98,172 research outputs found
Algorithms for morphological profile filters and their comparison
Morphological filters, regarded as the complement of mean-line based filters, are useful in the analysis of surface texture and the prediction of functional performance. The paper first recalls two existing algorithms, the naive algorithm and the motif combination algorithm, originally developed for the traditional envelope filter. With minor extension, they could be used to compute morphological filters. A recent novel approach based on the relationship between the alpha shape and morphological closing and opening operations is presented as well. Afterwards two novel algorithms are developed. By correlating the convex hull and morphological operations, the Graham scan algorithm, original developed for the convex hull is modified to compute the morphological envelopes. The alpha shape method depending on the Delaunay triangulation is costly and redundant for the computation for the alpha shape for a given radius. A recursive algorithm is proposed to solve this problem. A series of observations are presented for searching the contact points. Based on the proposed observations, the algorithm partitions the profile data into small segments and searches the contact points in a recursive manner. The paper proceeds to compare the five distinct algorithms in five aspects: algorithm verification, algorithm analysis, performance evaluation, end effects correction, and areal extension. By looking into these aspects, the merits and shortcomings of these algorithms are evaluated and compared
Geometric triangulations and the Teichm\"uller TQFT volume conjecture for twist knots
We construct a new infinite family of ideal triangulations and
H-triangulations for the complements of twist knots, using a method originating
from Thurston. These triangulations provide a new upper bound for the Matveev
complexity of twist knot complements. We then prove that these ideal
triangulations are geometric. The proof uses techniques of Futer and the second
author, which consist in studying the volume functional on the polyhedron of
angle structures. Finally, we use these triangulations to compute explicitly
the partition function of the Teichm\"uller TQFT and to prove the associated
volume conjecture for all twist knots, using the saddle point method.Comment: v4: 90 pages, 25 figures. Comments welcome. Some of the results in
this paper were announced in a note at the C. R. Acad. Sci. Paris, and some
were detailed in the arXiv v1. Since v3, we made minor corrections, we added
details in Section 2.9, and we added Remark 3.
Efficient moving point handling for incremental 3D manifold reconstruction
As incremental Structure from Motion algorithms become effective, a good
sparse point cloud representing the map of the scene becomes available
frame-by-frame. From the 3D Delaunay triangulation of these points,
state-of-the-art algorithms build a manifold rough model of the scene. These
algorithms integrate incrementally new points to the 3D reconstruction only if
their position estimate does not change. Indeed, whenever a point moves in a 3D
Delaunay triangulation, for instance because its estimation gets refined, a set
of tetrahedra have to be removed and replaced with new ones to maintain the
Delaunay property; the management of the manifold reconstruction becomes thus
complex and it entails a potentially big overhead. In this paper we investigate
different approaches and we propose an efficient policy to deal with moving
points in the manifold estimation process. We tested our approach with four
sequences of the KITTI dataset and we show the effectiveness of our proposal in
comparison with state-of-the-art approaches.Comment: Accepted in International Conference on Image Analysis and Processing
(ICIAP 2015
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