451 research outputs found
Steklov Spectral Geometry for Extrinsic Shape Analysis
We propose using the Dirichlet-to-Neumann operator as an extrinsic
alternative to the Laplacian for spectral geometry processing and shape
analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator,
cannot capture the spatial embedding of a shape up to rigid motion, and many
previous extrinsic methods lack theoretical justification. Instead, we consider
the Steklov eigenvalue problem, computing the spectrum of the
Dirichlet-to-Neumann operator of a surface bounding a volume. A remarkable
property of this operator is that it completely encodes volumetric geometry. We
use the boundary element method (BEM) to discretize the operator, accelerated
by hierarchical numerical schemes and preconditioning; this pipeline allows us
to solve eigenvalue and linear problems on large-scale meshes despite the
density of the Dirichlet-to-Neumann discretization. We further demonstrate that
our operators naturally fit into existing frameworks for geometry processing,
making a shift from intrinsic to extrinsic geometry as simple as substituting
the Laplace-Beltrami operator with the Dirichlet-to-Neumann operator.Comment: Additional experiments adde
Implicit meshes:unifying implicit and explicit surface representations for 3D reconstruction and tracking
This thesis proposes novel ways both to represent the static surfaces, and to parameterize their deformations. This can be used both by automated algorithms for efficient 3–D shape reconstruction, and by graphics designers for editing and animation. Deformable 3–D models can be represented either as traditional explicit surfaces, such as triangulated meshes, or as implicit surfaces. Explicit surfaces are widely accepted because they are simple to deform and render, however fitting them involves minimizing a non-differentiable distance function. By contrast, implicit surfaces allow fitting by minimizing a differentiable algebraic distance, but they are harder to meaningfully deform and render. Here we propose a method that combines the strength of both representations to avoid their drawbacks, and in this way build robust surface representation, called implicit mesh, suitable for automated shape recovery from video sequences. This surface representation lets us automatically detect and exploit silhouette constraints in uncontrolled environments that may involve occlusions and changing or cluttered backgrounds, which limit the applicability of most silhouette based methods. We advocate the use of Dirichlet Free Form Deformation (DFFD) as generic surface deformation technique that can be used to parameterize objects of arbitrary geometry defined as explicit meshes. It is based on the small set of control points and the generalized interpolant. Control points become model parameters and their change causes model's shape modification. Using such parameterization the problem dimensionality can be dramatically reduced, which is desirable property for most optimization algorithms, thus makes DFFD good tool for automated fitting. Combining DFFD as a generic parameterization method for explicit surfaces and implicit meshes as a generic surface representation we obtained a powerfull tool for automated shape recovery from images. However, we also argue that any other avaliable surface parameterization can be used. We demonstrate the applicability of our technique to 3–D reconstruction of the human upper-body including – face, neck and shoulders, and the human ear, from noisy stereo and silhouette data. We also reconstruct the shape of a high resolution human faces parametrized in terms of a Principal Component Analysis model from interest points and automatically detected silhouettes. Tracking of deformable objects using implicit meshes from silhouettes and interest points in monocular sequences is shown in following two examples: Modeling the deformations of a piece of paper represented by an ordinary triangulated mesh; tracking a person's shoulders whose deformations are expressed in terms of Dirichlet Free Form Deformations
Unwind: Interactive Fish Straightening
The ScanAllFish project is a large-scale effort to scan all the world's
33,100 known species of fishes. It has already generated thousands of
volumetric CT scans of fish species which are available on open access
platforms such as the Open Science Framework. To achieve a scanning rate
required for a project of this magnitude, many specimens are grouped together
into a single tube and scanned all at once. The resulting data contain many
fish which are often bent and twisted to fit into the scanner. Our system,
Unwind, is a novel interactive visualization and processing tool which
extracts, unbends, and untwists volumetric images of fish with minimal user
interaction. Our approach enables scientists to interactively unwarp these
volumes to remove the undesired torque and bending using a piecewise-linear
skeleton extracted by averaging isosurfaces of a harmonic function connecting
the head and tail of each fish. The result is a volumetric dataset of a
individual, straight fish in a canonical pose defined by the marine biologist
expert user. We have developed Unwind in collaboration with a team of marine
biologists: Our system has been deployed in their labs, and is presently being
used for dataset construction, biomechanical analysis, and the generation of
figures for scientific publication
Implicit Meshes for Effective Silhouette Handling
Using silhouettes in uncontrolled environments typically requires handling occlusions as well as changing or cluttered backgrounds, which limits the applicability of most silhouette based methods. For the purpose of 3-D shape modeling, we show that representing generic 3-D surfaces as implicit surfaces lets us effectively address these issues. This desirable behavior is completely independent from the way the surface deformations are parame-trized. To show this, we demonstrate our technique in three very different cases: Modeling the deformations of a piece of paper represented by an ordinary triangulated mesh; reconstruction and tracking a person's shoulders whose deformations are expressed in terms of Dirichlet Free Form Deformations; reconstructing the shape of a human face parametrized in terms of a Principal Component Analysis mode
Implicit Meshes for Effective Silhouette Handling
Using silhouettes in uncontrolled environments typically requires handling occlusions as well as changing or cluttered backgrounds, which limits the applicability of most silhouette based methods. For the purpose of 3--D shape modeling, we show that representing generic 3--D surfaces as implicit surfaces lets us effectively address these issues. This desirable behavior is completely independent from the way the surface deformations are parametrized. To show this, we demonstrate our technique in three very different cases: Modeling the deformations of a piece of paper represented by an ordinary triangulated mesh; reconstruction and tracking a person's shoulders whose deformations are expressed in terms of Dirichlet Free Form Deformations; reconstructing the shape of a human face parametrized in terms of a Principal Component Analysis model
Surface Deformation Models for Non-Rigid 3--D Shape Recovery
3--D detection and shape recovery of a non-rigid surface from video sequences require deformation models to effectively take advantage of potentially noisy image data. Here we introduce an approach to creating such models for deformable 3--D surfaces. We exploit the fact that the shape of an inextensible triangulated mesh can be parameterized in terms of a small subset of the angles between its facets. We use this set of angles to create a representative set of potential shapes, which we feed to a simple dimensionality reduction technique to produce low-dimensional 3--D deformation models. We show that these models can be used to accurately model a wide range of deforming 3--D surfaces from video sequences acquired under realistic conditions
Laplacian Meshes for Monocular 3D Shape Recovery
We show that by extending the Laplacian formalism, which was first introduced in the Graphics community to regularize 3D meshes, we can turn the monocular 3D shape reconstruction of a deformable surface given correspondences with a reference image into a well-posed problem. Furthermore, this does not require any training data and eliminates the need to pre-align the reference shape with the one to be reconstructed, as was done in earlier methods
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