE Transactions on Signal Processing
Physically Based Rendering, Second Edition: From Theory To Implementation
Physically Based Rendering, Second Edition: From Theory To Implementation
IEEE Transactions on Signal Processing
Gradient Estimation Revitalized
IEEE Transactions on Visualization and Computer Graphics
Toward High-Quality Gradient Estimation on Regular Lattices
IEEE Transactions on Visualization and Computer Graphics
Compressive Rendering: A Rendering Application of Compressed Sensing
IEEE Transactions on Visualization and Computer Graphics
Quantitative Fourier analysis of approximation techniques. I.Interpolators and projectors
IEEE Transactions on Signal Processing
B-spline signal processing. I. Theory
IEEE Transactions on Signal Processing
Hex-splines: a novel spline family for hexagonal lattices
IEEE Transactions on Image Processing
Quasi-Interpolating Spline Models for Hexagonally-Sampled Data
IEEE Transactions on Image Processing
Quasi-interpolation on the body centered cubic lattice
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
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We present a novel image representation method based on shift-invariant spaces. Unlike existing rendering methods, our proposed approach consists of two steps: an analog acquisition step that traces rays through the scene, and a subsequent digital processing step that filters the intermediate digital image to obtain the coefficients of a minimum-error continuous image approximation. Our approach can be easily incorporated in existing renderers with very little change and with little-to-no computational overhead. Additionally, we introduce the necessary tools needed to analyze the smoothing and post-aliasing properties of the minimum-error approximations. We provide examples of spaces --- generated by the uniform B-splines --- that can be readily used in conjunction with the two-dimensional Cartesian grid. Our experimental results demonstrate that minimum-error approximations significantly enhance image quality by preserving high-frequency details that are usually smoothed out by existing image anti-aliasing approaches.