Perceptual Color Correction Through Variational Techniques

Abstract

In this paper, we present a discussion about perceptual-based color correction of digital images in the framework of variational techniques. We propose a novel image functional whose minimization produces a perceptually inspired color enhanced version of the original. The variational formulation permits a more flexible local control of contrast adjustment and attachment to data. We show that a numerical implementation of the gradient descent technique applied to this energy functional coincides with the equation of automatic color enhancement (ACE), a particular perceptual-based model of color enhancement. Moreover, we prove that a numerical approximation of the Euler-Lagrange equation reduces the computational complexity of ACE from theta(N2) to theta(N log N), where N is the total number of pixels in the image.

Duality Principle for Image Regularization and Perceptual Color Correction Models

“…Regarding contrast modification, the pioneer variational approach is due to Sapiro and Caselles [23], who performed contrast enhancement for histogram equalization purpose. Since then, this variational formulation has been generalized and applied in different contexts: perceptual color correction [4], [20], tone mapping [14], and gamut mapping [25] to name a few. Connections have also been made between the variational formulation [4] and Retinex theory [5], [6].…”

Fusion-based Variational Image Dehazing

“…We typically observe a number of iterations between 6 and 12. The FFT technique proposed in [24] can also be applied here, delivering an O(n) complexity, which in our implementation requires 90 seconds to process a 1 MP image 1 . An algorithmic analysis of the minimization of the energy in [24], which lies at the core of the proposed technique, is available at [25].…”

Wasserstein regularization of imaging problem

“…based on the Euclidean norm, the Total Variation, the Sobolev norm, or the curvature of level set) and a supplementary term devoted to the desired contrast or color change (see e.g. [7,8,9]). As shown in these references, the intrinsic advantage of using this kind of variational framework is that it enables to preserve geometrical information of the original image and to control the regularity of the transformation so that it prevents the apparition of the aforementioned artefacts.…”

“…Indeed, most of approaches have been proposed for one-dimensional statistics (for instance in [8] for local histogram equalization). Recently in [9], the difficulty of designing penalty term with multi-dimensional data such as color cloud is circumvented by the use of cumulated histograms.…”