  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.
