title: Statistical modelling of local features of three-dimensional shapes
Creators: name: Liu, Yinuo
Publisher: name: University of Glasgow
Year: 2021
Subjects: subject: statistical modelling, multivariate analysis, shape analysis, computational geometry.

description: The rapid development of 3D imaging technology allows data to be collected directly in three-dimensional space. The high accuracy of the images requires further investigations on digitised objects, especially of local features. In the last decade, 3D Local features have played an important role in recognising and modelling real-world 3D objects. This thesis introduces a series of methods for 3D local features, including automatic keypoints detection, 3D model construction with curves, local region detection and statistical analysis of local features. Those methods are not only to build 3D local feature descriptors but also have a wide range of applications, such as shape comparison in medical facial treatments and evolutionary researches in biology. Conventional shape analysis, limited by the data-collection technology, project 3D objects into 2D space to analyse or focus on 3D discrete points which are not close to each other. Those points of anatomical meanings are called landmarks. Researchers used to manually place the landmarks on 2D or 3D images by eyes, but it generates the operator error which is not of interest but has a large influence on shape analysis. This thesis introduces a novel method to automatically estimate the landmarks on 3D models using Bayesian statistics. The Procrustes matching of the landmark sets shows that the variation of Bayesian placements is much smaller than the manual placements. Local shapes like $``$ridges$"$ and $``$valleys$"$, which are considered to contain rich geometric information, can be estimated based on landmarks. Existing methods rely heavily on landmarks, but in most cases, the number of landmarks is not enough and adding extra ones are time-and-labour consuming. A flexible and user-customisable method is introduced in this thesis to deal with complex surfaces marked with as few landmarks as possible. A simulation study is conducted, and the result shows that the method is stable and efficient in terms of local feature description. After the 3D curve is estimated, methods to analyse the local features using the curves are discussed. An algorithm to flexibly dissect the surface along the estimated curve is developed for extracting local pieces or divide the surface into pieces. The novelty of this method is that it applies directly on 3D shapes and dissects the shape along any 3D curves, such as the lip edge on a human facial model. Besides the novel method for 3D shapes, curvatures, which reflect the bending amount along the curves, are calculated. The curvatures of the same local feature on different individuals are aligned to analyse the average shape difference of groups, such as gender and age. A reconstruction procedure from the curvatures is discussed and the effect of noise on choosing the degree of freedom in smoothing is investigated. Another application of the estimated curves is in benchmarking the performance of different 3D camera systems. A new camera system developed by NCTech\textsuperscript{\textregistered}, Edinburgh, is assessed using the evaluation outcome of facial deformity surgeries in Brazil. It is designed to be child-friendly, portable and low-cost. Validation studies are carried out at three stages of the development, and both landmarks and curves are used to evaluate the performance of the new camera system on estimating local features in comparison with mature products from DI4D\textsuperscript{\textregistered} and Artec\textsuperscript{\textregistered}.