Local color distribution projection filtering using a homogeneous coordinate system

Abstract

In this paper, we present a denoising method of using multiple image composition based on the color transform of local color distribution of patches. In the method, the color of a guidance image is transformed so as to get close to a noisy input image by a patch-wise color transform. As a result, a noiseless image is obtained. Actually this method can be regarded as the generalized version of our previous method [1] and the guided filter [2], and gives improved images with more clear appearance. The existing methods have a restriction that a filter output form is expressed only by a linear transform, i.e., a first order polynomial. In this paper, we introduce a more general formula for this category of filtering with the guidance image. We deal with a quadratic formula for realizing more flexible transform instead of the previous linear transform, and moreover introduce more simple and flexible regularization.

Color transform between image pair using covariance correspondences of local color distributions

“…However, as a trade-off of not using these correspondences, discolorations (unevenness of color) are prone to arise in the color transformation. Thus the image qualities in motionless static regions are inferior to those of our conventional GF [4].…”

“…Our previous GF [4] and the proposed one in this paper have advantages and disadvantages, depending on the amount of noise and object motion. To utilize the advantages of both methods, we aim to classify the static and the dynamic regions, and apply a more appropriate GF for each region.…”

“…This GF has recently been applied to a variety of applications such as contrast correction [5] and stereo matching [6]. In particular, target applications of our GF described in this paper are denoising and tone mapping that can handle a set of input and guide images with different color and intensity [2,4,5].…”

“…In a corresponding pair of patches taken from the same scene in the input and guide images, but taken under different conditions (e.g., a different white balance), the shapes of the two color distributions tend to be similar, and thus one distribution can be approximated by the rotated and shifted version of the other distribution. Utilizing this feature, the existing GFs [1][2][3][4] deal with the problem of obtaining a transform matrix that minimizes the transformation error in each patch. Specifically, at a target pixel i and its neighboring pixels j in a patch Ωi, the local pixel colors of the guide image Ij ∈ R 3 (such as RGB or YCbCr) are transformed by a patchwise transform matrix Ai ∈ R 3×3 and an offset vector bi ∈ R 3 to make them more like the local pixel colors of the input image pj ∈ R 3 :…”

“…As for methods that use multiple images, this paper deals with guided filtering (GF) [1][2][3][4] that uses a guide (or called guidance) image under a different photographic conditions. This GF has recently been applied to a variety of applications such as contrast correction [5] and stereo matching [6].…”