Color Correction Using Root-Polynomial Regression

Abstract

Cameras record three color responses (RG B) which are device dependent. Camera coordinates are mapped to a standard color space, such as XYZ-useful for color measurement-by a mapping function, e.g., the simple 3×3 linear transform (usually derived through regression). This mapping, which we will refer to as linear color correction (LCC), has been demonstrated to work well in the number of studies. However, it can map RG Bs to XYZs with high error. The advantage of the LCC is that it is independent of camera exposure. An alternative and potentially more powerful method for color correction is polynomial color correction (PCC). Here, the R, G, and B values at a pixel are extended by the polynomial terms. For a given calibration training set PCC can significantly reduce the colorimetric error. However, the PCC fit depends on exposure, i.e., as exposure changes the vector of polynomial components is altered in a nonlinear way which results in hue and saturation shifts. This paper proposes a new polynomial-type regression loosely related to the idea of fractional polynomials which we call root-PCC (RPCC). Our idea is to take each term in a polynomial expansion and take its kth root of each k-degree term. It is easy to show terms defined in this way scale with exposure. RPCC is a simple (low complexity) extension of LCC. The experiments presented in this paper demonstrate that RPCC enhances color correction performance on real and synthetic data.

An automated, high-throughput method for standardizing image color profiles to improve image-based plant phenotyping

“…For example, variation within an image dataset can have a significant impact on phenotype inferences and so must be considered. For a given pixel that is stored in an image there are three values, one for each component (red, green, and blue; RGB) (Finlayson et al, 2015;Gunturk et al, 2005). Image brightness is an overview of how large the values are for each pixel, and image contrast is defined as the range of pixel values.…”

Camera Color Correction Using Normalized Signal Polynomial Regression

“…A model was evaluated using the leave-one-out method [6]. The model was built from all but one of the color patches and it was tested on the remaining color patch.…”

“…Unfortunately, the linear relation is not valid for the case using polynomial regression. Reference [6] proposed a method using root-polynomial regression for keeping the linear relation. Camera color device models using linear regression, polynomial regression, and rootpolynomial regression are called the linear regression model (LRM), polynomial regression model (PRM), and rootpolynomial regression model (RPRM), respectively.…”

“…The third order is also the optimal order for [6]. The number of terms in p is denoted as L. From (3) and (4), L= 19 and 13 for the third order PRM and RPRM, respectively.…”

Learning-Aided Physical Layer Authentication as an Intelligent Process

“…In order to overcome these difficulties, the kernel-based machine learning technique of [27]- [30] is applied for modeling the authentication problem in this paper. Although the family of parametric learning methods has become mature in the literature [31]- [35], as exemplified by the linear regression methods of [31] and the polynomial regression methods of [32], [33], these parametric techniques usually rely on the assumption of knowing the distribution of samples [36] and the decision tree based solutions [37]. However, these two nonparametric methods have a limited ability to deal with challenges C2-C4.…”