CN108961224A - A kind of coronary artery blood vessel Geometric model reconstruction method based on implicit stretching curved surface - Google Patents
A kind of coronary artery blood vessel Geometric model reconstruction method based on implicit stretching curved surface Download PDFInfo
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/0002—Inspection of images, e.g. flaw detection
- G06T7/0012—Biomedical image inspection
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/30—Subject of image; Context of image processing
- G06T2207/30004—Biomedical image processing
- G06T2207/30101—Blood vessel; Artery; Vein; Vascular
Abstract
A kind of coronary artery blood vessel Geometric model reconstruction method based on implicit stretching curved surface, is related to computer Medical Image Processing and three-dimensional reconstruction field.The vessel cross-sections information perpendicular with it can be constructed, and realize the accurate expression to each vascular cross-section lumen profile using 2D PSPS function according to the central axes of each apparatus derivatorius of coronary artery blood vessel extracted；Then, its corresponding implicit stretching curved surface IES according to these cross-sectional configurations, and smoothly mix to form three-dimensional vascular arborization model by these IES along central axes；Finally, the vascular arborization model smoothing of these implied expressions is mixed using SPBBO, constitute vascular arborization structure, and then realize the three-dimensional reconstruction to entire coronary artery vascular tree luminal surface model.
Description
Technical field
The present invention relates to computer Medical Image Processings and three-dimensional reconstruction field, are stretched more particularly, to one kind based on implicit
The coronary artery blood vessel Geometric model reconstruction method of curved surface (Implicit Extruded Surfaces, IES).
Background technique
Coronary artery disease (Coronary Artery Disease, CAD), also known as coronary heart disease are that the whole world generally acknowledges tight
One of human life and three big diseases of health are threatened again.Coronary artery CT angiography (Computed Tomography
Angiography, CTA) have many advantages, such as that hurtless measure, inspection are quick, low-cost, the one kind for having become assessment CAD has very much
The image check mode of future.Compared with simple visualization, individuation coronary artery is accurately reconstructed from CTA image
3-D geometric model, the coronary artery vascular morphology parameter that can greatly facilitate doctor's quantitative analysis important (including blood vessel segment length,
Volume, plaque volume and stenosis etc.), this judgement and intervention to the visible diagnosis, Treatment decsion of coronary artery disease
Evaluation of therapeutic effect etc. is all particularly important.
It is usually to be indicated by some discrete points using the blood vessel structure information that dividing method extracts, effect of visualization
It is extremely bad, and be difficult to meet subsequent shape of blood vessel analysis, haemodynamics simulation, vascular surgery planning and face with simulating etc.
The demand of bed application.Therefore, it is necessary to reconstruct continuous, entity blood vessel geometrical model using modeling technique.According to blood
The method of the expression way of pipe surface model, blood vessel Geometric Modeling can be summarized as two major classes: explicit modeling (explicit
Modeling) method and implicit modeling (implicit modeling) method.Explicit modeling method, which refers to, utilizes explicit expression
Mode, i.e. polygonal mesh or parameterized function, such as non-uniform rational B-spline (NURBS) function, to indicate blood vessel surface mould
Type information.On the other hand, implicit modeling method refers to using implicit function (implicit function) geometry for indicating blood vessel
Model information.A kind of typical method is (Oeltze, S.and Preim, B., the Visualization of of document 1
Vascular Structures with convolution surfaces:Method,Validation and
Evaluation,IEEE Transactions on Medical Imaging,vol.25,no.3,pp.540–549,2005)
The vascular pattern based on Convolution Surfaces proposed is rebuild.The smooth transition of apparatus derivatorius may be implemented in this method
And reach the visualization of blood vessels effect picture of high quality, however, since it assumes that vascular cross-section is circular, so it is constructed
Blood vessel geometrical model be morphologic approximation, be not accurate reconstructing blood vessel.Another method is document 2
(Schumann,C.,Neugebauer,M.,Bade,R.,Peitgen,H.-O.,and Preim,B.,Implicit vessel
surface reconstruction for visualization and CFD simulation,International
Journal of Computer Assisted Radiology and Surgery,vol.2,no.5,pp.275-286,
2008) the implicit blood vessel table based on MPUI (Multi-level Partition ofUnity Implicits) algorithm proposed
Face reconstruction technique.The technology can relatively accurately reconstruct the surface texture of blood vessel, and not have to stick to any hypothesized model.So
And due to the complexity of blood vessel structure, the blood vessel surface quality after rebuilding not is highly desirable.For the weight for reaching better quality
Build effect, (Hong, Q.Q., Li, Q., and Tian, J., Implicit the reconstruction of of document 3
vasculatures using bivariate piecewise algebraic splines,IEEE Transactions on
Medical Imaging, vol.31, no.3, pp.543-553,2012) it proposes based on segmentation algebra spline function (PAS)
Blood vessel modeling method can construct high quality and relatively accurate blood vessel geometrical model, but when blood vessel central axes are more curved
Qu Shi, the accuracy for constructing model will receive larger impact.Document 4 (Kretschmer, J., Godenschwager, C.,
Preim,B.,and Stamminger,M.,Interactive Patient-Specific Vascular Modeling
with Sweep Surfaces,IEEE Transactions on Visualization and Computer Graphics,
Vol.19, no.12, pp.2828-2837,2013.) a kind of blood vessel modeling method based on Sweep Surfaces is proposed, it should
Method can construct relatively accurate vascular pattern, but it can only guarantee the C1 continuity of model surface, and can not construct
One specific mathematic(al) representation.
Summary of the invention
It is an object of the invention to be directed to the shape feature of coronary artery blood vessel structure, and the advantage of implicit modeling technique is combined,
Design stretches curved surface (Implicit Extruded Surface) based on implicit, and to reconstruct entity, accurate, height smoothly connects
It is continuous, it provides a kind of based on the implicit coronary artery blood vessel Geometric model reconstruction method for stretching curved surface with mathematical analysis expression formula.
Firstly, the blood perpendicular with it can be constructed according to the central axes of each apparatus derivatorius of coronary artery blood vessel extracted
Pipe cross sectional information, and utilize 2D PSPS (Li, Q.and Tian, J., 2D piecewise algebraic splines
for implicit modeling,ACM Transactions on Graphics,vol.28,no.2,pp.1-19,2009)
Function realizes the accurate expression to each vascular cross-section lumen profile；Then, its corresponding implicit drawing according to these cross-sectional configurations
Curved surface IES is stretched, and smoothly mixes to form three-dimensional vascular arborization model by these IES along central axes；Finally, using
SPBBO(Li,Q.,Smooth Piecewise Polynomial Blending Operations for implicit
Shapes, Computer Graphics forum, vol.26, no.2, pp.157-171,2007) by the blood of these implied expressions
It mixes to vessel branches model smoothing, constitutes vascular arborization structure (bifurcation), and then realize to entire coronary artery blood vessel
The three-dimensional reconstruction of luminal surface model is set, the specific method is as follows:
1) accurate expression to each vascular cross-section lumen profile is realized using 2D PSPS function；
It is described to be realized using 2D PSPS function to the accurate expression of each vascular cross-section lumen profile in step 1)
Specific method can are as follows: the implicit modeling method of Most current is all to indicate cross section profile using round or elliptic curve, such side
Although method is simple, efficient, the cross section information of real blood vessels cannot be accurately expressed, this is because the cross section profile of real blood vessels
And it is not all the shape of rule, the blood vessel of special diseased region；In the quasi- tree-shaped modeling method proposed, free form will be utilized
(model-free) 2D PSPS realizes the accurate expression to irregular section profile, as the one strong of implicit modeling field
Big tool, 2D PSPS function has the advantages that all of traditional B-spline function based on 2D vector product, moreover, it has explicitly
Mathematical analysis expression formula.
The control point being made of for one group sequence counter-clockwise, corresponding Implicit Curves can be directly by 2D PSPS functionsIt expresses, wherein Δ indicates control point；δ is smoothing parameter；M is the Smoothness Index of PSPS function；H is phase
The height value answered.
2) its corresponding implicit stretching curved surface IES according to cross-sectional configuration, and smoothly mix these IES along central axes
Get up to form three-dimensional vascular arborization model；
In step 2), it is described according to cross-sectional configuration its it is corresponding implicit stretch curved surface IES, and along central axes by these
IES smoothly mix to form the specific method of three-dimensional vascular arborization model can are as follows:
In the quasi- tree modeling method proposed, the section of each implied expression will be carried out along given central axes
Weighted superposition constructs the tubular structure model with varied cross section profile, will construct implicit stretching curved surface corresponding to section
(IES), firstly, first constructing the two implicit surface F to intersect vertically according to central axes1(x, y, z)=0 and F2(x, y, z)=0,
Its intersection is a curve being implicitly fitted, and represents drawing path；Then, the 2D Implicit Curves of cross section will be indicated along intersection
It is stretched as 3D implicit surface, i.e., implicitly stretches curved surface, the implicit stretching curve surface definition are as follows:
One tubular structure model stretched along given central axes of the function representation.
To different cross section Ci(x, y) utilizes 1D PSPS function Bi(t) it is weighted superposition along given central axes,
To construct the tubular structure model with varied cross section profile, the implied expression formula of entire model is as follows:
3) the vascular arborization model smoothing of implied expression is mixed using SPBBO, constitutes vascular arborization structure
(bifurcation), it and then realizes to the three-dimensional reconstruction of entire coronary artery vascular tree luminal surface model.
It is described to be mixed the vascular arborization model smoothing of implied expression using SPBBO in step 3), constitute blood vessel point
Branch structure (bifurcation), and then realize the specific method to the three-dimensional reconstruction of entire coronary artery vascular tree luminal surface model
It can are as follows:
In the quasi- tree modeling method proposed, the different apparatus derivatorius of implied expression are mixed, to construct
Complete tree model, although the mixing for currently having various methods to carry out implied expression shape, most of is overstepping one's bounds
The polynomial hybrid manipulation of section, and it lacks flexibility to the control of blend range；Since the apparatus derivatorius that front constructs be by
The implicit function expression of piecewise polynomial, then the shape blending operation using piecewise polynomial mixes different apparatus derivatorius
It closes, the flexible control to blend range may be implemented in smooth segmentation multinomial hybrid manipulation (SPPBO), this is for realizing
Bulge-free blending is particularly important；In the present invention, using the conformal maximal function (smooth in the smooth part of extension
Shape-preserving maximum function) mixing of the realization to different apparatus derivatorius, it is defined as follows:
Wherein, | x |n,δSmooth absolute function containing smooth series n and blend range control parameter δ, it is assumed that F1And F2It is
The different apparatus derivatorius of two implied expressions then can be realized the mixing of the two implied expression shapes by following formula:
It can be seen that by analyzing above, in the modeling method proposed by the invention based on implicit stretching curved surface (IES), pair cross-section
The expression of profile, the expression of tubular model, apparatus derivatorius hybrid manipulation, be all to be described by corresponding mathematic(al) representation.
Coronary artery vascular pattern constructed by the i.e. quasi- modeling method based on implicit stretching curved surface proposed, is to have clear mathematical analysis table
Up to formula.
Detailed description of the invention
Fig. 1 is to construct smooth continuous Implicit Curves by one group of disperse node using 2D PSPS function.
Fig. 2 is by the way of implicitly stretching by the implicit stretching curved surface of the implicit cross-sectional configuration 3D of 2D.In Fig. 2, (a)
The drawing path that the implicit plane intersected by two indicates；(b) as the implicit section of 2D along drawing path Extrude Face made of
3D implicitly stretches curved surface.
Fig. 3 is the mixing that two apparatus derivatorius are realized using SPPBO hybrid manipulation.
Fig. 4 is the effect picture for the coronary artery blood vessel geometrical model rebuild.
Specific embodiment
Following embodiment will the present invention is further illustrated in conjunction with attached drawing.
Firstly, the blood perpendicular with it can be constructed according to the central axes of each apparatus derivatorius of coronary artery blood vessel extracted
Pipe cross sectional information, and utilize 2D PSPS (Li, Q.and Tian, J., 2D piecewise algebraic splines
For implicit modeling, ACMTransactions on Graphics, vol.28, no.2, pp.1-19,2009) letter
Number realizes the accurate expression to each vascular cross-section lumen profile；Then, its corresponding implicit stretching according to these cross-sectional configurations
Curved surface IES, and smoothly mix to form three-dimensional vascular arborization model by these IES along central axes；Finally, using
SPBBO(Li,Q.,Smooth Piecewise Polynomial Blending Operations for implicit
Shapes, Computer Graphicsforum, vol.26, no.2, pp.157-171,2007) by the blood of these implied expressions
It mixes to vessel branches model smoothing, constitutes vascular arborization structure (bifurcation), and then realize to entire coronary artery blood vessel
The three-dimensional reconstruction of luminal surface model is set, the specific method is as follows:
1) accurate expression to each vascular cross-section lumen profile is realized using 2D PSPS function:
The implicit modeling method of Most current is all to indicate cross section profile using round or elliptic curve, although such method
Simply, the cross section informations of real blood vessels cannot be expressed efficiently, but accurately, this is because the cross section profile of real blood vessels is not complete
It is the shape of rule, the blood vessel of special diseased region；In the quasi- tree-shaped modeling method proposed, free form will be utilized
(model-free) 2D PSPS realizes the accurate expression to irregular section profile, as the one strong of implicit modeling field
Big tool, 2D PSPS function has the advantages that all of traditional B-spline function based on 2D vector product, moreover, it has explicitly
Mathematical analysis expression formula.
The control point being made of for one group sequence counter-clockwise, corresponding Implicit Curves can be directly by 2D PSPS functionsExpress (as shown in Figure 1).Wherein Δ indicates control point；δ is smoothing parameter；M is the flat of PSPS function
Sliding index；H is corresponding height value.
2) according to these cross-sectional configurations its it is corresponding implicit stretch curved surface IES, and along central axes by these IES smoothly
It mixes to form three-dimensional vascular arborization model:
In the quasi- tree modeling method proposed, the section of each implied expression will be carried out along given central axes
Weighted superposition constructs the tubular structure model with varied cross section profile.To avoid too being bent generation because of central axes
Intersecting cross-sections problem will construct implicit stretching curved surface (IES) corresponding to section.Firstly, needing
The two implicit surface F to intersect vertically are first constructed according to central axes1(x, y, z)=0 and F2(x, y, z)=0, intersection is just
Be the curve being implicitly fitted, represent drawing path (shown in such as Fig. 2 (a)).Then, it can will indicate transversal along intersection
The 2D Implicit Curves in face are stretched as 3D implicit surface, i.e., implicitly stretch curved surface.For example, by
The cross section of implicit function expression, implicitly stretching curved surface may be defined as:
The function representation one tubular structure model stretched along given central axes (shown in such as Fig. 2 (b)).
To different cross section Ci(x, y) needs to utilize 1D PSPS function Bi(t) it is weighted along given central axes folded
Add, to construct the tubular structure model with varied cross section profile.The implied expression formula of entire model is as follows:
3) the vascular arborization model smoothing of these implied expressions is mixed using SPBBO, constitutes vascular arborization knot
Structure (bifurcation), and then realize the three-dimensional reconstruction to entire coronary artery vascular tree luminal surface model
In the quasi- tree modeling method proposed, the different apparatus derivatorius needs of implied expression are carefully mixed
It closes, to construct complete tree model.Although currently there is various methods to carry out the mixing of implied expression shape, its
Major part is the hybrid manipulation of non-piecewise polynomial, and it lacks flexibility to the control of blend range.What since front constructed
Apparatus derivatorius is expressed by the implicit function of piecewise polynomial, then using the shape blending operation of piecewise polynomial to difference point
Branch structure is mixed, even more reasonable.Smooth segmentation multinomial hybrid manipulation (SPPBO) may be implemented to blend range
Flexible control, this for realize bulge-free blending it is particularly important.In the present invention, using the smooth part of extension
Conformal maximal function (smooth shape-preserving maximum function) is realized and is mixed to different apparatus derivatorius
It closes (as shown in Figure 3), is defined as follows:
Wherein, | x |n,δSmooth absolute function containing smooth series n and blend range control parameter δ；Assuming that F1And F2It is
The different apparatus derivatorius of two implied expressions then can be realized the mixing of the two implied expression shapes by following formula:
It can be seen that by analyzing above, in the modeling method proposed by the invention based on implicit stretching curved surface (IES), pair cross-section
The expression of profile, the expression of tubular model, apparatus derivatorius hybrid manipulation, be all to be described by corresponding mathematic(al) representation.
I.e. it is quasi- propose based on coronary artery vascular pattern (as shown in Figure 4) constructed by the implicit modeling method for stretching curved surface, be have it is bright
Exact figures analytical expression.
Claims (4)
1. a kind of based on the implicit coronary artery blood vessel Geometric model reconstruction method for stretching curved surface, it is characterised in that its specific method is such as
Under:
1) accurate expression to each vascular cross-section lumen profile is realized using 2D PSPS function；
2) its corresponding implicit stretching curved surface IES according to cross-sectional configuration, and smoothly mix these IES along central axes
Form three-dimensional vascular arborization model；
3) the vascular arborization model smoothing of implied expression is mixed using SPBBO, constitutes vascular arborization structure
(bifurcation), it and then realizes to the three-dimensional reconstruction of entire coronary artery vascular tree luminal surface model.
2. a kind of based on the implicit coronary artery blood vessel Geometric model reconstruction method for stretching curved surface as described in claim 1, feature exists
In in step 1), the specific side realized using 2D PSPS function to the accurate expression of each vascular cross-section lumen profile
Method are as follows: in tree-shaped modeling method, the accurate expression to irregular section profile will be realized using free-form 2D PSPS,
The control point being made of for one group sequence counter-clockwise, corresponding Implicit Curves are directly by 2D PSPS functionExpression, wherein Δ indicates control point；D is smoothing parameter；M is the Smoothness Index of PSPS function；H is corresponding
Height value.
3. a kind of based on the implicit coronary artery blood vessel Geometric model reconstruction method for stretching curved surface as described in claim 1, feature exists
In in step 2), described according to cross-sectional configuration, it implicitly stretches curved surface IES accordingly, and puts down these IES along central axes
It mixes to form three-dimensional vascular arborization model slidingly method particularly includes:, will be along giving in tree modeling method
Determine central axes and the section of each implied expression be weighted superposition, constructs the tubular structure model with varied cross section profile,
Implicit stretching curved surface corresponding to section will be constructed, firstly, constructing two implicit surfaces to intersect vertically according to central axes
F1(x, y, z)=0 and F2(x, y, z)=0, intersection are a curve being implicitly fitted, and represent drawing path；Then, along friendship
The 2D Implicit Curves for indicating cross section are stretched as 3D implicit surface by line, i.e., implicitly stretch curved surface, and the implicit stretching curved surface is fixed
Justice are as follows:
One tubular structure model stretched along given central axes of the function representation；
To different cross section Ci(x, y) utilizes 1D PSPS function Bi(t) it is weighted superposition along given central axes, with structure
The tubular structure model with varied cross section profile is made, the implied expression formula of entire model is as follows:
4. a kind of based on the implicit coronary artery blood vessel Geometric model reconstruction method for stretching curved surface as described in claim 1, feature exists
It is described to be mixed the vascular arborization model smoothing of implied expression using SPBBO in step 3), constitute vascular arborization knot
Structure, and then realize to the three-dimensional reconstruction of entire coronary artery vascular tree luminal surface model method particularly includes:
In tree modeling method, the different apparatus derivatorius of implied expression are mixed, to construct complete tree-shaped knot
Structure model, the apparatus derivatorius that front constructs are expressed by the implicit function of piecewise polynomial, are grasped using the shape blending of piecewise polynomial
Different apparatus derivatorius of opposing are mixed, and smooth segmentation multinomial hybrid manipulation realizes the flexible control to blend range, are adopted
The mixing to different apparatus derivatorius is realized with the conformal maximal function in the smooth part of extension, is defined as follows:
Wherein, | x |n,δSmooth absolute function containing smooth series n and blend range control parameter δ, it is assumed that F1And F2It is two
The different apparatus derivatorius of implied expression, then realized the mixing of the two implied expression shapes by following formula:
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111968070A (en) * | 2020-04-22 | 2020-11-20 | 深圳睿心智能医疗科技有限公司 | Blood vessel detection method and device based on three-dimensional modeling |
| CN113626893A (en) * | 2021-08-27 | 2021-11-09 | 北京航空航天大学 | Computer mechanical analysis numerical simulation method based on implicit geometric model |
| CN115422856A (en) * | 2022-09-05 | 2022-12-02 | 青岛埃米博创医疗科技有限公司 | CFD teaching-oriented teaching blood vessel model generation method |
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| CN101283929A (en) * | 2008-06-05 | 2008-10-15 | 华北电力大学 | Rebuilding method of blood vessel three-dimensional model |
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111968070A (en) * | 2020-04-22 | 2020-11-20 | 深圳睿心智能医疗科技有限公司 | Blood vessel detection method and device based on three-dimensional modeling |
| CN111968070B (en) * | 2020-04-22 | 2023-12-05 | 深圳睿心智能医疗科技有限公司 | Blood vessel detection method and device based on three-dimensional modeling |
| CN113626893A (en) * | 2021-08-27 | 2021-11-09 | 北京航空航天大学 | Computer mechanical analysis numerical simulation method based on implicit geometric model |
| CN113626893B (en) * | 2021-08-27 | 2024-02-20 | 北京航空航天大学 | Computer mechanical analysis numerical simulation method based on implicit geometric model |
| CN115422856A (en) * | 2022-09-05 | 2022-12-02 | 青岛埃米博创医疗科技有限公司 | CFD teaching-oriented teaching blood vessel model generation method |
| CN115422856B (en) * | 2022-09-05 | 2023-08-08 | 青岛埃米博创医疗科技有限公司 | CFD teaching-oriented teaching blood vessel model generation method |
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