  Weighted Gaussian Curvature is an important measurement for images. However,
its conventional computation scheme has low performance, low accuracy and
requires that the input image must be second order differentiable. To tackle
these three issues, we propose a novel discrete computation scheme for the
weighted Gaussian curvature. Our scheme does not require the second order
differentiability. Moreover, our scheme is more accurate, has smaller support
region and computationally more efficient than the conventional schemes.
Therefore, our scheme holds promise for a large range of applications where the
weighted Gaussian curvature is needed, for example, image smoothing, cartoon
texture decomposition, optical flow estimation, etc.
