A Differential-Geometrical Framework for Color Image Quality Measures

We propose a differential-geometrical framework for color Image Quality Measures (IQMs). Our approach is based on the definition of a relevant image distortion measure in a Riemannian way. To do this, we use the concept of geodesic distance and apply the theoretical setting to exhibit closed-forms for all the differential geometric attributes of two well-know color spaces: Helmholtz and Stiles manifolds. With these formulae, we generalize some useful IQMs from the Euclidean framework to the Riemannian one. Finally, we present some experiments performed on real images, gradually distorted by different kinds of noise to conclude that the Riemannian IQMs are meaningful and relevant.

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