A Class of Nonlocal Variational Problems on a Vector Bundle for Color Image Local Contrast Reduction/Enhancement.

Thomas Batard (1) , Marcelo Bertalmío (1)

1 Image Processing for Enhanced Cinematography

We extend two existing variational models from the Euclidean space to a vector bundle over a Riemannian manifold. The Euclidean models , dedicated to regularize or enhance some color image features, are based on the concept of nonlocal gradient operator acting on a function of the Euclidean space. We then extend these models by generalizing this operator to a vector bundle over a Riemannian manifold with the help of the parallel transport map associated to some class of covariant derivatives. Through the dual formulations of the proposed models, we obtain the expressions of their solutions, which exhibit the functional spaces that describe the image features. Finally, for a well-chosen covariant derivative and its nonlocal extension, the proposed models perform local contrast modification (reduction or enhancement) and experiments show that they preserve more the aspect of the original image than the Euclidean models do while modifying equally its contrast.

Mots clés: nonlocal variational model; vector bundle; covariant derivative; image contrast reduction/enhancement; primal-dual algorithm

Domaines: Géométrie différentielle [math.DG]; Traitement des images [eess.IV]

Thomas Batard, Marcelo Bertalmío. A Class of Nonlocal Variational Problems on a Vector Bundle for Color Image Local Contrast Reduction/Enhancement. . 2016. ⟨hal-01202922v2⟩