Purpose
A fully automated segmentation algorithm, progressive surface resolution (PSR), is presented in this paper to determine the closed surface of approximately convex blob-like structures that ...are common in biomedical imaging. The PSR algorithm was applied to the cortical surface segmentation of 460 vertebral bodies on 46 low-dose chest CT images, which can be potentially used for automated bone mineral density measurement and compression fracture detection.
Methods
The target surface is realized by a closed triangular mesh, which thereby guarantees the enclosure. The surface vertices of the triangular mesh representation are constrained along radial trajectories that are uniformly distributed in 3D angle space. The segmentation is accomplished by determining for each radial trajectory the location of its intersection with the target surface. The surface is first initialized based on an input high confidence boundary image and then resolved progressively based on a dynamic attraction map in an order of decreasing degree of evidence regarding the target surface location.
Results
For the visual evaluation, the algorithm achieved acceptable segmentation for 99.35 % vertebral bodies. Quantitative evaluation was performed on 46 vertebral bodies and achieved overall mean Dice coefficient of 0.939 (with max
=
0.957, min
=
0.906 and standard deviation
=
0.011) using manual annotations as the ground truth.
Conclusions
Both visual and quantitative evaluations demonstrate encouraging performance of the PSR algorithm. This novel surface resolution strategy provides uniform angular resolution for the segmented surface with computation complexity and runtime that are linearly constrained by the total number of vertices of the triangular mesh representation.
We study the relationship between weighted graphs and stable maps between closed orientable surfaces as a global invariant and as a tool for building maps between surfaces. This work extends our ...previous results for the case of stable maps from closed orientable surfaces to the 2-sphere.
The paper deals with data filtering on closed surfaces using linear and nonlinear diffusion equations. We define a surface finite-volume method to approximate numerically parabolic partial ...differential equations on closed surfaces, namely on a sphere, ellipsoid or the Earth’s surface. The closed surface as a computational domain is approximated by a polyhedral surface created by planar triangles and we construct a dual co-volume grid. On the co-volumes we define a weak formulation of the problem by applying Green’s theorem to the Laplace–Beltrami operator. Then the finite-volume method is applied to discretize the weak formulation. Weak forms of elliptic operators are expressed through surface gradients. In our numerical scheme we use a piece-wise linear approximation of a solution in space and the backward Euler time discretization. Furthermore, we extend a linear diffusion on surface to the regularized surface Perona–Malik model. It represents a nonlinear diffusion equation, which at the same time reduces noise and preserves main edges and other details important for a correct interpretation of the real data. We present four numerical experiments. The first one has an illustrative character showing how an additive noise is filtered out from an artificial function defined on a sphere. Other three examples deal with the real geodetic data on the Earth’s surface, namely (i) we reduce a stripping noise from the GOCE satellite only geopotential model up to degree 240, (ii) we filter noise from the real GOCE measurements (the component
, and (iii) we reduce a stripping noise from the satellite only mean dynamic topography at oceans. In all experiments we focus on a comparison of the results obtained by both the linear and nonlinear models presenting advantages of the nonlinear diffusion.
N-flips in even triangulations on surfaces Kawarabayashi, Ken-ichi; Nakamoto, Atsuhiro; Suzuki, Yusuke
Journal of combinatorial theory. Series B,
2009, 2009-01-00, Letnik:
99, Številka:
1
Journal Article
Recenzirano
Odprti dostop
In this paper, we show that any two even triangulations on the same closed surface with the same and sufficiently large number of vertices can be transformed into each other by a sequence of two ...specifically defined deformations called an
N-flip and a
P
2
-flip, up to homeomorphism, if they have the same homological structure.
N-Flips in even triangulations on surfaces Kawarabayashi, Ken-ichi; Nakamoto, Atsuhiro; Suzuki, Yusuke
Electronic notes in discrete mathematics,
08/2008, Letnik:
31
Journal Article
In this paper, we show that any two even triangulations on the same closed surface with the same and sufficiently large number of vertices can be transformed into each other by a sequence of two ...specifically defined deformations called an
N-flip and a
P
2
-flip, up to homeomorphism, if they have the same homological structure.
We show that for any closed surface
F with
χ
(
F
)
⩽
−
4
(or
χ
(
F
)
⩽
−
2
), there exist graphs that triangulate the torus or the Klein bottle (or the projective plane) and that quadrangulate
F. We ...also give a sufficient condition for a graph triangulating a closed surface to quadrangulate some other surface.
In this paper, by algebraic method and Lyapunov function, we discuss the stability of non-hyperbolic equilibrium point in
R
3
, that the coefficient matrix of linearized system have a pair purely ...imaginary eigenvalues and a zero eigenvalue, with the perturbations of 3th-degree homogeneous and 3th-degree and 5th-degree homogeneous. We shall give the sufficiently conditions which can immediately distinguish that the equilibrium point is asymptotically stable or unstable and a ball-center by the coefficients of perturbed terms, meantime, we discuss the condition which produce invariant closed surface by changing the stability of equilibrium point with perturbation.
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