On the Extraction of Topologically Correct Thickness Measurements Using Khalimsky’s Cubic Complex

The extraction of thickness measurements from shapes with spherical topology has been an active area of research in medical imaging. Measuring the thickness of structures from automatic probabilistic segmentations is normally hindered by the presence of noise, partial volume (PV) effects and the limited resolution of medical images. Also, the complexity of certain shapes, like the highly convoluted and PV corrupted cerebral cortex, results in topologically inconsistent measurements. In this paper we explore the use of Khalimsky’s cubic complex for the extraction of topologically correct thickness measurements from probabilistic or fuzzy segmentations without explicit parametrisation of the edge. A sequence of element collapse operations is used to correct the topology of the segmentation. The Laplace equation is then solved between multiple equipotential lines and the thickness measured with an ordered upwind differencing method using an anisotropic grid with the probabilistic segmentation as a speed function. Experiments performed on digital phantoms show that the proposed method obtains topologically correct thickness measurements with an increase in accuracy when compared to two well established techniques. Furthermore, quantitative analysis on brain MRI data showed that the proposed algorithm is able to retrieve expected group differences between the cortical thickness of AD patients and controls with high statistical significance.