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

A quantitative assessment of 3D facial key point localization fitting 2D shape models to curvature information

This work addresses the localization of 11 prominent facial landmarks in 3D by fitting state of the art shape models to 2D data. Quantitative results are provided for 34 scans at high resolution (texture maps of 10 M-pixels) in terms of accuracy (with respect to manual measurements) and precision (repeatability on different images from the same individual). We obtain an average accuracy of approximately 3 mm, and median repeatability of inter-landmark distances typically below 2 mm, which are values comparable to current algorithms on automatic localization of facial landmarks. We also show that, in our experiments, the replacement of texture information by curvature features produced little change in performance, which is an important finding as it suggests the applicability of the method to any type of 3D data

Large-area visually augmented navigation for autonomous underwater vehicles

Submitted to the Joint Program in Applied Ocean Science & Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2005This thesis describes a vision-based, large-area, simultaneous localization and mapping (SLAM) algorithm that respects the low-overlap imagery constraints typical of autonomous underwater vehicles (AUVs) while exploiting the inertial sensor information that is routinely available on such platforms. We adopt a systems-level approach exploiting the complementary aspects of inertial sensing and visual perception from a calibrated pose-instrumented platform. This systems-level strategy yields a robust solution to underwater imaging that overcomes many of the unique challenges of a marine environment (e.g., unstructured terrain, low-overlap imagery, moving light source). Our large-area SLAM algorithm recursively incorporates relative-pose constraints using a view-based representation that exploits exact sparsity in the Gaussian canonical form. This sparsity allows for efficient O(n) update complexity in the number of images composing the view-based map by utilizing recent multilevel relaxation techniques. We show that our algorithmic formulation is inherently sparse unlike other feature-based canonical SLAM algorithms, which impose sparseness via pruning approximations. In particular, we investigate the sparsification methodology employed by sparse extended information filters (SEIFs) and offer new insight as to why, and how, its approximation can lead to inconsistencies in the estimated state errors. Lastly, we present a novel algorithm for efficiently extracting consistent marginal covariances useful for data association from the information matrix. In summary, this thesis advances the current state-of-the-art in underwater visual navigation by demonstrating end-to-end automatic processing of the largest visually navigated dataset to date using data collected from a survey of the RMS Titanic (path length over 3 km and 3100 m2 of mapped area). This accomplishment embodies the summed contributions of this thesis to several current SLAM research issues including scalability, 6 degree of freedom motion, unstructured environments, and visual perception.This work was funded in part by the CenSSIS ERC of the National Science Foundation under grant EEC-9986821, in part by the Woods Hole Oceanographic Institution through a grant from the Penzance Foundation, and in part by a NDSEG Fellowship awarded through the Department of Defense

Groupwise non-rigid registration for automatic construction of appearance models of the human craniofacial complex for analysis, synthesis and simulation

Finally, a novel application of 3D appearance modelling is proposed: a faster than real-time algorithm for statistically constrained quasi-mechanical simulation. Experiments demonstrate superior realism, achieved in the proposed method by employing statistical appearance models to drive the simulation, in comparison with the comparable state-of-the-art quasi-mechanical approaches.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Geometric surface processing via normal maps

technical reportThe generalization of signal and image processing to surfaces entails filtering the normals of the surface, rather than filtering the positions of points on a mesh. Using a variational framework, smooth surfaces minimize the norm of the derivative of the surface normals? i.e. total curvature. Penalty functions on the surface normals are computed using geometrybased shape metrics and minimized using gradient descent. This produces a set of partial differential equations (PDE). In this paper, we introduce a novel framework for implementing geometric processing tools for surfaces using a two step algorithm: (i) operating on the normal map of a surface, and (ii) manipulating the surface to fit the processed normals. The computational approach uses level set surface models; therefore, the processing does not depend on any underlying parameterization. Iterating this two-step process, we can implement geometric fourth-order flows efficiently by solving a set of coupled second-order PDEs. This paper will demonstrate that the framework provides for a wide range of surface processing operations, including edge-preserving smoothing and high-boost filtering. Furthermore, the generality of the implementation makes it appropriate for very complex surface models, e.g. those constructed directly from measured data

The design of a robust 3D Reconstruction system for video sequences in non controlled environments

Along this thesis, a novel and robust approach for obtaining 3D models from video sequences captured with hand-held cameras is adressed. This work defines a fully automatic pipeline that is able to deal with diferent types of sequences and acquiring devices. The designed and implemented system follows a divide and conquer approach. An smart frame decimation process reduces the temporal redundancy of the input video sequence and selects the best conditioned frames for the reconstruction step. Next, the video is split into overlapped clips with a fixed and small number of Key-frames. This allows to parallelize the Structure and Motion process which translates into a dramatic reduction in the computational complexity. The short length of the clips allows an intensive search for the best solution at each step of the reconstruction, which improves the overall system performance. The process of feature tracking is embedded within the reconstruction loop for each clip as a difference with other approaches. The last contribution of this thesis is a final registration step that merges all the processed clips to the same coordinate frame. This last step consists on a set of linear algorithms that combine information of the structure (3D points) and motion (cameras) shared by partial reconstructions of the same static scene to more accurately estimate their registration to the same coordinate system. The performance for the presented algorithm as well as for the global system is demonstrated in experiments with real data

Quantifying the urban forest environment using dense discrete return LiDAR and aerial color imagery for segmentation and object-level biomass assessment

The urban forest is becoming increasingly important in the contexts of urban green space and recreation, carbon sequestration and emission offsets, and socio-economic impacts. In addition to aesthetic value, these green spaces remove airborne pollutants, preserve natural resources, and mitigate adverse climate changes, among other benefits. A great deal of attention recently has been paid to urban forest management. However, the comprehensive monitoring of urban vegetation for carbon sequestration and storage is an under-explored research area. Such an assessment of carbon stores often requires information at the individual tree level, necessitating the proper masking of vegetation from the built environment, as well as delineation of individual tree crowns. As an alternative to expensive and time-consuming manual surveys, remote sensing can be used effectively in characterizing the urban vegetation and man-made objects. Many studies in this field have made use of aerial and multispectral/hyperspectral imagery over cities. The emergence of light detection and ranging (LiDAR) technology, however, has provided new impetus to the effort of extracting objects and characterizing their 3D attributes - LiDAR has been used successfully to model buildings and urban trees. However, challenges remain when using such structural information only, and researchers have investigated the use of fusion-based approaches that combine LiDAR and aerial imagery to extract objects, thereby allowing the complementary characteristics of the two modalities to be utilized. In this study, a fusion-based classification method was implemented between high spatial resolution aerial color (RGB) imagery and co-registered LiDAR point clouds to classify urban vegetation and buildings from other urban classes/cover types. Structural, as well as spectral features, were used in the classification method. These features included height, flatness, and the distribution of normal surface vectors from LiDAR data, along with a non-calibrated LiDAR-based vegetation index, derived from combining LiDAR intensity at 1064 nm with the red channel of the RGB imagery. This novel index was dubbed the LiDAR-infused difference vegetation index (LDVI). Classification results indicated good separation between buildings and vegetation, with an overall accuracy of 92% and a kappa statistic of 0.85. A multi-tiered delineation algorithm subsequently was developed to extract individual tree crowns from the identified tree clusters, followed by the application of species-independent biomass models based on LiDAR-derived tree attributes in regression analysis. These LiDAR-based biomass assessments were conducted for individual trees, as well as for clusters of trees, in cases where proper delineation of individual trees was impossible. The detection accuracy of the tree delineation algorithm was 70%. The LiDAR-derived biomass estimates were validated against allometry-based biomass estimates that were computed from field-measured tree data. It was found out that LiDAR-derived tree volume, area, and different distribution parameters of height (e.g., maximum height, mean of height) are important to model biomass. The best biomass model for the tree clusters and the individual trees showed an adjusted R-Squared value of 0.93 and 0.58, respectively. The results of this study showed that the developed fusion-based classification approach using LiDAR and aerial color (RGB) imagery is capable of producing good object detection accuracy. It was concluded that the LDVI can be used in vegetation detection and can act as a substitute for the normalized difference vegetation index (NDVI), when near-infrared multiband imagery is not available. Furthermore, the utility of LiDAR for characterizing the urban forest and associated biomass was proven. This work could have significant impact on the rapid and accurate assessment of urban green spaces and associated carbon monitoring and management

Groupwise non-rigid registration for automatic construction of appearance models of the human craniofacial complex for analysis, synthesis and simulation

Finally, a novel application of 3D appearance modelling is proposed: a faster than real-time algorithm for statistically constrained quasi-mechanical simulation. Experiments demonstrate superior realism, achieved in the proposed method by employing statistical appearance models to drive the simulation, in comparison with the comparable state-of-the-art quasi-mechanical approaches

Variational methods for shape and image registrations.

Estimating and analysis of deformation, either rigid or non-rigid, is an active area of research in various medical imaging and computer vision applications. Its importance stems from the inherent inter- and intra-variability in biological and biomedical object shapes and from the dynamic nature of the scenes usually dealt with in computer vision research. For instance, quantifying the growth of a tumor, recognizing a person\u27s face, tracking a facial expression, or retrieving an object inside a data base require the estimation of some sort of motion or deformation undergone by the object of interest. To solve these problems, and other similar problems, registration comes into play. This is the process of bringing into correspondences two or more data sets. Depending on the application at hand, these data sets can be for instance gray scale/color images or objects\u27 outlines. In the latter case, one talks about shape registration while in the former case, one talks about image/volume registration. In some situations, the combinations of different types of data can be used complementarily to establish point correspondences. One of most important image analysis tools that greatly benefits from the process of registration, and which will be addressed in this dissertation, is the image segmentation. This process consists of localizing objects in images. Several challenges are encountered in image segmentation, including noise, gray scale inhomogeneities, and occlusions. To cope with such issues, the shape information is often incorporated as a statistical model into the segmentation process. Building such statistical models requires a good and accurate shape alignment approach. In addition, segmenting anatomical structures can be accurately solved through the registration of the input data set with a predefined anatomical atlas. Variational approaches for shape/image registration and segmentation have received huge interest in the past few years. Unlike traditional discrete approaches, the variational methods are based on continuous modelling of the input data through the use of Partial Differential Equations (PDE). This brings into benefit the extensive literature on theory and numerical methods proposed to solve PDEs. This dissertation addresses the registration problem from a variational point of view, with more focus on shape registration. First, a novel variational framework for global-to-local shape registration is proposed. The input shapes are implicitly represented through their signed distance maps. A new Sumof- Squared-Differences (SSD) criterion which measures the disparity between the implicit representations of the input shapes, is introduced to recover the global alignment parameters. This new criteria has the advantages over some existing ones in accurately handling scale variations. In addition, the proposed alignment model is less expensive computationally. Complementary to the global registration field, the local deformation field is explicitly established between the two globally aligned shapes, by minimizing a new energy functional. This functional incrementally and simultaneously updates the displacement field while keeping the corresponding implicit representation of the globally warped source shape as close to a signed distance function as possible. This is done under some regularization constraints that enforce the smoothness of the recovered deformations. The overall process leads to a set of coupled set of equations that are simultaneously solved through a gradient descent scheme. Several applications, where the developed tools play a major role, are addressed throughout this dissertation. For instance, some insight is given as to how one can solve the challenging problem of three dimensional face recognition in the presence of facial expressions. Statistical modelling of shapes will be presented as a way of benefiting from the proposed shape registration framework. Second, this dissertation will visit th