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Digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids. Such methods have been widely used in many medical imaging applications, including image segmentation, visualization, manipulation, interpolation, registration, surface-tracking, object representation, correction, quantitative morphometry etc. Digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability, fidelity, and efficiency. This paper presents a comprehensive yet compact survey on results, principles, and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications. Specifically, this paper reviews methods related to distance analysis and path propagation, connectivity, surface-tracking, image segmentation, boundary and centerline detection, topology preservation and local topological properties, skeletonization, and object representation, correction, and quantitative morphometry. A common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity, path propagation, and neighborhood analysis. [ABSTRACT FROM AUTHOR]

This work presents the results of a new tool for 3-D segmentation, quantification and visualization of cardiac left atrium fibrosis, based on late gadolinium enhancement magnetic resonance imaging (LGE-MRI), for stratifying patients with atrial fibrillation (AF) that are candidates for radio-frequency catheter ablation. In this study 10 consecutive patients suffering AF with different grades of atrial fibrosis were considered. LGE-MRI and magnetic resonance angiography (MRA) images were used to detect and quantify fibrosis of the left atrium using a threshold and 2-D skeleton based approach. Quantification and 3-D volumetric views of atrial fibrosis were compared with quantification and 3-D bipolar voltage maps measured with an electro-anatomical mapping (EAM) system, the clinical reference standard technique for atrial substrate characterization. Segmentation and quantification of fibrosis areas proved to be clinically reliable among all different fibrosis stages. The proposed tool obtains discrepancies in fibrosis quantification less than 4% from EAM results and yields accurate 3-D volumetric views of fibrosis of left atrium. The novel 3-D visualization and quantification tool based on LGE-MRI allows detection of cardiac left atrium fibrosis areas. This noninvasive method provides a clinical alternative to EAM systems for quantification and localization of atrial fibrosis. [ABSTRACT FROM AUTHOR]

Trabecular bone (TB) is a complex quasi-random network of interconnected plates and rods. TB constantly remodels to adapt to the stresses to which it is subjected (Wolff's Law). In osteoporosis, this dynamic equilibrium between bone formation and resorption is perturbed, leading to bone loss and structural deterioration. Both bone loss and structural deterioration increase fracture risk. Bone's mechanical behavior can only be partially explained by variations in bone mineral density, which led to the notion of bone structural quality. Previously, we developed digital topological analysis (DTA) which classifies plates, rods, profiles, edges, and junctions in a TB skeletal representation. Although the method has become quite popular, a major limitation of DTA is that it provides only hard classifications of different topological entities, failing to distinguish between narrow and wide plates. Here, we present a new method called volumetric topological analysis (VTA) for regional quantification of TB topology. At each TB location, the method uniquely classifies its topology on the continuum between perfect plates and perfect rods, facilitating early detections of TB alterations from plates to rods according to the known etiology of osteoporotic bone loss. Several new ideas, including manifold distance transform, manifold scale, and feature propagation have been introduced here and combined with existing DTA and distance transform methods, leading to the new VTA technology. This method has been applied to multidetector computed tomography (CT) and micro-computed tomography (\mu\ CT) images of four cadaveric distal tibia and five distal radius specimens. Both intra- and inter-modality reproducibility of the method has been examined using repeat CT and \mu\ CT scans of distal tibia specimens. Also, the method's ability to predict experimental biomechanical properties of TB via CT imaging under in vivo conditions has been quantitatively examined and the results found are very encouraging. [ABSTRACT FROM PUBLISHER]