# Signal-specialized parametrization

Eurographics Workshop on Rendering 2002, 87-100.

Optimization of texture coordinates for accurate representation of given content.

**Abstract:**
To reduce memory requirements for texture mapping a model, we build a surface parametrization specialized
to its signal (such as color or normal). Intuitively, we want to allocate more texture samples in regions
with greater signal detail. Our approach is to minimize signal approximation error — the difference
between the original surface signal and its reconstruction from the sampled texture. Specifically, our
signal-stretch parametrization metric is derived from a Taylor expansion of signal error. For fast
evaluation, this metric is pre-integrated over the surface as a metric tensor. We minimize this nonlinear
metric using a novel coarse-to-fine hierarchical solver, further accelerated with a fine-to-coarse
propagation of the integrated metric tensor. Use of metric tensors permits anisotropic squashing of the
parametrization along directions of low signal gradient. Texture area can often be reduced by a factor of
4 for a desired signal accuracy compared to non-specialized parametrizations.

**Hindsights:**
See also our

follow-up work at SGP 2004
where we further improve the parameterization to account for the local linear reconstruction provided by
hardware texture sampling.