Abstract: Anisotropic differential operators are widely used in image enhancement processes. Recently, their property of smoothly extending functions to the whole image domain has begun to be exploited. Strong ellipticity of differential operators is a requirement that ensures existence of a unique solution. This condition is too restrictive for operators designed to extend image level sets: their own functionality implies that they should restrict to some vector field. The diffusion tensor that defines the diffusion operator links anisotropic processes with Riemmanian manifolds. In this context, degeneracy implies restricting diffusion to the varieties generated by the vector fields of positive eigenvalues, provided that an integrability condition is satisfied. We will use that any smooth vector field fulfills this integrability requirement to design line connection algorithms for contour completion. As application we present a segmenting strategy that assures convergent snakes whatever the geometry of the object to be modelled is.

Abstract: Endoscopic estimation of the degree of stenosis in central airway obstruction is subjective and highly variable. Objective: To determine the benefits of using SENSA (System for Endoscopic Stenosis Assessment), an image-based computational software, for obtaining objective stenosis index (SI) measurements among a group of expert bronchoscopists and general pulmonologists. Methods: A total of 7 expert bronchoscopists and 7 general pulmonologists were enrolled to validate SENSA usage. The SI obtained by the physicians and by SENSA were compared with a reference SI to set their precision in SI computation. We used SENSA to efficiently obtain this reference SI in 11 selected cases of benign stenosis. A Web platform with three user-friendly microtasks was designed to gather the data. The users had to visually estimate the SI from videos with and without contours of the normal and the obstructed area provided by SENSA. The users were able to modify the SENSA contours to define the reference SI using morphometric bronchoscopy. Results: Visual SI estimation accuracy was associated with neither bronchoscopic experience (p = 0.71) nor the contours of the normal and the obstructed area provided by the system (p = 0.13). The precision of the SI by SENSA was 97.7% (95% CI: 92.4-103.7), which is significantly better than the precision of the SI by visual estimation (p < 0.001), with an improvement by at least 15%. Conclusion: SENSA provides objective SI measurements with a precision of up to 99.5%, which can be calculated from any bronchoscope using an affordable scalable interface. Providing normal and obstructed contours on bronchoscopic videos does not improve physicians' visual estimation of the SI.

Abstract: Medial surfaces are powerful tools for shape description, but their use has been limited due to the sensibility existing methods to branching artifacts. Medial branching artifacts are associated to perturbations of the object boundary rather than to geometric features. Such instability is a main obstacle for a condent application in shape recognition and description. Medial branches correspond to singularities of the medial surface and, thus, they are problematic for existing morphological and energy-based algorithms. In this paper, we use algebraic geometry concepts in an energy-based approach to compute a medial surface presenting a stable branching topology. We also present an ecient GPU-CPU implementation using standard image processing tools. We show the method computational eciency and quality on a custom made synthetic database. Finally, we present some results on a medical imaging application for localization of abdominal pathologies.