Bayesian shape modelling of cross-sectional geological data.

Shape information is of great importance in many applications. For example, the oil-bearing capacity of sand bodies, the subterranean remnants of ancient rivers, is related to their cross-sectional shapes. The analysis of these shapes is therefore of some interest, but current classifications are simplistic and ad hoc. In this paper, we describe the first steps towards a coherent statistical analysis of these shapes by deriving the integrated likelihood for data shapes given class parameters. The result is of interest beyond this particular application

3-D Face Analysis and Identification Based on Statistical Shape Modelling

This paper presents an effective method of statistical shape representation for automatic face analysis and identification in 3-D. The method combines statistical shape modelling techniques and the non-rigid deformation matching scheme. This work is distinguished by three key contributions. The first is the introduction of a new 3-D shape registration method using hierarchical landmark detection and multilevel B-spline warping technique, which allows accurate dense correspondence search for statistical model construction. The second is the shape representation approach, based on Laplacian Eigenmap, which provides a nonlinear submanifold that links underlying structure of facial data. The third contribution is a hybrid method for matching the statistical model and test dataset which controls the levels of the model’s deformation at different matching stages and so increases chance of the successful matching. The proposed method is tested on the public database, BU-3DFE. Results indicate that it can achieve extremely high verification rates in a series of tests, thus providing real-world practicality

TVL₁shape approximation from scattered 3D data

With the emergence in 3D sensors such as laser scanners and 3D reconstruction from cameras, large 3D point clouds can now be sampled from physical objects within a scene. The raw 3D samples delivered by these sensors however, contain only a limited degree of information about the environment the objects exist in, which means that further geometrical high-level modelling is essential. In addition, issues like sparse data measurements, noise, missing samples due to occlusion, and the inherently huge datasets involved in such representations makes this task extremely challenging. This paper addresses these issues by presenting a new 3D shape modelling framework for samples acquired from 3D sensor. Motivated by the success of nonlinear kernel-based approximation techniques in the statistics domain, existing methods using radial basis functions are applied to 3D object shape approximation. The task is framed as an optimization problem and is extended using non-smooth L1 total variation regularization. Appropriate convex energy functionals are constructed and solved by applying the Alternating Direction Method of Multipliers approach, which is then extended using Gauss-Seidel iterations. This significantly lowers the computational complexity involved in generating 3D shape from 3D samples, while both numerical and qualitative analysis confirms the superior shape modelling performance of this new framework compared with existing 3D shape reconstruction techniques

Statistical Shape Modelling for the Levator Ani

Defective pelvic organ support due to injuries of the levator ani is a common problem in women and its intervention requires a thorough understanding of the structure. Three-dimensional surfaces of the levator ani have proved to be a promising method of studying this. In this paper, we propose to build a statistical shape model (SSM) of the levator ani and describe a segmentation technique based on a limited number of control points with the SSM. The SSM was achieved by the use of harmonic shape embedding with the MDL objective function to optimise parameterisation while segmentation was performed by fitting the model to a user defined set of control points. The value of the technique was demonstrated with data acquired from a group of 11 asymptomatic subjects.Accepted versio

Modelling of oedemous limbs and venous ulcers using partial differential equations

BACKGROUND: Oedema, commonly known as tissue swelling, occurs mainly on the leg and the arm. The condition may be associated with a range of causes such as venous diseases, trauma, infection, joint disease and orthopaedic surgery. Oedema is caused by both lymphatic and chronic venous insufficiency, which leads to pooling of blood and fluid in the extremities. This results in swelling, mild redness and scaling of the skin, all of which can culminate in ulceration. METHODS: We present a method to model a wide variety of geometries of limbs affected by oedema and venous ulcers. The shape modelling is based on the PDE method where a set of boundary curves are extracted from 3D scan data and are utilised as boundary conditions to solve a PDE, which provides the geometry of an affected limb. For this work we utilise a mixture of fourth order and sixth order PDEs, the solutions of which enable us to obtain a good representative shape of the limb and associated ulcers in question. RESULTS: A series of examples are discussed demonstrating the capability of the method to produce good representative shapes of limbs by utilising a series of curves extracted from the scan data. In particular we show how the method could be used to model the shape of an arm and a leg with an associated ulcer. CONCLUSION: We show how PDE based shape modelling techniques can be utilised to generate a variety of limb shapes and associated ulcers by means of a series of curves extracted from scan data. We also discuss how the method could be used to manipulate a generic shape of a limb and an associated wound so that the model could be fine-tuned for a particular patient

A statistical shape model for deformable surface

This short paper presents a deformable surface registration scheme which is based on the statistical shape modelling technique. The method consists of two major processing stages, model building and model fitting. A statistical shape model is first built using a set of training data. Then the model is deformed and matched to the new data by a modified iterative closest point (ICP) registration process. The proposed method is tested on real 3-D facial data from BU-3DFE database. It is shown that proposed method can achieve a reasonable result on surface registration, and can be used for patient position monitoring in radiation therapy and potentially can be used for monitoring of the radiation therapy progress for head and neck patients by analysis of facial articulation