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Extracting approximate symmetry planes is a
challenge due to the difficulty of accurately measuring numerical values.
Introducing the approximate symmetry planes of a 3D point set, this paper
presents a new method by gathering normal vectors of potential of the planes,
clustering the high probability ones, and then testing and verifying the
planes. An experiment showed that the method is effective, robust and
universal for extracting the complete approximate planes of symmetry of a
random 3D point set.
We establish fixed point theorems in complete fuzzy metric space by using
notion of altering distance, initiated by Khan et al. [Bull. Austral. Math. Soc. 30 (1984), 1-9]. Also, we find an
affirmative answer in fuzzy metric space to the problem of Sastry [TamkangJ. Math.,
31(3) (2000), 243-250].
The Coherent Point Drift (CPD) algorithm which
based on Gauss Mixture Model is a robust point set registration algorithm. However,
the selection of robustness weight which used to describe the noise may directly
affect the point set registration efficiency. For resolving the problem, this paper
presents a CPD registration algorithm which based on distance threshold constraint.
Before the point set registration, the inaccurate template point set by resampling
become the initial point set of point set matching, in order to eliminate some points
that the distance to target point set is too close and too far in the inaccurate
template point set, and set the weights of robustness as
. In the simulation experiments, we make two group experiments:
the first group is the registration of the inaccurate template point set and the
accurate target point set, while the second group is the registration of the accurate
template point set and the accurate target point set. The results of comparison
show that our method can solve the problem of selection for the weight. And it improves
the speed and precision of the original CPD registration.
In the paper, an improved algorithm is presented for Delaunay triangulation of the point-set in the plain. Based on the original algorithm, we propose the notion of removing circle. During the process of triangulation, and the circle dynamically moves, the algorithm which is simple and practical, therefore evidently accelerates the process of searching a new point, while generating a new triangle. Then it shows the effect of the algorithm in the finite element mesh.
In this paper, I
have provided a brief introduction on M?bius transformation and explored some
basic properties of this kind of transformation. For instance, M?bius
transformation is classified according to the invariant points. Moreover, we
can see that M?bius transformation is hyperbolic isometries that form a group
action PSL (2, R) on the upper half