  Existing 3D mesh shape evaluation metrics mainly focus on the overall shape
but are usually less sensitive to local details. This makes them inconsistent
with human evaluation, as human perception cares about both overall and
detailed shape. In this paper, we propose an analytic metric named Spectrum
Area Under the Curve Difference (SAUCD) that demonstrates better consistency
with human evaluation. To compare the difference between two shapes, we first
transform the 3D mesh to the spectrum domain using the discrete
Laplace-Beltrami operator and Fourier transform. Then, we calculate the Area
Under the Curve (AUC) difference between the two spectrums, so that each
frequency band that captures either the overall or detailed shape is equitably
considered. Taking human sensitivity across frequency bands into account, we
further extend our metric by learning suitable weights for each frequency band
which better aligns with human perception. To measure the performance of SAUCD,
we build a 3D mesh evaluation dataset called Shape Grading, along with manual
annotations from more than 800 subjects. By measuring the correlation between
our metric and human evaluation, we demonstrate that SAUCD is well aligned with
human evaluation, and outperforms previous 3D mesh metrics.
