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Defocus formation from a finite aperture is a well-known phenomenon, occurring in many forms of photographic media. Although defocus is often exploited for artistic reasons, a surprising amount of information about the scene structure is encoded in the camera's blurring function. The aim of this work is to explore how this can be leveraged to recover 3D geometry from scenes with complex reflectance. Depth from defocus (DFD) is a well-established field that aims to reconstruct scene geometry from analysis of the defocus appearance, usually by modelling the camera as a thin lens. While many existing methods achieve approximate depth maps suitable for some applications, the majority are limited to geometrically inconsistent single-view reconstructions. The first contribution generalises image formation to a thick lens, and proposes a novel calibration procedure for accurate defocus modelling. This approach is shown to significantly outperform traditional thin lens assumptions in macro-scale scene reconstruction. The second contribution generalises reconstruction to multiple views, and evaluates the com- plementary properties of defocus and stereo information in a novel reconstruction framework. Unlike conventional multi-view stereo (MVS), which depends on photometric consistency be- tween views, DFD requires only a single viewpoint for reconstruction. This makes defocus-based approaches naturally robust to view-dependent materials considered challenging for traditional MVS. Conversely, textures which are invariant to defocus can be suitable for correspondence. This complementary relationship is investigated to determine the benefits of combining defocus information with stereo cues; with performance evaluated on per-viewpoint depth maps as well as complete 3D reconstructions. The results demonstrate an improvement over DFD alone even in specular and reflective datasets, and outperform state-of-the-art MVS. The third contribution explores the novel application of neural rendering to defocus modelling. Specifically, the recent advances in deep learning are leveraged to solve for three latent variables encoded as pixel intensities in a focal stack: the scene depth and radiance, and the camera point spread function. This is in contrast to the majority of existing defocus-based literature, which assume at least one of these variables is known. These quantities are disentangled by modelling each as a multilayer perception network, and trained end-to-end on the appearance of each pixel under different camera settings. This approach allows novel refocused images to be rendered that accurately capture the bokeh produced by specular highlights with arbitrary aperture shapes. Since the networks are trained according to a convolutional defocus model, the synthesised images can generalise to unconstrained aperture diameters, and achieve depth of field effects that exceed what was observed during training.

Collagen IV networks play a key structural role in the human ocular lens capsule. However, their structure is not well understood, and is hypothesised to undergo significant changes over a lifetime, resulting in a loss of ability to accommodate different focal depths. In this thesis, a range of computational models and methods are developed, which aim to help better understand the properties of 2D networks of biopolymers, especially inspired by collagen IV. The available experimental images of collagen-containing networks are assessed and an image analysis protocol is developed. A Monte Carlo method is designed, which introduces disorder into simplified graph-based networks by switching edges. In addition, Molecular Dynamics is used to simulate coarse-grained polymers which attract one another at their headgroups. These coarse-grained polymers are shown to self-assemble into a variety of interesting network structures. The coarse-grained polymer approach is combined with a Molecular Statics scheme to calculate mechanical properties of the network, and understand how the networks behave when stretched. A model that can mimic the ageing of the network over a lifetime is developed. To better understand how lens capsule motion may damage collagen IV networks, the rupturing behaviour of the polymer networks is examined by stretching ordered hexagonal networks linearly and sinusoidally until they break. This is compared to the rupturing behaviour of networks containing defects. The MD method is used to assess the surface roughness and dimensionality of polymer networks, which is quantified by a fractal dimension. Finally, a new type of persistence diagram is used to quantify and visualise damage to ring structures in a network over time.