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This PhD thesis is concerned with the reconstruction of intricate shapes from scanning electron microscope (SEM) imagery. Since SEM images bear a certain resemblance to optical images, approaches developed in the wider field of computer vision can to a certain degree be applied to SEM images as well. I focus on two such approaches, namely Multiview Stereo (MVS) and Shape from Shading (SfS) and extend them to the SEM domain. The reconstruction of intricate shapes featuring thin protrusions and sparsely textured curved areas poses a significant challenge for current MVS techniques. The MVS methods I propose are designed to deal with such surfaces in particular, while also being robust to the specific problems inherent in the SEM modality: the absence of a static illumination and the unusually high noise level. I describe two different novel MVS methods aimed at narrow-baseline and medium-baseline imaging setups respectively. Both of them build on the assumption of pixelwise photoconsistency. In the SfS context, I propose a novel empirical reflectance model for SEM images that allows for an efficient inference of surface orientation from multiple observations. My reflectance model is able to model both secondary and backscattered electron emission under an arbitrary detector setup. I describe two additional methods of inferring shape using combinations of MVS and SfS approaches: the first builds on my medium-baseline MVS method, which assumes photoconsistency, and improves on it by estimating the surface orientation using my reflectance model. The second goes beyond photoconsistency and estimates the depths themselves using the reflectance model.

We present a new approach for macromolecular structure determination from multiple particles in electron cryo-tomography (cryo-ET) data sets. Whereas existing subtomogram averaging approaches are based on 3D data models, we propose to optimise a regularised likelihood target that approximates a function of the 2D experimental images. In addition, analogous to Bayesian polishing and contrast transfer function (CTF) refinement in single-particle analysis, we describe the approaches that exploit the increased signal-to-noise ratio in the averaged structure to optimise tilt-series alignments, beam-induced motions of the particles throughout the tilt-series acquisition, defoci of the individual particles, as well as higher-order optical aberrations of the microscope. Implementation of our approaches in the open-source software package RELION aims to facilitate their general use, particularly for those researchers who are already familiar with its single-particle analysis tools. We illustrate for three applications that our approaches allow structure determination from cryo-ET data to resolutions sufficient for de novo atomic modelling., This work was funded by the UK Research and Innovation (UKRI) Medical Research Council (MC_UP_A025_1013 to SHWS; and MC_UP_1201/16 to JAGB), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (ERC-CoG-2014, grant 648432, MEMBRANEFUSION to JAGB and ERC StG-2019, grant 852915 CRYTOCOP to GZ); the Swiss National Science Foundation (grant 205321_179041/1 to DC-D), the Max Planck Society (to JAGB) and the UKRI Biotechnology and Biological Sciences Research Council (grant BB/T002670/1 to GZ). TAMB is a recipient of a Sir Henry Dale Fellowship, jointly funded by the Wellcome Trust and the Royal Society (202231/Z/16/Z). JZ was partially funded by the European Union’s Horizon 2020 research and innovation program (ERC-ADG-2015, grant 692726, GlobalBioIm to Michael Unser).