Color Sparse Representations for Image Processing: Review, Models, and Prospects

Quentin Barthélemy (1, 2) , Anthony Larue (1) , Jerome I. Mars (2)

1 LOAD (CEA, LIST) - Laboratoire Outils d'Analyse des Données (CEA, LIST)
2 GIPSA-SIGMAPHY - GIPSA - Signal Images Physique

Sparse representations have been extended to deal with color images composed of three channels. A review of dictionary-learning-based sparse representations for color images is made here, detailing the differences between the models, and comparing their results on real data and simulated data. These models are considered in a unifying framework that is based on the degrees of freedom of the linear filtering/transformation of the color channels. Moreover, this allows it to be shown that the scalar quaternionic linear model is equivalent to constrained matrix-based color filtering, which highlights the filtering implicitly applied through this model. Based on this reformulation, the new color filtering model is introduced, using unconstrained filters. In this model, spatial morphologies of color images are encoded by atoms, and colors are encoded by color filters. Color variability is no longer captured in increasing the dictionary size, but with color filters, this gives an efficient color representation.

Mots clés: DECOMPOSITION; HYPERCOMPLEX; ALGORITHM; DICTIONARIES; COMPONENT ANALYSIS; FOURIER-TRANSFORMS; MATRIX-FACTORIZATION; OVERCOMPLETE REPRESENTATIONS; color filter; LINEAR INVERSE PROBLEMS; quaternion; model; color image; dictionary learning; Index Terms—Sparse representation; sparse coding; machine learning; artificial intelligence; online learning

Domaines: Traitement du signal et de l'image [eess.SP]

Quentin Barthélemy, Anthony Larue, Jerome I. Mars. Color Sparse Representations for Image Processing: Review, Models, and Prospects. IEEE Transactions on Image Processing, 2015, 24 (11), pp.3978-3989. ⟨10.1109/TIP.2015.2458175⟩. ⟨hal-01187517⟩