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-tofine 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 nonspecialized parametrizations.