In this paper, we propose a novel method for the registration of volumetric images of the brain that optimizes the alignment of both cortical and subcortical structures. In order to achieve this, relevant geometrical information is extracted from a surface-based morph and diffused into the volume using the Navier operator of elasticity, resulting in a volumetric warp that aligns cortical folding patterns. This warp field is then refined with an intensity driven optical flow procedure that registers noncortical regions, while preserving the cortical alignment. The result is a combined surface and volume morph (CVS) that accurately registers both cortical and subcortical regions, establishing a single coordinate system suitable for the entire brain.

Based on recent work on Stochastic Partial Differential Equations (SPDEs), this paper presents a simple and well-founded method to implement the stochastic evolution of a curve. First, we explain why great care should be taken when considering such an evolution in a Level Set framework. To guarantee the well-posedness of the evolution and to make it independent of the implicit representation of the initial curve, a Stratonovich differential has to be introduced. To implement this differential, a standard Ito plus drift approximation is proposed to turn an implicit scheme into an explicit one. Subsequently, we consider shape optimization techniques, which are a common framework to address various applications in Computer Vision, like segmentation, tracking, stereo vision etc. The objective of our approach is to improve these methods through the introduction of stochastic motion principles. The extension we propose can deal with local minima and with complex cases where the gradient of the objective function with respect to the shape is impossible to derive exactly. Finally, as an application, we focus on image segmentation methods, leading to what we call Stochastic Active Contours.

Entorhinal cortex displays a distinctive organization in layer II and forms small elevations on its surface called entorhinal verrucae. In Alzheimer’s disease, the verrucae disappear due to neurofibrillary tangle formation and neuronal death. Isosurface models were reconstructed from high resolution ex vivo MRI volumes scanned at 7.0 T and individual verruca were measured quantitatively for height, width, volume, and surface area on control and mild Alzheimer’s cases. Mean verruca height was 0.13 ± 0.04 mm for our cognitively normal (controls) sample set whereas for mild AD samples mean height was 0.11 mm ± 0.05 mm (p < 0.001) in entorhinal cortex (n=10 cases). These quantitative methods were validated by a significant correlation of verrucae height and volume with qualitative verrucae ratings (n=36 cases). Entorhinal surfaces were significantly different from other cortical heights such as, cingulate, frontal, occipital, parietal and temporal cortices. Colocalization of verrucae with entorhinal islands was confirmed in ex vivo MRI and, moreover, verrucae ratings were negatively correlated to Braak and Braak pathological stage. This study characterizes novel methods to measure individual entorhinal verruca size, and shows that verrucae size correlates to Alzheimer’s pathology. Taken together, these results suggest that verrucae may have the potential to serve as an early and specific morphological marker for mild cognitive impairment and Alzheimer’s disease.