Digital Topology and Geometry in Medical Imaging: A Survey

Abstract

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.

A semi-automatic framework of measuring pulmonary arterial metrics at anatomic airway locations using CT imaging

“…To generate an accurate centerline connecting two endpoints, a minimum-cost path approach 18 was applied. Here, a medialness measure called collision impact 19 was used to define the cost function to impose the centerness of a path.…”

Trabecular bone characterization on the continuum of plates and rods usingin vivoMR imaging and volumetric topological analysis

“…A few examples of trabecular connectivity loss in the binary skeleton shown in (b) are highlighted in green; the matching regions in the fuzzy skeleton are also highlighted. It should be noted that the examples of in-plane connectivity loss of TB network as shown in (b) do not contradict with 3D topology preservation using simple points [29], which guaranteed by most skeletonization algorithms [39]. …”

Classification of anomalous region in human cerebrovascular structure using random forest

“…Here we have generated digital flow to resemble the blood flow in vascular structure. Digital topology has been used for the studies related to this [14], [15], [16]. Using the digital flow based model we have generated different hemodynamic parameters like velocity, wall shear stress etc and from those hemodynamic parameter and some flow based parameter we have designed the feature set which has been used to classify the anomalous part and normal part of the cerebrovascular structure.…”