Tensor Calculus in Digital Colorimetry

Abstract

Any object can have many implementations in the form of digital images and any digital image can be processed many times increasing or decreasing accuracy and reliability. Digital colorimetry faces the need to work out issues of ensuring accuracy, metrological traceability and reliability. The purpose of this work was to generalize approaches to the description of multidimensional quantized spaces and show the possibilities of their adaptation to digital colorimetry. This approach will minimize the private and global risks in measurements. For color identification digital colorimetry uses standard color models and spaces. Most of them are empirical and are improved during the transition from standard to real observation conditions taking into account the phenomena of vision and the age of observers. From the point of view of measurement, a digital image can be represented by a combinatorial model of an information and measurement channel with the appearance of the phenomenon of a color covariance hypercube requiring a significant amount of memory for data storage and processing. The transition from the covariance hypercube to high-dimensional matrices and tensors of the first, second and higher ranks provides the prospect of optimizing the color parameters of a digital image by the criterion of information entropy. Tensor calculus provides opportunities for expanding the dynamic range in color measurements describing multidimensional vector fields and quantized spaces with indexing tensors and decomposing them into matrices of low orders. The proposed complex approach based on tensor calculus. According to this approach the color space is a set of directed vector fields undergoing sampling, quantization and coding operations. Also it is a dynamic open system exchanging information with the environment at a given level and to identify color with specified levels of accuracy, reliability, uncertainty and entropy.