A Natural Norm for Color Processing
ACCV '98 Proceedings of the Third Asian Conference on Computer Vision-Volume I - Volume I
A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
SIAM Journal on Matrix Analysis and Applications
Statistical variability in nonlinear spaces: application to shape analysis and dt-mri
Statistical variability in nonlinear spaces: application to shape analysis and dt-mri
Riemannian curvature-driven flows for tensor-valued data
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Image quality assessment: from error visibility to structural similarity
IEEE Transactions on Image Processing
An information fidelity criterion for image quality assessment using natural scene statistics
IEEE Transactions on Image Processing
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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 formulæ, 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.