1,927 research outputs found
Fast B-spline Curve Fitting by L-BFGS
We propose a novel method for fitting planar B-spline curves to unorganized
data points. In traditional methods, optimization of control points and foot
points are performed in two very time-consuming steps in each iteration: 1)
control points are updated by setting up and solving a linear system of
equations; and 2) foot points are computed by projecting each data point onto a
B-spline curve. Our method uses the L-BFGS optimization method to optimize
control points and foot points simultaneously and therefore it does not need to
perform either matrix computation or foot point projection in every iteration.
As a result, our method is much faster than existing methods
Registration of 3D Point Clouds and Meshes: A Survey From Rigid to Non-Rigid
Three-dimensional surface registration transforms multiple three-dimensional data sets into the same coordinate system so as to align overlapping components of these sets. Recent surveys have covered different aspects of either rigid or nonrigid registration, but seldom discuss them as a whole. Our study serves two purposes: 1) To give a comprehensive survey of both types of registration, focusing on three-dimensional point clouds and meshes and 2) to provide a better understanding of registration from the perspective of data fitting. Registration is closely related to data fitting in which it comprises three core interwoven components: model selection, correspondences and constraints, and optimization. Study of these components 1) provides a basis for comparison of the novelties of different techniques, 2) reveals the similarity of rigid and nonrigid registration in terms of problem representations, and 3) shows how overfitting arises in nonrigid registration and the reasons for increasing interest in intrinsic techniques. We further summarize some practical issues of registration which include initializations and evaluations, and discuss some of our own observations, insights and foreseeable research trends
A Minimalist Approach to Type-Agnostic Detection of Quadrics in Point Clouds
This paper proposes a segmentation-free, automatic and efficient procedure to
detect general geometric quadric forms in point clouds, where clutter and
occlusions are inevitable. Our everyday world is dominated by man-made objects
which are designed using 3D primitives (such as planes, cones, spheres,
cylinders, etc.). These objects are also omnipresent in industrial
environments. This gives rise to the possibility of abstracting 3D scenes
through primitives, thereby positions these geometric forms as an integral part
of perception and high level 3D scene understanding.
As opposed to state-of-the-art, where a tailored algorithm treats each
primitive type separately, we propose to encapsulate all types in a single
robust detection procedure. At the center of our approach lies a closed form 3D
quadric fit, operating in both primal & dual spaces and requiring as low as 4
oriented-points. Around this fit, we design a novel, local null-space voting
strategy to reduce the 4-point case to 3. Voting is coupled with the famous
RANSAC and makes our algorithm orders of magnitude faster than its conventional
counterparts. This is the first method capable of performing a generic
cross-type multi-object primitive detection in difficult scenes. Results on
synthetic and real datasets support the validity of our method.Comment: Accepted for publication at CVPR 201
Physics Of Eclipsing Binaries. II. Towards the Increased Model Fidelity
The precision of photometric and spectroscopic observations has been
systematically improved in the last decade, mostly thanks to space-borne
photometric missions and ground-based spectrographs dedicated to finding
exoplanets. The field of eclipsing binary stars strongly benefited from this
development. Eclipsing binaries serve as critical tools for determining
fundamental stellar properties (masses, radii, temperatures and luminosities),
yet the models are not capable of reproducing observed data well either because
of the missing physics or because of insufficient precision. This led to a
predicament where radiative and dynamical effects, insofar buried in noise,
started showing up routinely in the data, but were not accounted for in the
models. PHOEBE (PHysics Of Eclipsing BinariEs; http://phoebe-project.org) is an
open source modeling code for computing theoretical light and radial velocity
curves that addresses both problems by incorporating missing physics and by
increasing the computational fidelity. In particular, we discuss triangulation
as a superior surface discretization algorithm, meshing of rotating single
stars, light time travel effect, advanced phase computation, volume
conservation in eccentric orbits, and improved computation of local intensity
across the stellar surfaces that includes photon-weighted mode, enhanced limb
darkening treatment, better reflection treatment and Doppler boosting. Here we
present the concepts on which PHOEBE is built on and proofs of concept that
demonstrate the increased model fidelity.Comment: 60 pages, 15 figures, published in ApJS; accompanied by the release
of PHOEBE 2.0 on http://phoebe-project.or
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
Numerical Fitting-based Likelihood Calculation to Speed up the Particle Filter
The likelihood calculation of a vast number of particles is the computational
bottleneck for the particle filter in applications where the observation
information is rich. For fast computing the likelihood of particles, a
numerical fitting approach is proposed to construct the Likelihood Probability
Density Function (Li-PDF) by using a comparably small number of so-called
fulcrums. The likelihood of particles is thereby analytically inferred,
explicitly or implicitly, based on the Li-PDF instead of directly computed by
utilizing the observation, which can significantly reduce the computation and
enables real time filtering. The proposed approach guarantees the estimation
quality when an appropriate fitting function and properly distributed fulcrums
are used. The details for construction of the fitting function and fulcrums are
addressed respectively in detail. In particular, to deal with multivariate
fitting, the nonparametric kernel density estimator is presented which is
flexible and convenient for implicit Li-PDF implementation. Simulation
comparison with a variety of existing approaches on a benchmark 1-dimensional
model and multi-dimensional robot localization and visual tracking demonstrate
the validity of our approach.Comment: 42 pages, 17 figures, 4 tables and 1 appendix. This paper is a
draft/preprint of one paper submitted to the IEEE Transaction
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