3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques

Semantically Informed Multiview Surface Refinement

We present a method to jointly refine the geometry and semantic segmentation of 3D surface meshes. Our method alternates between updating the shape and the semantic labels. In the geometry refinement step, the mesh is deformed with variational energy minimization, such that it simultaneously maximizes photo-consistency and the compatibility of the semantic segmentations across a set of calibrated images. Label-specific shape priors account for interactions between the geometry and the semantic labels in 3D. In the semantic segmentation step, the labels on the mesh are updated with MRF inference, such that they are compatible with the semantic segmentations in the input images. Also, this step includes prior assumptions about the surface shape of different semantic classes. The priors induce a tight coupling, where semantic information influences the shape update and vice versa. Specifically, we introduce priors that favor (i) adaptive smoothing, depending on the class label; (ii) straightness of class boundaries; and (iii) semantic labels that are consistent with the surface orientation. The novel mesh-based reconstruction is evaluated in a series of experiments with real and synthetic data. We compare both to state-of-the-art, voxel-based semantic 3D reconstruction, and to purely geometric mesh refinement, and demonstrate that the proposed scheme yields improved 3D geometry as well as an improved semantic segmentation

Patch-based Convolutional Neural Network for Whole Slide Tissue Image Classification

Convolutional Neural Networks (CNN) are state-of-the-art models for many image classification tasks. However, to recognize cancer subtypes automatically, training a CNN on gigapixel resolution Whole Slide Tissue Images (WSI) is currently computationally impossible. The differentiation of cancer subtypes is based on cellular-level visual features observed on image patch scale. Therefore, we argue that in this situation, training a patch-level classifier on image patches will perform better than or similar to an image-level classifier. The challenge becomes how to intelligently combine patch-level classification results and model the fact that not all patches will be discriminative. We propose to train a decision fusion model to aggregate patch-level predictions given by patch-level CNNs, which to the best of our knowledge has not been shown before. Furthermore, we formulate a novel Expectation-Maximization (EM) based method that automatically locates discriminative patches robustly by utilizing the spatial relationships of patches. We apply our method to the classification of glioma and non-small-cell lung carcinoma cases into subtypes. The classification accuracy of our method is similar to the inter-observer agreement between pathologists. Although it is impossible to train CNNs on WSIs, we experimentally demonstrate using a comparable non-cancer dataset of smaller images that a patch-based CNN can outperform an image-based CNN

Coplanar Repeats by Energy Minimization

This paper proposes an automated method to detect, group and rectify arbitrarily-arranged coplanar repeated elements via energy minimization. The proposed energy functional combines several features that model how planes with coplanar repeats are projected into images and captures global interactions between different coplanar repeat groups and scene planes. An inference framework based on a recent variant of $\alpha$-expansion is described and fast convergence is demonstrated. We compare the proposed method to two widely-used geometric multi-model fitting methods using a new dataset of annotated images containing multiple scene planes with coplanar repeats in varied arrangements. The evaluation shows a significant improvement in the accuracy of rectifications computed from coplanar repeats detected with the proposed method versus those detected with the baseline methods.Comment: 14 pages with supplemental materials attache

Discrete curvature approximations and segmentation of polyhedral surfaces

The segmentation of digitized data to divide a free form surface into patches is one of the key steps required to perform a reverse engineering process of an object. To this end, discrete curvature approximations are introduced as the basis of a segmentation process that lead to a decomposition of digitized data into areas that will help the construction of parametric surface patches. The approach proposed relies on the use of a polyhedral representation of the object built from the digitized data input. Then, it is shown how noise reduction, edge swapping techniques and adapted remeshing schemes can participate to different preparation phases to provide a geometry that highlights useful characteristics for the segmentation process. The segmentation process is performed with various approximations of discrete curvatures evaluated on the polyhedron produced during the preparation phases. The segmentation process proposed involves two phases: the identification of characteristic polygonal lines and the identification of polyhedral areas useful for a patch construction process. Discrete curvature criteria are adapted to each phase and the concept of invariant evaluation of curvatures is introduced to generate criteria that are constant over equivalent meshes. A description of the segmentation procedure is provided together with examples of results for free form object surfaces

On Using Physical Analogies for Feature and Shape Extraction in Computer Vision

There is a rich literature of approaches to image feature extraction in computer vision. Many sophisticated approaches exist for low- and high-level feature extraction but can be complex to implement with parameter choice guided by experimentation, but impeded by speed of computation. We have developed new ways to extract features based on notional use of physical paradigms, with parameterisation that is more familiar to a scientifically-trained user, aiming to make best use of computational resource. We describe how analogies based on gravitational force can be used for low-level analysis, whilst analogies of water flow and heat can be deployed to achieve high-level smooth shape detection. These new approaches to arbitrary shape extraction are compared with standard state-of-art approaches by curve evolution. There is no comparator operator to our use of gravitational force. We also aim to show that the implementation is consistent with the original motivations for these techniques and so contend that the exploration of physical paradigms offers a promising new avenue for new approaches to feature extraction in computer vision