Signal-specialized parameterization for piecewise linear reconstruction

Signal-specialized parameterization for piecewise linear reconstruction
Geetika Tewari, John Snyder, Pedro Sander, Steven Gortler, Hugues Hoppe.
Symposium on Geometry Processing 2004, 57-66.
Optimizing texture coordinates based on nonlinearity of texture content.
Abstract: We propose a metric for surface parameterization specialized to its signal that can be used to create more efficient, high-quality texture maps. Derived from Taylor expansion of signal error, our metric predicts the signal approximation error - the difference between the original surface signal and its reconstruction from the sampled texture. Unlike previous methods, our metric assumes piecewise-linear reconstruction, and thus makes a good approximation to bilinear reconstruction employed in graphics hardware. We achieve significant savings in texture area for a desired signal accuracy compared to the signal-specialized parameterization metric proposed by Sander et al. in the 2002 Eurographics Workshop on Rendering.
Hindsights: Many of our ideas (signal-specialization, integrated metric tensor, atlas packing, etc.) have been adapted in the UVAtlas technology of the Microsoft Direct3D SDK.