401 research outputs found
Neural function approximation on graphs: shape modelling, graph discrimination & compression
Graphs serve as a versatile mathematical abstraction of real-world phenomena in numerous scientific disciplines. This thesis is part of the Geometric Deep Learning subject area, a family of learning paradigms, that capitalise on the increasing volume of non-Euclidean data so as to solve real-world tasks in a data-driven manner. In particular, we focus on the topic of graph function approximation using neural networks, which lies at the heart of many relevant methods. In the first part of the thesis, we contribute to the understanding and design of Graph Neural Networks (GNNs). Initially, we investigate the problem of learning on signals supported on a fixed graph. We show that treating graph signals as general graph spaces is restrictive and conventional GNNs have limited expressivity. Instead, we expose a more enlightening perspective by drawing parallels between graph signals and signals on Euclidean grids, such as images and audio. Accordingly, we propose a permutation-sensitive GNN based on an operator analogous to shifts in grids and instantiate it on 3D meshes for shape modelling (Spiral Convolutions). Following, we focus on learning on general graph spaces and in particular on functions that are invariant to graph isomorphism. We identify a fundamental trade-off between invariance, expressivity and computational complexity, which we address with a symmetry-breaking mechanism based on substructure encodings (Graph Substructure Networks). Substructures are shown to be a powerful tool that provably improves expressivity while controlling computational complexity, and a useful inductive bias in network science and chemistry. In the second part of the thesis, we discuss the problem of graph compression, where we analyse the information-theoretic principles and the connections with graph generative models. We show that another inevitable trade-off surfaces, now between computational complexity and compression quality, due to graph isomorphism. We propose a substructure-based dictionary coder - Partition and Code (PnC) - with theoretical guarantees that can be adapted to different graph distributions by estimating its parameters from observations. Additionally, contrary to the majority of neural compressors, PnC is parameter and sample efficient and is therefore of wide practical relevance. Finally, within this framework, substructures are further illustrated as a decisive archetype for learning problems on graph spaces.Open Acces
Investigating human-perceptual properties of "shapes" using 3D shapes and 2D fonts
Shapes are generally used to convey meaning. They are used in video games, films and other multimedia, in diverse ways. 3D shapes may be destined for virtual scenes or represent objects to be constructed in the real-world. Fonts add character to an otherwise plain block of text, allowing the writer to make important points more visually prominent or distinct from other text. They can indicate the structure of a document, at a glance. Rather than studying shapes through traditional geometric shape descriptors, we provide alternative methods to describe and analyse shapes, from a lens of human perception. This is done via the concepts of Schelling Points and Image Specificity. Schelling Points are choices people make when they aim to match with what they expect others to choose but cannot communicate with others to determine an answer. We study whole mesh selections in this setting, where Schelling Meshes are the most frequently selected shapes. The key idea behind image Specificity is that different images evoke different descriptions; but ‘Specific’ images yield more consistent descriptions than others. We apply Specificity to 2D fonts. We show that each concept can be learned and predict them for fonts and 3D shapes, respectively, using a depth image-based convolutional neural network. Results are shown for a range of fonts and 3D shapes and we demonstrate that font Specificity and the Schelling meshes concept are useful for visualisation, clustering, and search applications. Overall, we find that each concept represents similarities between their respective type of shape, even when there are discontinuities between the shape geometries themselves. The ‘context’ of these similarities is in some kind of abstract or subjective meaning which is consistent among different people
Feature Driven Learning Techniques for 3D Shape Segmentation
Segmentation is a fundamental problem in 3D shape analysis and machine learning. The abil-ity to partition a 3D shape into meaningful or functional parts is a vital ingredient of many down stream applications like shape matching, classification and retrieval. Early segmentation methods were based on approaches like fitting primitive shapes to parts or extracting segmen-tations from feature points. However, such methods had limited success on shapes with more complex geometry. Observing this, research began using geometric features to aid the segmen-tation, as certain features (e.g. Shape Diameter Function (SDF)) are less sensitive to complex geometry. This trend was also incorporated in the shift to set-wide segmentations, called co-segmentation, which provides a consistent segmentation throughout a shape dataset, meaning similar parts have the same segment identifier. The idea of co-segmentation is that a set of same class shapes (i.e. chairs) contain more information about the class than a single shape would, which could lead to an overall improvement to the segmentation of the individual shapes. Over the past decade many different approaches of co-segmentation have been explored covering supervised, unsupervised and even user-driven active learning. In each of the areas, there has been widely adopted use of geometric features to aid proposed segmentation algorithms, with each method typically using different combinations of features. The aim of this thesis is to ex-plore these different areas of 3D shape segmentation, perform an analysis of the effectiveness of geometric features in these areas and tackle core issues that currently exist in the literature.Initially, we explore the area of unsupervised segmentation, specifically looking at co-segmentation, and perform an analysis of several different geometric features. Our analysis is intended to compare the different features in a single unsupervised pipeline to evaluate their usefulness and determine their strengths and weaknesses. Our analysis also includes several features that have not yet been explored in unsupervised segmentation but have been shown effective in other areas.Later, with the ever increasing popularity of deep learning, we explore the area of super-vised segmentation and investigate the current state of Neural Network (NN) driven techniques. We specifically observe limitations in the current state-of-the-art and propose a novel Convolu-tional Neural Network (CNN) based method which operates on multi-scale geometric features to gain more information about the shapes being segmented. We also perform an evaluation of several different supervised segmentation methods using the same input features, but with vary-ing complexity of model design. This is intended to see if the more complex models provide a significant performance increase.Lastly, we explore the user-driven area of active learning, to tackle the large amounts of inconsistencies in current ground truth segmentation, which are vital for most segmentation methods. Active learning has been used to great effect for ground truth generation in the past, so we present a novel active learning framework using deep learning and geometric features to assist the user in co-segmentation of a dataset. Our method emphasises segmentation accu-racy while minimising user effort, providing an interactive visualisation for co-segmentation analysis and the application of automated optimisation tools.In this thesis we explore the effectiveness of different geometric features across varying segmentation tasks, providing an in-depth analysis and comparison of state-of-the-art methods
Automatic face recognition using stereo images
Face recognition is an important pattern recognition problem, in the study of both natural and artificial learning problems. Compaxed to other biometrics, it is non-intrusive, non- invasive and requires no paxticipation from the subjects. As a result, it has many applications varying from human-computer-interaction to access control and law-enforcement to crowd surveillance. In typical optical image based face recognition systems, the systematic vaxiability arising from representing the three-dimensional (3D) shape of a face by a two-dimensional (21)) illumination intensity matrix is treated as random vaxiability. Multiple examples of the face displaying vaxying pose and expressions axe captured in different imaging conditions. The imaging environment, pose and expressions are strictly controlled and the images undergo rigorous normalisation and pre-processing. This may be implemented in a paxtially or a fully automated system. Although these systems report high classification accuracies (>90%), they lack versatility and tend to fail when deployed outside laboratory conditions. Recently, more sophisticated 3D face recognition systems haxnessing the depth information have emerged. These systems usually employ specialist equipment such as laser scanners and structured light projectors. Although more accurate than 2D optical image based recognition, these systems are equally difficult to implement in a non-co-operative environment. Existing face recognition systems, both 2D and 3D, detract from the main advantages of face recognition and fail to fully exploit its non-intrusive capacity. This is either because they rely too much on subject co-operation, which is not always available, or because they cannot cope with noisy data. The main objective of this work was to investigate the role of depth information in face recognition in a noisy environment. A stereo-based system, inspired by the human binocular vision, was devised using a pair of manually calibrated digital off-the-shelf cameras in a stereo setup to compute depth information. Depth values extracted from 2D intensity images using stereoscopy are extremely noisy, and as a result this approach for face recognition is rare. This was cofirmed by the results of our experimental work. Noise in the set of correspondences, camera calibration and triangulation led to inaccurate depth reconstruction, which in turn led to poor classifier accuracy for both 3D surface matching and 211) 2 depth maps. Recognition experiments axe performed on the Sheffield Dataset, consisting 692 images of 22 individuals with varying pose, illumination and expressions
Automatic Landmarking for Non-cooperative 3D Face Recognition
This thesis describes a new framework for 3D surface landmarking and evaluates its performance for feature localisation on human faces. This framework has two main parts that can be designed and optimised independently. The first one is a keypoint detection system that returns positions of interest for a given mesh surface by using a learnt dictionary of local shapes. The second one is a labelling system, using model fitting approaches that establish a one-to-one correspondence between the set of unlabelled input points and a learnt representation of the class of object to detect.
Our keypoint detection system returns local maxima over score maps that are generated from an arbitrarily large set of local shape descriptors. The distributions of these descriptors (scalars or histograms) are learnt for known landmark positions on a training dataset in order to generate a model. The similarity between the input descriptor value for a given vertex and a model shape is used as a descriptor-related score.
Our labelling system can make use of both hypergraph matching techniques and rigid registration techniques to reduce the ambiguity attached to unlabelled input keypoints for which a list of model landmark candidates have been seeded. The soft matching techniques use multi-attributed hyperedges to reduce ambiguity, while the registration techniques use scale-adapted rigid transformation computed from 3 or more points in order to obtain one-to-one correspondences.
Our final system achieves better or comparable (depending on the metric) results than the state-of-the-art while being more generic. It does not require pre-processing such as cropping, spike removal and hole filling and is more robust to occlusion of salient local regions, such as those near the nose tip and inner eye corners. It is also fully pose invariant and can be used with kinds of objects other than faces, provided that labelled training data is available
- …