Quantification of the plant endoplasmic reticulum

One of the challenges of quantitative approaches to biological sciences is the lack of understanding of the interplay between form and function. Each cell is full of complex-shaped objects, which moreover change their form over time. To address this issue, we exploit recent advances in confocal microscopy, by using data collected from a series of optical sections taken at short regular intervals along the optical axis to reconstruct the Endoplasmic Reticulum (ER) in 3D, obtain its skeleton, then associate to each of its edges key geometric and dynamic characteristics obtained from the original filled in ER specimen. These properties include the total length, surface area, and volume of the ER specimen, as well as the length surface area, and volume of each of its branches. In a view to benefit from the well established graph theory algorithms, we abstract the obtained skeleton by a mathematical entity that is a graph. We achieve this by replacing the inner points in each edge in the skeleton by the line segment connecting its end points. We then attach to this graph the ER geometric properties as weights, allowing therefore a more precise quantitative characterisation, by thinning the filled in ER to its essential features. The graph plays a major role in this study and is the final and most abstract quantification of the ER. One of its advantages is that it serves as a geometric invariant, both in static and dynamic samples. Moreover, graph theoretic features, such as the number of vertices and their degrees, and the number of edges and their lengths are robust against different kinds of small perturbations. We propose a methodology to associate parameters such as surface areas and volumes to its individual edges and monitor their variations with time. One of the main contributions of this thesis is the use of the skeleton of the ER to analyse the trajectories of moving junctions using confocal digital videos. We report that the ER could be modeled by a network of connected cylinders (0.87μm±0.36 in diameter) with a majority of 3-way junctions. The average length, surface area and volume of an ER branch are found to be 2.78±2.04μm, 7.53±5.59μm2 and 1.81±1.86μm3 respectively. Using the analysis of variance technique we found that there are no significant differences in four different locations across the cell at 0.05 significance level. The apparent movement of the junctions in the plant ER consists of different types, namely: (a) the extension and shrinkage of tubules, and (b) the closing and opening of loops. The average velocity of a junction is found to be 0.25μm/sec±0.23 and lies in the range 0 to 1.7μm/sec which matches the reported actin filament range

Automated CAD Model Generation for Structural Optimisation

Computer-aided design (CAD) models play a crucial role in the design, manufacturing and maintenance of products. Therefore, the mesh-based finite element descriptions common in structural optimisation must be first translated into CAD models. Currently, this translation either can be performed semi-manually or fails to reserve the structural optimality found by the structural optimisation due to the intrinsic difference in geometric representation between finite element mesh and CAD model. This thesis propose a fully automated and topologically accurate approach to synthesise structurally sound parametric CAD models from topology-optimised finite element models to fill the long-existing gap between structural optimisation and CAD systems. This approach successfully preserves the optimal structural performance during the mesh-CAD conversion. The solution provided in this thesis is to first convert the topology-optimised structure into a spatial frame structure and then to regenerate it in a CAD system using standard constructive solid geometry (CSG) operations. The obtained parametric CAD models are compact, that is, have as few as possible geometric parameters, which makes them ideal for editing and further processing within a CAD system. The critical task of converting the topology-optimised structure into an optimal spatial frame structure is accomplished in several steps. The first step is to generate a one-voxel-wide voxel chain model from the topology-optimised voxel model using a topology-preserving skeletonisation algorithm from digital topology. The undirected graph defined by the voxel chain model yields a spatial frame structure after processing it with the proposed graph algorithms. Subsequently, the cross-sections and layout of the frame members are optimised to recover its optimality, which may have been compromised during the conversion process. At last, the obtained frame structure is generated in a CAD system by repeatedly combining primitive solids, like cylinders and spheres, using boolean operations. The resulting solid model is a boundary representation (B-Rep) consisting of trimmed non-uniform rational B-spline (NURBS) curves and surfaces. The numerical studies in this thesis clarify that the converted spatial frame structures are with equivalent structural performance. Moreover, CAD models generated from the spatial frame structures have significantly fewer geometric degree of freedom compared to the topology-optimised structures. Though the numerical studies use topology-optimised structures as input and compact CSG models as output, this thesis also provides the way to extend the proposed generation process to taking other optimised meshes and producing outputs of various geometric representations. This offers a wide range of possible applications and brings new thoughts to industrial design and manufacturing.Chinese Scholarship Counci

High-performance geometric vascular modelling

Image-based high-performance geometric vascular modelling and reconstruction is an essential component of computer-assisted surgery on the diagnosis, analysis and treatment of cardiovascular diseases. However, it is an extremely challenging task to efficiently reconstruct the accurate geometric structures of blood vessels out of medical images. For one thing, the shape of an individual section of a blood vessel is highly irregular because of the squeeze of other tissues and the deformation caused by vascular diseases. For another, a vascular system is a very complicated network of blood vessels with different types of branching structures. Although some existing vascular modelling techniques can reconstruct the geometric structure of a vascular system, they are either time-consuming or lacking sufficient accuracy. What is more, these techniques rarely consider the interior tissue of the vascular wall, which consists of complicated layered structures. As a result, it is necessary to develop a better vascular geometric modelling technique, which is not only of high performance and high accuracy in the reconstruction of vascular surfaces, but can also be used to model the interior tissue structures of the vascular walls.This research aims to develop a state-of-the-art patient-specific medical image-based geometric vascular modelling technique to solve the above problems. The main contributions of this research are:- Developed and proposed the Skeleton Marching technique to reconstruct the geometric structures of blood vessels with high performance and high accuracy. With the proposed technique, the highly complicated vascular reconstruction task is reduced to a set of simple localised geometric reconstruction tasks, which can be carried out in a parallel manner. These locally reconstructed vascular geometric segments are then combined together using shape-preserving blending operations to faithfully represent the geometric shape of the whole vascular system.- Developed and proposed the Thin Implicit Patch method to realistically model the interior geometric structures of the vascular tissues. This method allows the multi-layer interior tissue structures to be embedded inside the vascular wall to illustrate the geometric details of the blood vessel in real world

Lincoln's Annotated Spatio-Temporal Strawberry Dataset (LAST-Straw)

Automated phenotyping of plants for breeding and plant studies promises to provide quantitative metrics on plant traits at a previously unattainable observation frequency. Developers of tools for performing high-throughput phenotyping are, however, constrained by the availability of relevant datasets on which to perform validation. To this end, we present a spatio-temporal dataset of 3D point clouds of strawberry plants for two varieties, totalling 84 individual point clouds. We focus on the end use of such tools - the extraction of biologically relevant phenotypes - and demonstrate a phenotyping pipeline on the dataset. This comprises of the steps, including; segmentation, skeletonisation and tracking, and we detail how each stage facilitates the extraction of different phenotypes or provision of data insights. We particularly note that assessment is focused on the validation of phenotypes, extracted from the representations acquired at each step of the pipeline, rather than singularly focusing on assessing the representation itself. Therefore, where possible, we provide \textit{in silico} ground truth baselines for the phenotypes extracted at each step and introduce methodology for the quantitative assessment of skeletonisation and the length trait extracted thereof. This dataset contributes to the corpus of freely available agricultural/horticultural spatio-temporal data for the development of next-generation phenotyping tools, increasing the number of plant varieties available for research in this field and providing a basis for genuine comparison of new phenotyping methodology

Discrete bisector function and Euclidean skeleton in 2D and 3D

International audienceWe propose a new definition and an exact algorithm for the discrete bisector function, which is an important tool for analyzing and filtering Euclidean skeletons. We also introduce a new thinning algorithm which produces homotopic discrete Euclidean skeletons. These algorithms, which are valid both in 2D and 3D, are integrated in a skeletonization method which is based on exact transformations, allows the filtering of skeletons, and is computationally efficient

Quantification of the plant endoplasmic reticulum

One of the challenges of quantitative approaches to biological sciences is the lack of understanding of the interplay between form and function. Each cell is full of complex-shaped objects, which moreover change their form over time. To address this issue, we exploit recent advances in confocal microscopy, by using data collected from a series of optical sections taken at short regular intervals along the optical axis to reconstruct the Endoplasmic Reticulum (ER) in 3D, obtain its skeleton, then associate to each of its edges key geometric and dynamic characteristics obtained from the original filled in ER specimen. These properties include the total length, surface area, and volume of the ER specimen, as well as the length surface area, and volume of each of its branches. In a view to benefit from the well established graph theory algorithms, we abstract the obtained skeleton by a mathematical entity that is a graph. We achieve this by replacing the inner points in each edge in the skeleton by the line segment connecting its end points. We then attach to this graph the ER geometric properties as weights, allowing therefore a more precise quantitative characterisation, by thinning the filled in ER to its essential features. The graph plays a major role in this study and is the final and most abstract quantification of the ER. One of its advantages is that it serves as a geometric invariant, both in static and dynamic samples. Moreover, graph theoretic features, such as the number of vertices and their degrees, and the number of edges and their lengths are robust against different kinds of small perturbations. We propose a methodology to associate parameters such as surface areas and volumes to its individual edges and monitor their variations with time. One of the main contributions of this thesis is the use of the skeleton of the ER to analyse the trajectories of moving junctions using confocal digital videos. We report that the ER could be modeled by a network of connected cylinders (0.87μm±0.36 in diameter) with a majority of 3-way junctions. The average length, surface area and volume of an ER branch are found to be 2.78±2.04μm, 7.53±5.59μm2 and 1.81±1.86μm3 respectively. Using the analysis of variance technique we found that there are no significant differences in four different locations across the cell at 0.05 significance level. The apparent movement of the junctions in the plant ER consists of different types, namely: (a) the extension and shrinkage of tubules, and (b) the closing and opening of loops. The average velocity of a junction is found to be 0.25μm/sec±0.23 and lies in the range 0 to 1.7μm/sec which matches the reported actin filament range.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research Council (Great Britain) (EPSRC)University of Warwick. Molecular Organisation and Assembly in Cells (MOAC)Rodger, AlisonGBUnited Kingdo

Analysis of Dynamic Magnetic Resonance Breast Images

Dynamic Magnetic Resonance Imaging is a non-invasive technique that provides an image sequence based on dynamic information for locating lesions and investigating their structures. In this thesis we develop new methodology for analysing dynamic Magnetic Resonance image sequences of the breast. This methodology comprises an image restoration step that reduces random distortions affecting the data and an image classification step that identifies normal, benign or malignant tumoral tissues. In the first part of this thesis we present a non-parametric and a parametric approach for image restoration and classification. Both methods are developed within the Bayesian framework. A prior distribution modelling both spatial homogeneity and temporal continuity between neighbouring image pixels is employed. Statistical inference is performed by means of a Metropolis-Hastings algorithm with a specially chosen proposal distribution that out-performs other algorithms of the same family. We also provide novel procedures for estimating the hyper-parameters of the prior models and the normalizing constant so making the Bayesian methodology automatic. In the second part of this thesis we present new methodology for image classification based on deformable templates of a prototype shape. Our approach uses higher level knowledge about the tumour structure than the spatio-temporal prior distribution of our Bayesian methodology. The prototype shape is deformed to identify the structure of the malignant tumoral tissue by minimizing a novel objective function over the parameters of a set of non-affine transformations. Since these transformations can destroy the connectivity of the shape, we develop a new filter that restores connectivity without smoothing the shape. The restoration and classification results obtained from a small sample of image sequences are very encouraging. In order to validate these results on a larger sample, in the last part of the thesis we present a user friendly software package that implements our methodology

Robust Modular Feature-Based Terrain-Aided Visual Navigation and Mapping

The visual feature-based Terrain-Aided Navigation (TAN) system presented in this thesis addresses the problem of constraining inertial drift introduced into the location estimate of Unmanned Aerial Vehicles (UAVs) in GPS-denied environment. The presented TAN system utilises salient visual features representing semantic or human-interpretable objects (roads, forest and water boundaries) from onboard aerial imagery and associates them to a database of reference features created a-priori, through application of the same feature detection algorithms to satellite imagery. Correlation of the detected features with the reference features via a series of the robust data association steps allows a localisation solution to be achieved with a finite absolute bound precision defined by the certainty of the reference dataset. The feature-based Visual Navigation System (VNS) presented in this thesis was originally developed for a navigation application using simulated multi-year satellite image datasets. The extension of the system application into the mapping domain, in turn, has been based on the real (not simulated) flight data and imagery. In the mapping study the full potential of the system, being a versatile tool for enhancing the accuracy of the information derived from the aerial imagery has been demonstrated. Not only have the visual features, such as road networks, shorelines and water bodies, been used to obtain a position ’fix’, they have also been used in reverse for accurate mapping of vehicles detected on the roads into an inertial space with improved precision. Combined correction of the geo-coding errors and improved aircraft localisation formed a robust solution to the defense mapping application. A system of the proposed design will provide a complete independent navigation solution to an autonomous UAV and additionally give it object tracking capability

Geometric and Topological Methods for Applications to Materials and Data Skeletonisation

Crystal Structure Prediction (CSP) aims to speed up functional materials discovery by using supercomputers to predict whether an input molecule can form stable crystal struc- tures with desirable properties. The process produces large datasets where each entry is a simulated arrangement of copies of the input molecule to form a crystal. However, these datasets have little structure themselves, and it is the aim of this thesis to contribute towards simplifying and analysing such datasets. Crystals are unbounded collections of atoms or molecules, extending infinitely in the space they lie within. As such, rigorously quantifying the geometric similarity of crystal structures, and even just identifying identical structures, is a challenging problem. To solve it, we seek a continuous, complete, isometry classification of crystals. Consequently, by modelling crystals as periodic point sets, we introduce the density fingerprint, which is invariant under isometries, Lipschitz continuous, and complete for an open and dense space of crystal structures. Such a classification will be able to identify and remove near- duplicates from these large CSP datasets, and potentially even guide future searches. We describe how this fingerprint can be computed using periodic higher Voronoi zones. This geometric concept of concentric regions around a fixed centre characterises relative positions of points from the centre in a periodic point set. We present an algorithm to compute these zones in addition to proving key structural properties. We later discuss research into skeletonisation algorithms, proving theoretical guarantees of the homological persistent skeleton (HoPeS), subsequently formulating and performing an experimental comparison of HoPeS with other relevant algorithms. Such algorithms, if effectively used, can be applied to large datasets including those produced by CSP to reveal the shape of the data, helping to highlight regions of interest and branches that merit further study