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Method for performing medical volume data vectorization through three-variable biharmonic B-spline function

A vectorization and volume data technology, applied in the field of vectorization of medical volume data, can solve the problems of inaccuracy and precision limitation

Active Publication Date: 2014-04-02
BEIHANG UNIV
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

For the double Laplacian, many methods are constructed using the iterative Laplacian method, however, in irregular grids, their accuracy is limited, Feng et al. improved the approximation accuracy to cubic by adding the cubic constraint, But in 3D space, this is still not accurate enough

Method used

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  • Method for performing medical volume data vectorization through three-variable biharmonic B-spline function
  • Method for performing medical volume data vectorization through three-variable biharmonic B-spline function
  • Method for performing medical volume data vectorization through three-variable biharmonic B-spline function

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Experimental program
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Embodiment Construction

[0041] 1. Bivariate Bihomonic and B-spline review

[0042] Bivariate harmonic B-spline Δφ based on harmonic equation y (x) = δ(x-y), where Δ is the Laplacian operator. δ is the Dirac delta function. In a two-dimensional plane, the solution of this equation is Green's theorem is:

[0043]

[0044] where n is the boundary The outer normal vector of . The above integral is equal to 1 if the point y ∈ Ω, and 0 otherwise. The discrete form of the above integral is:

[0045]

[0046] where t j is the jth node, means t j a ring neighborhood of . is node t j The Voronoi region of v ij is the connection node t i and t j edge, e ij is perpendicular to v ij The edges of the Voronoi diagram.

[0047] Similarly, the biharmonic equation Δ 2 φ y The solution of (x)=δ(x-y) on the two-dimensional plane is φ y ( x ) = 1 8 π...

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Abstract

The invention provides a method for performing medical volume data vectorization through a three-variable biharmonic B-spline function. A method based on quadratic programming is provided to construct a three-variable biharmonic B-spline primary function, and aiming at specialized function sets, the method calculates a discrete laplace operator, so as to minimize an error function. The method analyzes that the primary function approximately meets local conditions and unit partition conditions. According to the invention, based on the biharmonic B-spline function, the novel volume data vectorization method is designed. An implicit function is taken as vectorization expression and is optimized through a linear programming method, so that three-dimensional medical volume data vectorization is accomplished.

Description

technical field [0001] The invention relates to a method for vectorizing medical volume data by using three-variable biharmonic and B-spline functions. Background technique [0002] Many scholars have proposed a variety of discrete data interpolation methods before. Radius basis function is a kind of commonly used basis function (Buhmann M.D., Buhmann M.D.: Radial Basis Functions. Cambridge University Press, New York, NY, USA, 2003.), such as Gaussian function, thin plate spline and so on. In many cases, each basis function is independent of each other, so that the unit decomposition condition (that is, the sum of all basis functions is equal to 1) cannot be satisfied. Spline functions, such as cubic splines, polycube splines (Wang H., He Y., Li X., Gu X., Qin H.: Polycube splines.Comput.Aided Des.40, 6( June2008), 721–733.), Voronoi spline (Voronoi spline) (Mirzargar M., Entezari A.: Voronoi splines.IEEE Transactions on Signal Processing58, 9(2010), 4572–4582.), etc. can ...

Claims

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Application Information

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IPC IPC(8): G06T15/08G06T7/00
Inventor 侯飞王莉莉秦洪张玉茹赵沁平
Owner BEIHANG UNIV
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