168 research outputs found
Roto-Translation Covariant Convolutional Networks for Medical Image Analysis
We propose a framework for rotation and translation covariant deep learning
using group convolutions. The group product of the special Euclidean
motion group describes how a concatenation of two roto-translations
results in a net roto-translation. We encode this geometric structure into
convolutional neural networks (CNNs) via group convolutional layers,
which fit into the standard 2D CNN framework, and which allow to generically
deal with rotated input samples without the need for data augmentation.
We introduce three layers: a lifting layer which lifts a 2D (vector valued)
image to an -image, i.e., 3D (vector valued) data whose domain is
; a group convolution layer from and to an -image; and a
projection layer from an -image to a 2D image. The lifting and group
convolution layers are covariant (the output roto-translates with the
input). The final projection layer, a maximum intensity projection over
rotations, makes the full CNN rotation invariant.
We show with three different problems in histopathology, retinal imaging, and
electron microscopy that with the proposed group CNNs, state-of-the-art
performance can be achieved, without the need for data augmentation by rotation
and with increased performance compared to standard CNNs that do rely on
augmentation.Comment: 8 pages, 2 figures, 1 table, accepted at MICCAI 201
Roto-Translation Equivariant Convolutional Networks: Application to Histopathology Image Analysis
Rotation-invariance is a desired property of machine-learning models for
medical image analysis and in particular for computational pathology
applications. We propose a framework to encode the geometric structure of the
special Euclidean motion group SE(2) in convolutional networks to yield
translation and rotation equivariance via the introduction of SE(2)-group
convolution layers. This structure enables models to learn feature
representations with a discretized orientation dimension that guarantees that
their outputs are invariant under a discrete set of rotations. Conventional
approaches for rotation invariance rely mostly on data augmentation, but this
does not guarantee the robustness of the output when the input is rotated. At
that, trained conventional CNNs may require test-time rotation augmentation to
reach their full capability. This study is focused on histopathology image
analysis applications for which it is desirable that the arbitrary global
orientation information of the imaged tissues is not captured by the machine
learning models. The proposed framework is evaluated on three different
histopathology image analysis tasks (mitosis detection, nuclei segmentation and
tumor classification). We present a comparative analysis for each problem and
show that consistent increase of performances can be achieved when using the
proposed framework
Principled Design and Implementation of Steerable Detectors
We provide a complete pipeline for the detection of patterns of interest in
an image. In our approach, the patterns are assumed to be adequately modeled by
a known template, and are located at unknown position and orientation. We
propose a continuous-domain additive image model, where the analyzed image is
the sum of the template and an isotropic background signal with self-similar
isotropic power-spectrum. The method is able to learn an optimal steerable
filter fulfilling the SNR criterion based on one single template and background
pair, that therefore strongly responds to the template, while optimally
decoupling from the background model. The proposed filter then allows for a
fast detection process, with the unknown orientation estimation through the use
of steerability properties. In practice, the implementation requires to
discretize the continuous-domain formulation on polar grids, which is performed
using radial B-splines. We demonstrate the practical usefulness of our method
on a variety of template approximation and pattern detection experiments
Limits of economy and fidelity for programmable assembly of size-controlled triply-periodic polyhedra
We propose and investigate an extension of the Caspar-Klug symmetry
principles for viral capsid assembly to the programmable assembly of
size-controlled triply-periodic polyhedra, discrete variants of the Primitive,
Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of
programmable DNA origami colloids, we demonstrate that the economy of design in
these crystalline assemblies -- in terms of the growth of the number of
distinct particle species required with the increased size-scale (e.g.
periodicity) -- is comparable to viral shells. We further test the role of
geometric specificity in these assemblies via dynamical assembly simulations,
which show that conditions for simultaneously efficient and high-fidelity
assembly require an intermediate degree of flexibility of local angles and
lengths in programmed assembly. Off-target misassembly occurs via incorporation
of a variant of disclination defects, generalized to the case of hyperbolic
crystals. The possibility of these topological defects is a direct consequence
of the very same symmetry principles that underlie the economical design,
exposing a basic tradeoff between design economy and fidelity of programmable,
size controlled assembly.Comment: 15 pages, 5 figures, 6 supporting movies (linked), Supporting
Appendi
On deep generative modelling methods for protein-protein interaction
Proteins form the basis for almost all biological processes, identifying the interactions that proteins have with themselves, the environment, and each other are critical to understanding their biological function in an organism, and thus the impact of drugs designed to affect them. Consequently a significant body of research and development focuses on methods to analyse and predict protein structure and interactions. Due to the breadth of possible interactions and the complexity of structures, \textit{in sillico} methods are used to propose models of both interaction and structure that can then be verified experimentally. However the computational complexity of protein interaction means that full physical simulation of these processes requires exceptional computational resources and is often infeasible. Recent advances in deep generative modelling have shown promise in correctly capturing complex conditional distributions. These models derive their basic principles from statistical mechanics and thermodynamic modelling. While the learned functions of these methods are not guaranteed to be physically accurate, they result in a similar sampling process to that suggested by the thermodynamic principles of protein folding and interaction. However, limited research has been applied to extending these models to work over the space of 3D rotation, limiting their applicability to protein models. In this thesis we develop an accelerated sampling strategy for faster sampling of potential docking locations, we then address the rotational diffusion limitation by extending diffusion models to the space of and finally present a framework for the use of this rotational diffusion model to rigid docking of proteins
The Impact of Dynamics in Protein Assembly
Predicting the assembly of multiple proteins into specific complexes is critical to understanding their biological function in an organism, and thus the design of drugs to address their malfunction. Consequently, a significant body of research and development focuses on methods for elucidating protein quaternary structure. In silico techniques are used to propose models that decode experimental data, and independently as a structure prediction tool. These computational methods often consider proteins as rigid structures, yet proteins are inherently flexible molecules, with both local side-chain motion and larger conformational dynamics governing their behaviour. This treatment is particularly problematic for any protein docking engine, where even a simple rearrangement of the side-chain and backbone atoms at the interface of binding partners complicates the successful determination of the correct docked pose. Herein, we present a means of representing protein surface, electrostatics and local dynamics within a single volumetric descriptor, before applying it to a series of physical and biophysical problems to validate it as representative of a protein. We leverage this representation in a protein-protein docking context and demonstrate that its application bypasses the need to compensate for, and predict, specific side-chain packing at the interface of binding partners for both water-soluble and lipid-soluble protein complexes. We find little detriment in the quality of returned predictions with increased flexibility, placing our protein docking approach as highly competitive versus comparative methods. We then explore the role of larger, conformational dynamics in protein quaternary structure prediction, by exploiting large-scale Molecular Dynamics simulations of the SARS-CoV-2 spike glycoprotein to elucidate possible high-order spike-ACE2 oligomeric states. Our results indicate a possible novel path to therapeutics following the COVID-19 pandemic. Overall, we find that the structure of a protein alone is inadequate in understanding its function through its possible binding modes. Therefore, we must also consider the impact of dynamics in protein assembly
- …