15,194 research outputs found
Trifocal Relative Pose from Lines at Points and its Efficient Solution
We present a new minimal problem for relative pose estimation mixing point
features with lines incident at points observed in three views and its
efficient homotopy continuation solver. We demonstrate the generality of the
approach by analyzing and solving an additional problem with mixed point and
line correspondences in three views. The minimal problems include
correspondences of (i) three points and one line and (ii) three points and two
lines through two of the points which is reported and analyzed here for the
first time. These are difficult to solve, as they have 216 and - as shown here
- 312 solutions, but cover important practical situations when line and point
features appear together, e.g., in urban scenes or when observing curves. We
demonstrate that even such difficult problems can be solved robustly using a
suitable homotopy continuation technique and we provide an implementation
optimized for minimal problems that can be integrated into engineering
applications. Our simulated and real experiments demonstrate our solvers in the
camera geometry computation task in structure from motion. We show that new
solvers allow for reconstructing challenging scenes where the standard two-view
initialization of structure from motion fails.Comment: This material is based upon work supported by the National Science
Foundation under Grant No. DMS-1439786 while most authors were in residence
at Brown University's Institute for Computational and Experimental Research
in Mathematics -- ICERM, in Providence, R
Beyond Gr\"obner Bases: Basis Selection for Minimal Solvers
Many computer vision applications require robust estimation of the underlying
geometry, in terms of camera motion and 3D structure of the scene. These robust
methods often rely on running minimal solvers in a RANSAC framework. In this
paper we show how we can make polynomial solvers based on the action matrix
method faster, by careful selection of the monomial bases. These monomial bases
have traditionally been based on a Gr\"obner basis for the polynomial ideal.
Here we describe how we can enumerate all such bases in an efficient way. We
also show that going beyond Gr\"obner bases leads to more efficient solvers in
many cases. We present a novel basis sampling scheme that we evaluate on a
number of problems
A Global Approach for Solving Edge-Matching Puzzles
We consider apictorial edge-matching puzzles, in which the goal is to arrange
a collection of puzzle pieces with colored edges so that the colors match along
the edges of adjacent pieces. We devise an algebraic representation for this
problem and provide conditions under which it exactly characterizes a puzzle.
Using the new representation, we recast the combinatorial, discrete problem of
solving puzzles as a global, polynomial system of equations with continuous
variables. We further propose new algorithms for generating approximate
solutions to the continuous problem by solving a sequence of convex
relaxations
Extraction of cylinders and cones from minimal point sets
We propose new algebraic methods for extracting cylinders and cones from
minimal point sets, including oriented points. More precisely, we are
interested in computing efficiently cylinders through a set of three points,
one of them being oriented, or through a set of five simple points. We are also
interested in computing efficiently cones through a set of two oriented points,
through a set of four points, one of them being oriented, or through a set of
six points. For these different interpolation problems, we give optimal bounds
on the number of solutions. Moreover, we describe algebraic methods targeted to
solve these problems efficiently
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