Weighted Mean Curvature
This work addresses image processing tasks by providing an incremental improvement in spatial priors for regularization and inference.
The paper tackles the need for robust spatial priors in image processing by introducing weighted mean curvature (WMC) as a novel prior, demonstrating its favorable properties and achieving processing speeds over 33.2 giga-pixels/second on GPU with superior quantitative performance compared to total-variation and mean curvature.
In image processing tasks, spatial priors are essential for robust computations, regularization, algorithmic design and Bayesian inference. In this paper, we introduce weighted mean curvature (WMC) as a novel image prior and present an efficient computation scheme for its discretization in practical image processing applications. We first demonstrate the favorable properties of WMC, such as sampling invariance, scale invariance, and contrast invariance with Gaussian noise model; and we show the relation of WMC to area regularization. We further propose an efficient computation scheme for discretized WMC, which is demonstrated herein to process over 33.2 giga-pixels/second on GPU. This scheme yields itself to a convolutional neural network representation. Finally, WMC is evaluated on synthetic and real images, showing its superiority quantitatively to total-variation and mean curvature.