Image Atlas Construction via Intrinsic Averaging on the Manifold of Images.

In this paper, we propose a novel algorithm for computing an atlas from a collection of images. In the literature, atlases have almost always been computed as some types of means such as the straightforward Euclidean means or the more general Karcher means on Riemannian manifolds. In the context of images, the paper's main contribution is a geometric framework for computing image atlases through a two-step process: the localization of mean and the realization of it as an image. In the localization step, a few nearest neighbors of the mean among the input images are determined, and the realization step then proceeds to reconstruct the atlas image using these neighbors. Decoupling the localization step from the realization step provides the flexibility that allows us to formulate a general algorithm for computing image atlas. More specifically, we assume the input images belong to some smooth manifold M modulo image rotations. We use a graph structure to represent the manifold, and for the localization step, we formulate a convex optimization problem in ℝ(k) (k the number of input images) to determine the crucial neighbors that are used in the realization step to form the atlas image. The algorithm is both unbiased and rotation-invariant. We have evaluated the algorithm using synthetic and real images. In particular, experimental results demonstrate that the atlases computed using the proposed algorithm preserve important image features and generally enjoy better image quality in comparison with atlases computed using existing methods.