5,626 research outputs found
Point triangulation through polyhedron collapse using the lâ norm
Multi-camera triangulation of feature points based on a minimisation of the overall l(2) reprojection error can get stuck in suboptimal local minima or require slow global optimisation. For this reason, researchers have proposed optimising the l(infinity) norm of the l(2) single view reprojection errors, which avoids the problem of local minima entirely. In this paper we present a novel method for l(infinity) triangulation that minimizes the l(infinity) norm of the l(infinity) reprojection errors: this apparently small difference leads to a much faster but equally accurate solution which is related to the MLE under the assumption of uniform noise. The proposed method adopts a new optimisation strategy based on solving simple quadratic equations. This stands in contrast with the fastest existing methods, which solve a sequence of more complex auxiliary Linear Programming or Second Order Cone Problems. The proposed algorithm performs well: for triangulation, it achieves the same accuracy as existing techniques while executing faster and being straightforward to implement
Towards an Iterative Algorithm for the Optimal Boundary Coverage of a 3D Environment
This paper presents a new optimal algorithm for locating a set of sensors in 3D able to see the boundaries of a polyhedral environment. Our approach is iterative and is based on a lower bound on the sensors' number and on a restriction of the original problem requiring each face to be observed in its entirety by at least one sensor. The lower bound allows evaluating the quality of the solution obtained at each step, and halting the algorithm if the solution is satisfactory. The algorithm asymptotically converges to the optimal solution of the unrestricted problem if the faces are subdivided into smaller part
An Upper Bound on the Average Size of Silhouettes
It is a widely observed phenomenon in computer graphics that the size of the
silhouette of a polyhedron is much smaller than the size of the whole
polyhedron. This paper provides, for the first time, theoretical evidence
supporting this for a large class of objects, namely for polyhedra that
approximate surfaces in some reasonable way; the surfaces may be non-convex and
non-differentiable and they may have boundaries. We prove that such polyhedra
have silhouettes of expected size where the average is taken over
all points of view and n is the complexity of the polyhedron
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