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.