Static/Dynamic Filtering for Mesh Geometry

The joint bilateral filter, which enables feature-preserving signal smoothing according to the structural information from a guidance, has been applied for various tasks in geometry processing. Existing methods either rely on a static guidance that may be inconsistent with the input and lead to unsatisfactory results, or a dynamic guidance that is automatically updated but sensitive to noises and outliers. Inspired by recent advances in image filtering, we propose a new geometry filtering technique called static/dynamic filter, which utilizes both static and dynamic guidances to achieve state-of-the-art results. The proposed filter is based on a nonlinear optimization that enforces smoothness of the signal while preserving variations that correspond to features of certain scales. We develop an efficient iterative solver for the problem, which unifies existing filters that are based on static or dynamic guidances. The filter can be applied to mesh face normals followed by vertex position update, to achieve scale-aware and feature-preserving filtering of mesh geometry. It also works well for other types of signals defined on mesh surfaces, such as texture colors. Extensive experimental results demonstrate the effectiveness of the proposed filter for various geometry processing applications such as mesh denoising, geometry feature enhancement, and texture color filtering

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

Detail-preserving and Content-aware Variational Multi-view Stereo Reconstruction

Accurate recovery of 3D geometrical surfaces from calibrated 2D multi-view images is a fundamental yet active research area in computer vision. Despite the steady progress in multi-view stereo reconstruction, most existing methods are still limited in recovering fine-scale details and sharp features while suppressing noises, and may fail in reconstructing regions with few textures. To address these limitations, this paper presents a Detail-preserving and Content-aware Variational (DCV) multi-view stereo method, which reconstructs the 3D surface by alternating between reprojection error minimization and mesh denoising. In reprojection error minimization, we propose a novel inter-image similarity measure, which is effective to preserve fine-scale details of the reconstructed surface and builds a connection between guided image filtering and image registration. In mesh denoising, we propose a content-aware $\ell_{p}$-minimization algorithm by adaptively estimating the $p$ value and regularization parameters based on the current input. It is much more promising in suppressing noise while preserving sharp features than conventional isotropic mesh smoothing. Experimental results on benchmark datasets demonstrate that our DCV method is capable of recovering more surface details, and obtains cleaner and more accurate reconstructions than state-of-the-art methods. In particular, our method achieves the best results among all published methods on the Middlebury dino ring and dino sparse ring datasets in terms of both completeness and accuracy.Comment: 14 pages,16 figures. Submitted to IEEE Transaction on image processin