Soft Edge Smoothness Prior for Alpha Channel Super Resolution

Abstract

Effective image prior is necessary for image super resolution, due to its severely under-determined nature. Although the edge smoothness prior can be effective, it is generally difficult to have analytical forms to evaluate the edge smoothness, especially for soft edges that exhibit gradual intensity transitions. This paper finds the connection between the soft edge smoothness and a soft cut metric on an image grid by generalizing the Geocuts method [5], and proves that the soft edge smoothness measure approximates the average length of all level lines in an intensity image. This new finding not only leads to an analytical characterization of the soft edge smoothness prior, but also gives an intuitive geometric explanation. Regularizing the super resolution problem by this new form of prior can simultaneously minimize the length of all level lines, and thus resulting in visually appealing results. In addition, this paper presents a novel combination of this soft edge smoothness prior and the alpha matting technique for color image super resolution, by normalizing edge segments with their alpha channel description, to achieve a unified treatment of edges with different contrast and scale.

Image super-resolution as sparse representation of raw image patches

“…In Figure 6, we apply our method to the same raccoon face image with magnification factor 3. Since there are no explicit edges in most part of the image, methods proposed in [12], [23], and [6] would have tremendous difficulty here. Compared to neighbor embedding [5], our method gives clearer fur and sharper whiskers.…”

“…In Figure 5, we compare our method with several other methods on an image of the Parthenon used in [6], including back projection, neighbor embedding [5], and the recently Figure 4. The flower and girl image magnified by a factor of 3.…”

“…proposed method based on a learned soft edge prior [6]. The result from back projection has many jagged effects along the edges.…”

“…The girl image magnified by a factor of 4. From left to right: low-resolution input, back projection, learning-based method in [12], soft edge prior [6], and our method. prior method [6], our method generates shaper edges and is more faithful to the original facial texture.…”

“…Top row: low-resolution input, bicubic interpolation, back projection. Bottom row: neighbor embedding [5], soft edge prior [6], and our method.…”