Image Filtering

Sparse Norm Filter

Chengxi Ye, Dacheng Tao, Mingli Song, David W. Jacobs, Min Wu

Fig1. Examples of filtering results using different norms. (a) Left: original image Middle: smoothed image via minimizing the l⁰ energy. Right: sharpened image. (b) Up: image with pepper and salt noise. Down: smoothed result by minimizing the l¹ norm. (c) Left: drag-and-drop editing. Right: seamlessly editing using l² norm filtering.

Abstract

Optimization-based filtering smoothes an image by minimizing a fidelity function and simultaneously preserves edges by exploiting a sparse norm penalty over gradients. It has obtained promising performance in practical problems, such as detail manipulation, HDR compression and deblurring, and thus has received increasing attentions in fields of graphics, computer vision and image processing. This paper derives a new type of image filter called sparse norm filter (SNF) from optimization-based filtering. SNF has a very simple form, introduces a general class of filtering techniques, and explains several classic filters as special implementations of SNF, e.g. the averaging filter and the median filter. It has advantages of being halo free, easy to implement, and low time and memory costs (comparable to those of the bilateral filter). Thus, it is more generic than a smoothing operator and can better adapt to different tasks. We validate the proposed SNF by a wide variety of applications including edge-preserving smoothing, outlier tolerant filtering, detail manipulation, HDR compression, non-blind deconvolution, image segmentation, and colorization.

Full manuscript:

http://arxiv.org/abs/1305.3971