5,880 research outputs found
Three New Algorithms for Projective Bundle Adjustment with Minimum Parameters
Bundle adjustment is a technique used to compute the maximum likelihood estimate of structure and motion from image feature correspondences. It practice, large non-linear systems have to be solved, most of the time using an iterative optimization process starting from a sub-optimal solution obtained by using linear methods. The behaviour, in terms of convergence, and the computational cost of this process depend on the parameterization used to represent the problem, i.e. of structure and motion. In this paper, we address the problem of finding a minimal parameterization of projective structure and motion, i.e. when camera calibration is not available. Most of the existing parameterizations are either sub-optimal, in the sense that they do change the cost function, or quite complicated to implement, requiring different closed-form expressions, also called maps, to model every case. Without loss of generality, we restrict the problem to the minimal parameterization of the two-view projective motion, equivalent to the fundamental matrix. We propose to classify existing ways allowing to obtain a minimal set of parameters into three categories and present three new algorithms, one for each category. These algorithms are simple to implement and yield minimal parameterizations. We also address the problem of minimally parameterizing homogeneous entities. We present what we call mapped coordinates, a tool allowing to optimize homogeneous entities over a minimal number of parameters. We make extensive use of this tool for both structure and motion parameterization. We compare these algorithms with existing ones using both simulated data and real images. In the light of these experiments, it appears that the new algorithms perform better than existing ones in terms of computational cost while achieving equivalent performances in terms of convergence
Automated Top View Registration of Broadcast Football Videos
In this paper, we propose a novel method to register football broadcast video
frames on the static top view model of the playing surface. The proposed method
is fully automatic in contrast to the current state of the art which requires
manual initialization of point correspondences between the image and the static
model. Automatic registration using existing approaches has been difficult due
to the lack of sufficient point correspondences. We investigate an alternate
approach exploiting the edge information from the line markings on the field.
We formulate the registration problem as a nearest neighbour search over a
synthetically generated dictionary of edge map and homography pairs. The
synthetic dictionary generation allows us to exhaustively cover a wide variety
of camera angles and positions and reduce this problem to a minimal per-frame
edge map matching procedure. We show that the per-frame results can be improved
in videos using an optimization framework for temporal camera stabilization. We
demonstrate the efficacy of our approach by presenting extensive results on a
dataset collected from matches of football World Cup 2014
Calipso: Physics-based Image and Video Editing through CAD Model Proxies
We present Calipso, an interactive method for editing images and videos in a
physically-coherent manner. Our main idea is to realize physics-based
manipulations by running a full physics simulation on proxy geometries given by
non-rigidly aligned CAD models. Running these simulations allows us to apply
new, unseen forces to move or deform selected objects, change physical
parameters such as mass or elasticity, or even add entire new objects that
interact with the rest of the underlying scene. In Calipso, the user makes
edits directly in 3D; these edits are processed by the simulation and then
transfered to the target 2D content using shape-to-image correspondences in a
photo-realistic rendering process. To align the CAD models, we introduce an
efficient CAD-to-image alignment procedure that jointly minimizes for rigid and
non-rigid alignment while preserving the high-level structure of the input
shape. Moreover, the user can choose to exploit image flow to estimate scene
motion, producing coherent physical behavior with ambient dynamics. We
demonstrate Calipso's physics-based editing on a wide range of examples
producing myriad physical behavior while preserving geometric and visual
consistency.Comment: 11 page
Bridging the computational gap between mesoscopic and continuum modeling of red blood cells for fully resolved blood flow
We present a computational framework for the simulation of blood flow with
fully resolved red blood cells (RBCs) using a modular approach that consists of
a lattice Boltzmann solver for the blood plasma, a novel finite element based
solver for the deformable bodies and an immersed boundary method for the
fluid-solid interaction. For the RBCs, we propose a nodal projective FEM
(npFEM) solver which has theoretical advantages over the more commonly used
mass-spring systems (mesoscopic modeling), such as an unconditional stability,
versatile material expressivity, and one set of parameters to fully describe
the behavior of the body at any mesh resolution. At the same time, the method
is substantially faster than other FEM solvers proposed in this field, and has
an efficiency that is comparable to the one of mesoscopic models. At its core,
the solver uses specially defined potential energies, and builds upon them a
fast iterative procedure based on quasi-Newton techniques. For a known
material, our solver has only one free parameter that demands tuning, related
to the body viscoelasticity. In contrast, state-of-the-art solvers for
deformable bodies have more free parameters, and the calibration of the models
demands special assumptions regarding the mesh topology, which restrict their
generality and mesh independence. We propose as well a modification to the
potential energy proposed by Skalak et al. 1973 for the red blood cell
membrane, which enhances the strain hardening behavior at higher deformations.
Our viscoelastic model for the red blood cell, while simple enough and
applicable to any kind of solver as a post-convergence step, can capture
accurately the characteristic recovery time and tank-treading frequencies. The
framework is validated using experimental data, and it proves to be scalable
for multiple deformable bodies
Autocalibration with the Minimum Number of Cameras with Known Pixel Shape
In 3D reconstruction, the recovery of the calibration parameters of the
cameras is paramount since it provides metric information about the observed
scene, e.g., measures of angles and ratios of distances. Autocalibration
enables the estimation of the camera parameters without using a calibration
device, but by enforcing simple constraints on the camera parameters. In the
absence of information about the internal camera parameters such as the focal
length and the principal point, the knowledge of the camera pixel shape is
usually the only available constraint. Given a projective reconstruction of a
rigid scene, we address the problem of the autocalibration of a minimal set of
cameras with known pixel shape and otherwise arbitrarily varying intrinsic and
extrinsic parameters. We propose an algorithm that only requires 5 cameras (the
theoretical minimum), thus halving the number of cameras required by previous
algorithms based on the same constraint. To this purpose, we introduce as our
basic geometric tool the six-line conic variety (SLCV), consisting in the set
of planes intersecting six given lines of 3D space in points of a conic. We
show that the set of solutions of the Euclidean upgrading problem for three
cameras with known pixel shape can be parameterized in a computationally
efficient way. This parameterization is then used to solve autocalibration from
five or more cameras, reducing the three-dimensional search space to a
two-dimensional one. We provide experiments with real images showing the good
performance of the technique.Comment: 19 pages, 14 figures, 7 tables, J. Math. Imaging Vi
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