The Discrete Cosine Maximum Ignorance Assumption

Abstract

The performance of colour correction algorithms are dependent on the reflectance sets used. Sometimes, when the testing reflectance set is changed the ranking of colour correction algorithms also changes. To remove dependence on dataset we can make assumptions about the set of all possible reflectances. In the Maximum Ignorance with Positivity (MIP) assumption we assume that all reflectances with per wavelength values between 0 and 1 are equally likely. A weakness in the MIP is that it fails to take into account the correlation of reflectance functions between wavelengths (many of the assumed reflectances are, in reality, not possible). In this paper, we take the view that the maximum ignorance assumption has merit but, hitherto it has been calculated with respect to the wrong coordinate basis. Here, we propose the Discrete Cosine Maximum Ignorance assumption (DCMI), where all reflectances that have coordinates between max and min bounds in the Discrete Cosine Basis coordinate system are equally likely. Here, the correlation between wavelengths is encoded and this results in the set of all plausible reflectances 'looking like' typical reflectances that occur in nature. This said the DCMI model is also a superset of all measured reflectance sets. Experiments show that, in colour correction, adopting the DCMI results in similar colour correction performance as using a particular reflectance set.

Mondrian Representation of Real World Scene Statistics

“…5, maximum autocorrelation is seen along the main diagonal and minimum autocorrelation is seen everywhere else. In fact, this corresponds to the so-called Maximum Ignorance with Positivity assumption [2] that was made in connection with camera characterisation (colour correction), where the vectors are all possible spectral colour signals with positive power.…”

“…The autocorrelation matrix describes the correlation between all pairs of elements of a vector or vectors that represent the same stimuli. In the domain of imaging, it is widely used to describe the spectral statistics of surface reflectance and illumination spectra [1] and is central to colour characterisation and calibration [2,3,4]. Autocorrelation matrices are also used in the context of lightness perception algorithms [5], where the vectors that we autocorrelate describe paths of pixel values through images [6].…”

Practical RGB-to-XYZ Color Transformation Matrix Estimation under Different Lighting Conditions for Graffiti Documentation

“…One way to address the variation in the RGB-to-XYZ matrix is via the WPP constraint [ 12 , 13 ], which normalizes the RGB and XYZ data into the range [0, 1] using the reflectance closest to a perfect white diffuser. Effectively, all RAW RGB and CIE XYZ values are divided by the RGB and XYZ coordinates corresponding to a white patch on a color reference target.…”

“…in which tonal range refers to the image's potential different tones, a number defined by the bit depth of the image (e.g., a 12-bit RAW image maximally contains 2 12 -1 or 4095 tonal levels).…”

“…Different methodologies have been developed to estimate this RGB-to-XYZ transformation matrix [ 7 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ]. For all of them, it is highly recommended to use RAW RGB values for the computations since RAW data tend to be linear to the image radiance [ 11 , 20 ].…”