A Discrete Scheme for Computing Image's Weighted Gaussian Curvature
This work addresses performance and accuracy issues in image processing tasks like smoothing and decomposition, though it appears incremental as it builds on existing curvature computation methods.
The paper tackled the problem of computing weighted Gaussian curvature for images by proposing a novel discrete scheme that eliminates the need for second-order differentiability, resulting in improved accuracy, smaller support region, and higher computational efficiency compared to conventional methods.
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.