# Weighted Mean Curvature

## TL;DR

This paper introduces weighted mean curvature (WMC) as a new image prior, demonstrating its favorable properties, efficient computation, and superiority over existing methods like total variation in image processing tasks.

## Contribution

The paper presents a novel weighted mean curvature prior, an efficient GPU computation scheme, and a convolutional neural network implementation, advancing image regularization techniques.

## Key findings

- WMC exhibits sampling, scale, and contrast invariance.
- The computation scheme processes over 33.2 giga-pixels/second on GPU.
- WMC outperforms total variation and mean curvature in experiments.

## Abstract

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.