22,494 research outputs found
A Novel Self-Intersection Penalty Term for Statistical Body Shape Models and Its Applications in 3D Pose Estimation
Statistical body shape models are widely used in 3D pose estimation due to
their low-dimensional parameters representation. However, it is difficult to
avoid self-intersection between body parts accurately. Motivated by this fact,
we proposed a novel self-intersection penalty term for statistical body shape
models applied in 3D pose estimation. To avoid the trouble of computing
self-intersection for complex surfaces like the body meshes, the gradient of
our proposed self-intersection penalty term is manually derived from the
perspective of geometry. First, the self-intersection penalty term is defined
as the volume of the self-intersection region. To calculate the partial
derivatives with respect to the coordinates of the vertices, we employed
detection rays to divide vertices of statistical body shape models into
different groups depending on whether the vertex is in the region of
self-intersection. Second, the partial derivatives could be easily derived by
the normal vectors of neighboring triangles of the vertices. Finally, this
penalty term could be applied in gradient-based optimization algorithms to
remove the self-intersection of triangular meshes without using any
approximation. Qualitative and quantitative evaluations were conducted to
demonstrate the effectiveness and generality of our proposed method compared
with previous approaches. The experimental results show that our proposed
penalty term can avoid self-intersection to exclude unreasonable predictions
and improves the accuracy of 3D pose estimation indirectly. Further more, the
proposed method could be employed universally in triangular mesh based 3D
reconstruction
Bending invariant meshes and application to groupwise correspondences
We introduce a new bending invariant representation of a triangular mesh S. The bending invariant mesh X of S is a deformation of S that has the property that the geodesic distance between each pair of vertices on S is approximated well by the Euclidean distance between the corresponding vertices on X. Furthermore, X is intersection-free. The main advantage of the bending invariant mesh compared to previous approaches is that mesh-based features on X can be used to facilitate applications such as shape recognition or shape registration. We apply bending invariant meshes to find dense point-to-point correspondences between a number of deformed surfaces corresponding to different postures of the same non-rigid object in a fully automatic way. 1
Dual virtual element method for discrete fractures networks
Discrete fracture networks is a key ingredient in the simulation of physical
processes which involve fluid flow in the underground, when the surrounding
rock matrix is considered impervious. In this paper we present two different
models to compute the pressure field and Darcy velocity in the system. The
first allows a normal flow out of a fracture at the intersections, while the
second grants also a tangential flow along the intersections. For the numerical
discretization, we use the mixed virtual finite element method as it is known
to handle grid elements of, almost, any arbitrary shape. The flexibility of the
discretization allows us to loosen the requirements on grid construction, and
thus significantly simplify the flow discretization compared to traditional
discrete fracture network models. A coarsening algorithm, from the algebraic
multigrid literature, is also considered to further speed up the computation.
The performance of the method is validated by numerical experiments
Simple and Robust Boolean Operations for Triangulated Surfaces
Boolean operations of geometric models is an essential issue in computational
geometry. In this paper, we develop a simple and robust approach to perform
Boolean operations on closed and open triangulated surfaces. Our method mainly
has two stages: (1) We firstly find out candidate intersected-triangles pairs
based on Octree and then compute the inter-section lines for all pairs of
triangles with parallel algorithm; (2) We form closed or open
intersection-loops, sub-surfaces and sub-blocks quite robustly only according
to the cleared and updated topology of meshes while without coordinate
computations for geometric enti-ties. A novel technique instead of
inside/outside classification is also proposed to distinguish the resulting
union, subtraction and intersection. Several examples have been given to
illus-trate the effectiveness of our approach.Comment: Novel method for determining Union, Subtraction and Intersectio
Holomorphic vector fields and quadratic differentials on planar triangular meshes
Given a triangulated region in the complex plane, a discrete vector field
assigns a vector to every vertex. We call such a vector
field holomorphic if it defines an infinitesimal deformation of the
triangulation that preserves length cross ratios. We show that each holomorphic
vector field can be constructed based on a discrete harmonic function in the
sense of the cotan Laplacian. Moreover, to each holomorphic vector field we
associate in a M\"obius invariant fashion a certain holomorphic quadratic
differential. Here a quadratic differential is defined as an object that
assigns a purely imaginary number to each interior edge. Then we derive a
Weierstrass representation formula, which shows how a holomorphic quadratic
differential can be used to construct a discrete minimal surface with
prescribed Gau{\ss} map and prescribed Hopf differential.Comment: 17 pages; final version, to appear in "Advances in Discrete
Differential Geometry", ed. A. I. Bobenko, Springer, 2016; references adde
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