Optimal transport has emerged as a promising and useful tool for supporting modern image processing applications such as medical imaging and scientific visualization. Indeed, the optimal transport theory enables great flexibility in modeling problems related to image registration, as different optimization resources can be successfully used as well as the choice of suitable matching models to align the images. In this paper, we introduce an automated framework for fundus image registration which unifies optimal transport theory, image processing tools, and graph matching schemes into a functional and concise methodology. Given two ocular fundus images, we construct representative graphs which embed in their structures spatial and topological information from the eye's blood vessels. The graphs produced are then used as input by our optimal transport model in order to establish a correspondence between their sets of nodes. Finally, geometric transformations are performed between the images so as to accomplish the registration task properly. Our formulation relies on the solid mathematical foundation of optimal transport as a constrained optimization problem, being also robust when dealing with outliers created during the matching stage. We demonstrate the accuracy and effectiveness of the present framework throughout a comprehensive set of qualitative and quantitative comparisons against several influential state-of-the-art methods on various fundus image databases.

Image registration is an important pre-processing step in several computer vision applications, being crucial in medical imaging systems where patients are examined and diagnosed almost exclusively by images. For fundus images, in which microscopic differences are significant to better support medical decisions, an accurate registration is imperative. Historically, geometric transformations derived from quadratic models have been widely used as a benchmark to perform registration on fundus images, but in this paper, we demonstrate that quadratic and other high-order mappings are not necessarily the best choices for this purpose, even for well-established state-of-the-art registration methods. From a novel overlapping metric designed to determine the best image transformation that maximizes the registration accuracy, we improve the assertiveness of several methods of the literature while still preserving the same computational burden initially reached by those methods.

Existing algorithms for building layouts from geometric primitives are typically designed to cope with requirements such as orthogonal alignment, overlap removal, optimal area usage, hierarchical organization, among others. However, most techniques are able to tackle just a few of those requirements simultaneously, impairing their use and flexibility. In this work we propose a novel methodology for building layouts from geometric primitives that concurrently addresses a wider range of requirements. Relying on multidimensional projection and mixed integer optimization, our approach arranges geometric objects in the visual space so as to generate well structured layouts that preserve the semantic relation among objects while still making an efficient use of display area. Moreover, scalability is handled through a hierarchical representation scheme combined with navigation tools. A comprehensive set of quantitative comparisons against existing geometry-based layouts and applications on text, image, and video data set visualization prove the effectiveness of our approach.

Image inpainting is a challenging topic in computer vision that seeks to recover the natural aspect of an image where data has been partially damaged or occluded by undesired objects. A common drawback not addressed by most inpainting methodologies is that the user must manually provide the inpainting mask as input data to the method. Selecting the inpainting mask is tedious, time consuming and it often requires artistic skills to precisely determine the mask. In this work we design a new tool that allows users to easily select the desirable mask. The proposed framework combines the high-adherence on image contours of the Laplacian Coordinates segmentation approach with the efficiency of a recent inpainting technique that unifies anisotropic diffusion, inner product-based filling order mechanism and exemplar-based completion. The user can interact with the object that he/she intends to edit by stroking small parts of the object so as to proceed with the segmentation and inpainting task. Our comparisons show that the proposed framework has good performance in terms of applicability and effectiveness when compared against other existing techniques in the literature.