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A visualisation tool is presented to facilitate the study on large-scale communications networks. This tool provides a simple and effective way to summarise the topology of a complex network at a coarse level.

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…

We show that the dimension of the geometric shape formed by the phenomenologically valid points inside a multi-dimensional parameter space can be used to characterise different new physics models and to define a quantitative measure for the…

Estimating 3D human pose and shape from 2D images is a crucial yet challenging task. While prior methods with model-based representations can perform reasonably well on whole-body images, they often fail when parts of the body are occluded…

A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…

We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…

The visibility graph of a simple polygon represents visibility relations between its vertices. Knowing the correct order of the vertices around the boundary of a polygon and its visibility graph, it is an open problem to locate the vertices…

Evaluating the built environment based on visibility has been long used as a tool for human-centric design. The origins of isovists and visibility graphs are within interior spaces, while more recently, these evaluation techniques have been…

Text documents are complex high dimensional objects. To effectively visualize such data it is important to reduce its dimensionality and visualize the low dimensional embedding as a 2-D or 3-D scatter plot. In this paper we explore…

We present a new skeletal representation along with a matching framework to address the deformable shape recognition problem. The disconnectedness arises as a result of excessive regularization that we use to describe a shape at an…

Sketching is used as a ubiquitous tool of expression by novices and experts alike. In this thesis I explore two methods that help a system provide a geometric machine-understanding of sketches, and in-turn help a user accomplish a…

This paper contributes a set of quality metrics for identification and visual analysis of structured missingness in high-dimensional data. Missing values in data are a frequent challenge in most data generating domains and may cause a range…

A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilising projections onto a space spanned by a…

Sculptors often deviate from geometric accuracy in order to enhance the appearance of their sculpture. These subtle stylizations may emphasize anatomy, draw the viewer's focus to characteristic features of the subject, or symbolize textures…

This paper presents a new axis-based shape representation scheme along with a matching framework to address the problem of generic shape recognition. The main idea is to define the relative spatial arrangement of local symmetry axes and…

In many applications, one is interested in the shape of an object, like the contour of a bone or the trajectory of joints of a tennis player, irrespective of the way these shapes are parameterized. However for analysis of these shape…

In this article, we develop foundational theory for geometries of the space of closed $G_2$-structures in a given cohomology class as an infinite-dimensional manifold. We introduce Sobolev-type metrics, construct their Levi-Civita…

A witness drawing of a graph is a visualization that clearly shows a given property of a graph. We study and implement various drawing paradigms for witness drawings to clearly show that graphs have bounded pathwidth or treewidth. Our…

Approximate convex decomposition aims to decompose a 3D shape into a set of almost convex components, whose convex hulls can then be used to represent the input shape. It thus enables efficient geometry processing algorithms specifically…