Extending minkowski norm illuminant estimation

The ability to obtain colour images invariant to changes of illumination is called colour constancy. An algorithm for colour constancy takes sensor responses - digital images - as input, estimates the ambient light and returns a corrected image in which the illuminant influence over the colours has been removed. In this thesis we investigate the step of illuminant estimation for colour constancy and aim to extend the state of the art in this field. We first revisit the Minkowski Family Norm framework for illuminant estimation. Because, of all the simple statistical approaches, it is the most general formulation and, crucially, delivers the best results. This thesis makes four technical contributions. First, we reformulate the Minkowski approach to provide better estimation when a constraint on illumination is employed. Second, we show how the method can (by orders of magnitude) be implemented to run much faster than previous algorithms. Third, we show how a simple edge based variant delivers improved estimation compared with the state of the art across many datasets. In contradistinction to the prior state of the art our definition of edges is fixed (a simple combination of first and second derivatives) i.e. we do not tune our algorithm to particular image datasets. This performance is further improved by incorporating a gamut constraint on surface colour -our 4th contribution. The thesis finishes by considering our approach in the context of a recent OSA competition run to benchmark computational algorithms operating on physiologically relevant cone based input data. Here we find that Constrained Minkowski Norms operi ii ating on spectrally sharpened cone sensors (linear combinations of the cones that behave more like camera sensors) supports competition leading illuminant estimation

Rank-based camera spectral sensitivity estimation

In order to accurately predict a digital camera response to spectral stimuli, the spectral sensitivity functions of its sensor need to be known. These functions can be determined by direct measurement in the lab—a difficult and lengthy procedure—or through simple statistical inference. Statistical inference methods are based on the observation that when a camera responds linearly to spectral stimuli, the device spectral sensitivities are linearly related to the camera rgb response values, and so can be found through regression. However, for rendered images, such as the JPEG images taken by a mobile phone, this assumption of linearity is violated. Even small departures from linearity can negatively impact the accuracy of the recovered spectral sensitivities, when a regression method is used. In our work, we develop a novel camera spectral sensitivity estimation technique that can recover the linear device spectral sensitivities from linear images and the effective linear sensitivities from rendered images. According to our method, the rank order of a pair of responses imposes a constraint on the shape of the underlying spectral sensitivity curve (of the sensor). Technically, each rank-pair splits the space where the underlying sensor might lie in two parts (a feasible region and an infeasible region). By intersecting the feasible regions from all the ranked-pairs, we can find a feasible region of sensor space. Experiments demonstrate that using rank orders delivers equal estimation to the prior art. However, the Rank-based method delivers a step-change in estimation performance when the data is not linear and, for the first time, allows for the estimation of the effective sensitivities of devices that may not even have “raw mode.” Experiments validate our method

Cubical Gamut Mapping Colour Constancy

A new color constancy algorithm called Cubical Gamut Mapping (CGM) is introduced. CGM is computationally very simple, yet performs better than many currently known algorithms in terms of median illumination estimation error. Moreover, it can be tuned to minimize the maximum error. Being able to reduce the maximum error, possibly at the expense of increased median error, is an advantage over many published color constancy algorithms, which may perform quite well in terms of median illumination-estimation error, but have very poor worst-case performance. CGM is based on principles similar to existing gamut mapping algorithms; however, it represents the gamut of image chromaticities as a simple cube characterized by the image’s maximum and minimum rgb chromaticities rather than their more complicated convex hull. It also uses the maximal RGBs as an additional source of information about the illuminant. The estimate of the scene illuminant is obtained by linearly mapping the chromaticity of the maximum RGB, minimum rgb and maximum rgb values. The algorithm is trained off-line on a set of synthetically generated images. Linear programming techniques for optimizing the mapping both in terms of the sum of errors and in terms of the maximum error are used. CGM uses a very simple image pre-processing stage that does not require image segmentation. For each pixel in the image, the pixels in the Nby- N surrounding block are averaged. The pixels for which at least one of the neighbouring pixels in the N-by-N surrounding block differs from the average by more than a given threshold are removed. This pre-processing not only improves CGM, but also improves the performance of other published algorithms such as max RGB and Grey World