Measuring cellular traction forces on non-planar substrates

Animal cells use traction forces to sense the mechanics and geometry of their environment. Measuring these traction forces requires a workflow combining cell experiments, image processing and force reconstruction based on elasticity theory. Such procedures have been established before mainly for planar substrates, in which case one can use the Green's function formalism. Here we introduce a worksflow to measure traction forces of cardiac myofibroblasts on non-planar elastic substrates. Soft elastic substrates with a wave-like topology were micromolded from polydimethylsiloxane (PDMS) and fluorescent marker beads were distributed homogeneously in the substrate. Using feature vector based tracking of these marker beads, we first constructed a hexahedral mesh for the substrate. We then solved the direct elastic boundary volume problem on this mesh using the finite element method (FEM). Using data simulations, we show that the traction forces can be reconstructed from the substrate deformations by solving the corresponding inverse problem with a L1-norm for the residue and a L2-norm for 0th order Tikhonov regularization. Applying this procedure to the experimental data, we find that cardiac myofibroblast cells tend to align both their shapes and their forces with the long axis of the deformable wavy substrate.Comment: 34 pages, 9 figure

Accurate Light Field Depth Estimation with Superpixel Regularization over Partially Occluded Regions

Depth estimation is a fundamental problem for light field photography applications. Numerous methods have been proposed in recent years, which either focus on crafting cost terms for more robust matching, or on analyzing the geometry of scene structures embedded in the epipolar-plane images. Significant improvements have been made in terms of overall depth estimation error; however, current state-of-the-art methods still show limitations in handling intricate occluding structures and complex scenes with multiple occlusions. To address these challenging issues, we propose a very effective depth estimation framework which focuses on regularizing the initial label confidence map and edge strength weights. Specifically, we first detect partially occluded boundary regions (POBR) via superpixel based regularization. Series of shrinkage/reinforcement operations are then applied on the label confidence map and edge strength weights over the POBR. We show that after weight manipulations, even a low-complexity weighted least squares model can produce much better depth estimation than state-of-the-art methods in terms of average disparity error rate, occlusion boundary precision-recall rate, and the preservation of intricate visual features

Compact Model Representation for 3D Reconstruction

3D reconstruction from 2D images is a central problem in computer vision. Recent works have been focusing on reconstruction directly from a single image. It is well known however that only one image cannot provide enough information for such a reconstruction. A prior knowledge that has been entertained are 3D CAD models due to its online ubiquity. A fundamental question is how to compactly represent millions of CAD models while allowing generalization to new unseen objects with fine-scaled geometry. We introduce an approach to compactly represent a 3D mesh. Our method first selects a 3D model from a graph structure by using a novel free-form deformation FFD 3D-2D registration, and then the selected 3D model is refined to best fit the image silhouette. We perform a comprehensive quantitative and qualitative analysis that demonstrates impressive dense and realistic 3D reconstruction from single images.Comment: 9 pages, 6 figure

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

A Two-stage Method for Inverse Medium Scattering

We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with mixed regularization. The first step is strictly direct and of sampling type, and faithfully detects the scatterer support. The second step is an innovative application of nonsmooth mixed regularization, and it accurately resolves the scatterer sizes as well as intensities. The model is efficiently solved by a semi-smooth Newton-type method. Numerical results for two- and three-dimensional examples indicate that the approach is accurate, computationally efficient, and robust with respect to data noise.Comment: 18 pages, 5 figure

Surface Modeling and Analysis Using Range Images: Smoothing, Registration, Integration, and Segmentation

This dissertation presents a framework for 3D reconstruction and scene analysis, using a set of range images. The motivation for developing this framework came from the needs to reconstruct the surfaces of small mechanical parts in reverse engineering tasks, build a virtual environment of indoor and outdoor scenes, and understand 3D images. The input of the framework is a set of range images of an object or a scene captured by range scanners. The output is a triangulated surface that can be segmented into meaningful parts. A textured surface can be reconstructed if color images are provided. The framework consists of surface smoothing, registration, integration, and segmentation. Surface smoothing eliminates the noise present in raw measurements from range scanners. This research proposes area-decreasing flow that is theoretically identical to the mean curvature flow. Using area-decreasing flow, there is no need to estimate the curvature value and an optimal step size of the flow can be obtained. Crease edges and sharp corners are preserved by an adaptive scheme. Surface registration aligns measurements from different viewpoints in a common coordinate system. This research proposes a new surface representation scheme named point fingerprint. Surfaces are registered by finding corresponding point pairs in an overlapping region based on fingerprint comparison. Surface integration merges registered surface patches into a whole surface. This research employs an implicit surface-based integration technique. The proposed algorithm can generate watertight models by space carving or filling the holes based on volumetric interpolation. Textures from different views are integrated inside a volumetric grid. Surface segmentation is useful to decompose CAD models in reverse engineering tasks and help object recognition in a 3D scene. This research proposes a watershed-based surface mesh segmentation approach. The new algorithm accurately segments the plateaus by geodesic erosion using fast marching method. The performance of the framework is presented using both synthetic and real world data from different range scanners. The dissertation concludes by summarizing the development of the framework and then suggests future research topics

Eigenvector Model Descriptors for Solving an Inverse Problem of Helmholtz Equation: Extended Materials

We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited number of coefficients associated with a basis of eigenvectors of a diffusion equation, following the regularization by discretization approach. We compare several choices for the diffusion coefficient in the partial differential equations, which are extracted from the field of image processing. We first investigate their efficiency for image decomposition (accuracy of the representation with respect to the number of variables and denoising). Next, we implement the method in the quantitative reconstruction procedure for seismic imaging, following the Full Waveform Inversion method, where the difficulty resides in that the basis is defined from an initial model where none of the actual structures is known. In particular, we demonstrate that the method is efficient for the challenging reconstruction of media with salt-domes. We employ the method in two and three-dimensional experiments and show that the eigenvector representation compensates for the lack of low frequency information, it eventually serves us to extract guidelines for the implementation of the method.Comment: 45 pages, 37 figure

Continuous Modeling of 3D Building Rooftops From Airborne LIDAR and Imagery

In recent years, a number of mega-cities have provided 3D photorealistic virtual models to support the decisions making process for maintaining the cities' infrastructure and environment more effectively. 3D virtual city models are static snap-shots of the environment and represent the status quo at the time of their data acquisition. However, cities are dynamic system that continuously change over time. Accordingly, their virtual representation need to be regularly updated in a timely manner to allow for accurate analysis and simulated results that decisions are based upon. The concept of "continuous city modeling" is to progressively reconstruct city models by accommodating their changes recognized in spatio-temporal domain, while preserving unchanged structures. However, developing a universal intelligent machine enabling continuous modeling still remains a challenging task. Therefore, this thesis proposes a novel research framework for continuously reconstructing 3D building rooftops using multi-sensor data. For achieving this goal, we first proposes a 3D building rooftop modeling method using airborne LiDAR data. The main focus is on the implementation of an implicit regularization method which impose a data-driven building regularity to noisy boundaries of roof planes for reconstructing 3D building rooftop models. The implicit regularization process is implemented in the framework of Minimum Description Length (MDL) combined with Hypothesize and Test (HAT). Secondly, we propose a context-based geometric hashing method to align newly acquired image data with existing building models. The novelty is the use of context features to achieve robust and accurate matching results. Thirdly, the existing building models are refined by newly proposed sequential fusion method. The main advantage of the proposed method is its ability to progressively refine modeling errors frequently observed in LiDAR-driven building models. The refinement process is conducted in the framework of MDL combined with HAT. Markov Chain Monte Carlo (MDMC) coupled with Simulated Annealing (SA) is employed to perform a global optimization. The results demonstrates that the proposed continuous rooftop modeling methods show a promising aspects to support various critical decisions by not only reconstructing 3D rooftop models accurately, but also by updating the models using multi-sensor data