2020/03/14 by Stanislav Katina, Katina, Stanislav, Liberty Vittert +3 · 1 citation
Mathematics · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Methodology (stat.ME) #Morphological variations and asymmetry
paper · pdf · doi:10.48550/arxiv.2003.08817
openalex publication_date 2020/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The advent of high resolution imaging has made data on surface shape\nwidespread. Methods for the analysis of shape based on landmarks are well\nestablished but high resolution data require a functional approach. The\nstarting point is a systematic and consistent description of each surface\nshape. Three innovative forms of analysis are then introduced. The first uses\nsurface integration to address issues of registration, principal component\nanalysis and the measurement of asymmetry, all in functional form.\nComputational issues are handled through discrete approximations to integrals,\nbased in this case on appropriate surface area weighted sums. The second\ninnovation is to focus on sub-spaces where interesting behaviour such as group\ndifferences are exhibited, rather than on individual principal components. The\nthird innovation concerns the comparison of individual shapes with a relevant\ncontrol set, where the concept of a normal range is extended to the highly\nmultivariate setting of surface shape. This has particularly strong\napplications to medical contexts where the assessment of individual patients is\nvery important. All of these ideas are developed and illustrated in the\nimportant context of human facial shape, with a strong emphasis on the\neffective visual communication of effects of interest.\n