CN106408541B - Industrial part 3-D image smooth surface method based on Cone-Beam CT - Google Patents

Industrial part 3-D image smooth surface method based on Cone-Beam CT Download PDF

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CN106408541B
CN106408541B CN201610872054.6A CN201610872054A CN106408541B CN 106408541 B CN106408541 B CN 106408541B CN 201610872054 A CN201610872054 A CN 201610872054A CN 106408541 B CN106408541 B CN 106408541B
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曾理
王佳熙
沈宽
王成祥
郭雨濛
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Chongqing University
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Abstract

The invention discloses one kind to be based on Cone-Beam CT (Computed Tomography, computer tomography) industrial part 3-D image smooth surface method, radiographic source and planar array detector are individually positioned in the two sides of industrial part by the present invention before scanning, after scanning starts, by the center of radiographic source alignment planar array detector, radiographic source and planar array detector rotate a circle to obtain complete data for projection around the center of industrial part, then it sends obtained data for projection to control and image processing system and utilizes Feldkamp, Davis, and Kress (FDK) algorithm for reconstructing carries out three-dimensional image reconstruction.The surface for obtaining obtaining after the 3-D image of industrial part it using three-dimensional robust Chan-Vese (3D-RCV) algorithm, finally uses the non local surface recovery algorithm based on level set to carry out come the surface to industrial part 3-D image smooth.After this method is handled, the surface of industrial part 3-D image reduces a large amount of noise while boundary obtains protection, and is also remake in some places on surface, makes surface more smooth.

Description

Industrial part 3-D image smooth surface method based on Cone-Beam CT
Technical field
The invention belongs to technical field of image processing, and it is flat to be related to a kind of industrial part 3-D image surface based on Cone-Beam CT Sliding method.
Background technique
The 3-D image of industrial part will receive the interference of various noise, Er Qiesan during acquisition and transmission The surface of dimension image must be obtained by the method divided or be fitted, this can all cause some artifacts, such as hole or not Continuous part.This can seriously affect the visual effect of 3-D image, can also bring centainly to subsequent image analysis and understanding Difficulty.In order to inhibit noise, improving image quality, need to carry out image smooth surface processing, and the quality of smooth quality Subsequent processing will be will have a direct impact on.So the research of the smooth surface technology of 3-D image has biggish practical significance.
In the prior art, the image smoothing method algorithm based on airspace and transform domain is simple, and computation complexity is not high, executes Speed is fast, but they also have many deficiencies, and most apparent is a little exactly to keep not ideal enough to the texture and details of image, it Denoising while obscured the important information such as edge, texture and details.Image smoothing method based on partial differential equation Denoise that effect is obvious and relatively good to the protection of edge details, but because they are smooth this assumes that image is point Piece constant, so they can generate alias in the part of image smoother.Buades in 2005 proposes non local equal Value-based algorithm, it is used occurring many periodically redundancies in image, and gray scale similar block is searched in the overall situation and is filled Divide using the correlation between pixel, it can not only remove noise, moreover it is possible to better Protect edge information feature.Dong Bin is mentioned within 2008 Non local surface recovery algorithm based on level set out, it is indicated surface using implicit Level Set Method, not only counted in this way Value is simple, moreover it is possible to make topologies change flexible and changeable, it can be such that the surface of 3-D image subtracts while boundary obtains protection A large amount of noise is lacked, and some places on surface are also obtained and remake, and make whole surface more smooth.
Summary of the invention
In view of this, the purpose of the present invention is to provide a kind of industrial part 3-D image smooth surface based on Cone-Beam CT Radiographic source and planar array detector are individually positioned in the Ministry of Industry to be scanned according to certain amplification ratio before scanning by method, this method The two sides of part, after scanning starts, by the center of radiographic source alignment planar array detector, radiographic source and detector are in industrial part The heart rotates a circle to obtain complete data for projection, then sends the data for projection of acquisition to control and image processing system simultaneously Three-dimensional image reconstruction is carried out using FDK algorithm for reconstructing；It is obtained after obtaining the 3-D image of industrial part using 3D-RCV algorithm Its surface is finally carried out using based on the non local surface recovery algorithm of level set come the surface to industrial part 3-D image Smoothly.After this method is handled, the surface of industrial part 3-D image reduces a large amount of while boundary obtains protection Noise, and also remake in some places on surface, make surface more smooth.
In order to achieve the above objectives, the invention provides the following technical scheme:
A kind of industrial part 3-D image smooth surface method based on Cone-Beam CT, method includes the following steps:
S1: detection device installation: the detection device include radiographic source (1), planar array detector (2) and control with image at Reason system (5), the radiographic source (1), planar array detector (2) signal line be connected with control with image processing system (5), penetrate The center of the circuit orbit (3) of line source is overlapped with the center of circle of industrial part (4) a certain cross section, radiographic source (1), planar array detector (2) it is separately fixed on respective circuit orbit, the cone beam that radiographic source (1) is generated covers industrial part (4) all regions；
S2: radiographic source and detector are rotated a circle around the center of industrial part to obtain complete data for projection: being controlled Under control with image processing system (5), first by radiographic source (1) alignment planar array detector (2) center, radiographic source (1) and Planar array detector (2) rotates a circle to obtain complete data for projection around the center of industrial part, is then delivered to control and figure As storage in processing system (5)；
S3: the 3-D image of industrial part the three-dimensional image reconstruction of industrial part: is rebuild according to obtained data for projection；
S4: the surface of industrial part 3-D image is obtained using 3D-RCV algorithm；
S5: flat using being carried out based on the non local surface recovery algorithm of level set come the 3-D image surface to industrial part It is sliding；
S6: the sharpening result on display 3-D image surface.
Further, in step s3, the 3-D image that the data for projection that the basis obtains rebuilds industrial part is specific Include: S31: data for projection is weighted；S32: one-dimensional filtering is carried out to the data for projection after weighting in conjunction with ramp filter； S33: three-dimensional weighted back projection is carried out to the filter result of step S32；
Specific algorithm is as follows:
1) data for projection that planar array detector actual acquisition arrives is p (β, a, b), then after data for projection weighting are as follows:
Wherein, β indicates the angle of central ray and y-axis, and a, b respectively represent horizontal position on planar array detector and vertical Position coordinates, R indicate radiographic source to the distance of rotation center；
2) one-dimensional filtering is carried out to the data for projection p ' (β, a, b) after weighting
Wherein " * " represents convolution operator,Q is integration variable；
3) by the data for projection after convolutionThe data for projection being converted on dummy detector The then reconstruction formula at point (x, y, z) to be reconstructed are as follows:
Wherein (x, y, z) indicates that the three-dimensional coordinate of point to be reconstructed, f (x, y, z) indicate the image grayscale at (x, y, z), U (x, y, β)=R+xcos β+ysin β,Indicate corresponding ray on dummy detector Horizontal position coordinate,Indicate that corresponding ray is vertical on dummy detector Position coordinates.
Further, in step s 4, the surface that industrial part 3-D image is obtained using 3D-RCV algorithm passes through solution Following partial differential equation obtain:
Wherein, I (y) is the gray value of point q (x, y, z) in the neighborhood N (x) of point x, and x, y, z respectively represents cartesian coordinate The value of corresponding three coordinate components of point in system,For level set function,For the initial profile of definition,For FunctionGradient, HεFor the regularization form of Heaviside function, δεFor the regularization form that one-dimensional Dirac estimates, ε is positive Divergence, c are asked in constant, div () expressioniIndicate that image is divided into inside target i.e. contoured surface and two outside background i.e. contoured surface Average gray when a homogeneous region, μ, v >=0, λ1,λ2> 0 is every weight coefficient, and t is the artificial variables introduced, and m is just Then change constant, σ is the standard deviation of Gaussian function, and r is the radius of neighborhood N (x).
Further, in step s 5, the use is based on the non local surface recovery algorithm of level set come to industrial part 3-D image surface carry out it is smooth specifically includes the following steps:
S51: symbolization distance function φ indicates the surface of 3-D image:
Wherein, t indicates the pixel of image, its coordinate is (x, y, z), and ∑ indicates the inside of object boundary, and S indicates area The boundary of domain ∑；
S52: it is calculated in narrow taking of 0 level set of φ, narrow band is denoted as ∑η, η is narrow band Width；
S53: selection weights omega (x, y) and similar function D (x, y):
Wherein: b1And b2It is two regularization parameters, NηIt is x in ∑ηIn neighborhood, φ [x] is 3D of the center φ at x Block；
S54: it is as follows that using finite difference calculus discrete Iteration is obtained to the gradient descent flow of energy function J (u):
ωjlIt can be calculated by the formula of S53, dt is enabled are as follows:
J has traversed ∑ηIn all mesh point；
S55: given to stop iterative steps k.
The beneficial effects of the present invention are: method provided by the invention can be good at overcoming existing in the prior art ask Topic, so that the surface of industrial part 3-D image reduces a large amount of noise while boundary obtains protection, and on surface Some place also remake, make surface more smooth.
Detailed description of the invention
In order to keep the purpose of the present invention, technical scheme and beneficial effects clearer, the present invention provides following attached drawing and carries out Illustrate:
Fig. 1 is industrial part Scan Architecture schematic diagram of the invention；
Fig. 2 is the FDK algorithm for reconstructing geometry schematic diagram of circular path Cone-Beam CT of the invention；
Fig. 3 is the industrial part 3-D image smooth surface method flow diagram of the invention based on Cone-Beam CT.
Specific embodiment
Below in conjunction with attached drawing, a preferred embodiment of the present invention will be described in detail.
Fig. 1 is industrial part Scan Architecture schematic diagram of the invention, as shown, by radiographic source (1), planar array detector (2) it is separately fixed on respective circuit orbit, using the intersection point of start ray source (1) to industrial part (4) central axis as coordinate Origin O establishes rectangular coordinate system in space O-xyz, and x-axis is the line of origin and radiographic source (1) and positive direction is to be directed toward from origin Radiographic source (1), y-axis are along industrial part (4) laterally and perpendicular to the reference axis of x-axis (Fig. 2), z-axis be in industrial part (4) Mandrel line be overlapped reference axis and using industrial part side as positive direction (Fig. 1).Using coordinate origin O as rotation center, (x, Y, z) it indicates to be reconstructed a point coordinate, dummy detector is introduced at coordinate origin O and position perpendicular to central ray crossing, and is penetrated Line source (1) is located at S, the central ray of SO ' expression taper ray, and SK indicates a ray by being reconstructed point, K ' expression K point In the projection of detector central core (z=0), it is reconstructed point and is projected as M on straight line SK ', central ray and y-axis are at angle β, κ For the cone angle (the FDK algorithm for reconstructing geometry schematic diagram that Fig. 2 is circular path Cone-Beam CT of the invention) of ray SK.
Fig. 3 is the industrial part 3-D image smooth surface method flow diagram of the invention based on Cone-Beam CT, as shown, Industrial part 3-D image smooth surface method based on Cone-Beam CT the following steps are included:
S1. detection device install: cone-beam CT scan device, including radiographic source (1), planar array detector (2) and control with Image processing system (5), signal line and the control and image processing system (5) of the radiographic source (1), planar array detector (2) It is connected, the center of the circuit orbit (3) of radiographic source is overlapped with the center of circle of industrial part (4) a certain cross section, radiographic source (1), face Array detector (2) is separately fixed on respective circuit orbit, and the cone beam that radiographic source (1) is generated covers work All regions of industry component (4)；
S2. it scans: in the case where controlling the control with image processing system (5), radiographic source (1) being directed at planar array detector first (2) center, radiographic source (1) and planar array detector (2) rotate a circle to obtain complete projection number around the center of industrial part According to being then delivered to storage in control and image processing system (5)；
S3. the reconstruction of the 3-D image of industrial part: rebuilding the 3-D image of industrial part according to obtained data for projection, Mainly include three steps: S31. is weighted data for projection；S32. combine ramp filter to the data for projection after weighting Carry out one-dimensional filtering；S33. three-dimensional weighted back projection is carried out to the filter result of step S32.
The algorithm for reconstructing that the present invention uses is as follows:
(1) data for projection that planar array detector actual acquisition arrives is p (β, a, b), then after data for projection weighting are as follows:
Wherein, β indicates the angle of central ray and y-axis, and a, b respectively represent horizontal position on planar array detector and vertical Position coordinates, R indicate radiographic source to the distance of rotation center.
(2) one-dimensional filtering is carried out to the data for projection p ' (β, a, b) after weighting
Wherein " * " represents convolution operator,Q is integration variable.
(3) by the data for projection after convolutionThe data for projection being converted on dummy detectorThe then reconstruction formula at point (x, y, z) to be reconstructed are as follows:
Wherein (x, y, z) indicates that the three-dimensional coordinate of point to be reconstructed, f (x, y, z) indicate the image grayscale at (x, y, z), U (x, y, β)=R+xcos β+ysin β,Indicate corresponding ray on dummy detector Horizontal position coordinate,Indicate that corresponding ray is vertical on dummy detector Position coordinates.
S4. the surface of industrial part 3-D image is obtained using 3D-RCV algorithm；
It is obtained by solving following partial differential equation:
Wherein, I (y) is the gray value of point q (x, y, z) in the neighborhood N (x) of point x, and x, y, z respectively represents cartesian coordinate The value of corresponding three coordinate components of point in system,For level set function,For the initial profile of definition,For FunctionGradient, HεFor the regularization form of Heaviside function, δεFor the regularization form that one-dimensional Dirac estimates, ε is positive Divergence, c are asked in constant, div () expressioniIndicate that image is divided into inside target i.e. contoured surface and two outside background i.e. contoured surface Average gray when a homogeneous region, μ, v >=0, λ1,λ2> 0 is every weight coefficient, and t is the artificial variables introduced, and m is just Then change constant, σ is the standard deviation of Gaussian function, and r is the radius of neighborhood N (x)；
S5. it is smooth to carry out to surface to use the non local surface recovery algorithm based on level set.
The smoothing algorithm that the present invention uses is as follows:
S51: symbolization distance function φ indicates the surface of 3-D image:
Wherein, t indicates the pixel of image, its coordinate is (x, y, z), and ∑ indicates the inside of object boundary, and S indicates area The boundary of domain ∑；
S52: it is calculated in narrow taking of 0 level set of φ, narrow band is denoted as ∑η, η is narrow band Width；
S53: selection weights omega (x, y) and similar function D (x, y):
Wherein: b1And b2It is two regularization parameters, NηIt is x in ∑ηIn neighborhood, φ [x] is 3D of the center φ at x Block；
S54: it is as follows that using finite difference calculus discrete Iteration is obtained to the gradient descent flow of energy function J (u):
ωjlIt can be calculated by the formula of S53, dt is enabled are as follows:
J has traversed ∑ηIn all mesh point；
S55: given to stop iterative steps k.
S6. the sharpening result on 3-D image surface is shown.
Finally, it is stated that preferred embodiment above is only used to illustrate the technical scheme of the present invention and not to limit it, although logical It crosses above preferred embodiment the present invention is described in detail, however, those skilled in the art should understand that, can be Various changes are made to it in form and in details, without departing from claims of the present invention limited range.

Claims (2)

1. a kind of industrial part 3-D image smooth surface method based on Cone-Beam CT, it is characterised in that: this method includes following Step:
S1: detection device installation: the detection device includes radiographic source (1), planar array detector (2) and control and image procossing system Unite (5), the radiographic source (1), planar array detector (2) signal line be connected with image processing system (5) with controlling, radiographic source The center of circuit orbit (3) be overlapped with the center of circle of industrial part (4) a certain cross section, radiographic source (1), planar array detector (2) It is separately fixed on respective circuit orbit, the cone beam that radiographic source (1) is generated covers industrial part (4) All regions；
S2: radiographic source and detector are rotated a circle around the center of industrial part to obtain complete data for projection: in control and figure Under the control of picture processing system (5), first by the center of radiographic source (1) alignment planar array detector (2), radiographic source (1) and face battle array Detector (2) rotates a circle to obtain complete data for projection around the center of industrial part, is then delivered at control and image Storage in reason system (5)；
S3: the three-dimensional of industrial part the three-dimensional image reconstruction of industrial part: is rebuild using FDK algorithm according to obtained data for projection Image；
S4: the surface of industrial part 3-D image is obtained using three-dimensional robust 3D-RCV algorithm；
S5: smooth using being carried out based on the non local surface recovery algorithm of level set come the 3-D image surface to industrial part；
S6: the sharpening result on display 3-D image surface；
In step s 4, the surface of industrial part 3-D image is obtained using 3D-RCV algorithm by solving following partial differential side Journey obtains:
Wherein, I (y) is the gray value of point q (x, y, z) in the neighborhood N (x) of point x, and x, y, z respectively represents in cartesian coordinate system Corresponding three coordinate components of point value,For level set function,For the initial profile of definition,For functionGradient, HεFor the regularization form of Heaviside function, δεFor the regularization form that one-dimensional Dirac estimates, ε is normal Divergence, c are asked in number, div () expressioniIndicate that image is divided into inside target i.e. contoured surface and two outside background i.e. contoured surface Average gray when homogeneous region, μ, v >=0, λ1,λ2> 0 is every weight coefficient, and t is the artificial variables introduced, and m is canonical Change constant, σ is the standard deviation of Gaussian function, and r is the radius of neighborhood N (x)；
In step S5, the use is based on the non local surface recovery algorithm of level set come the 3-D image surface to industrial part Carry out it is smooth specifically includes the following steps:
S51: symbolization distance function φ indicates the surface of 3-D image:
Wherein, t indicates the pixel of image, its coordinate is (x, y, z), and ∑ indicates the inside of object boundary, and S indicates region ∑ Boundary；
S52: it is calculated in narrow taking of 0 level set of φ, narrow band is denoted as ∑η, η is the width of narrow band；
S53: selection weights omega (x, y) and similar function D (x, y):
Wherein: b1And b2It is two regularization parameters, NηIt is x in ∑ηIn neighborhood, φ [x] is 3D block of the center φ at x；
S54: it is as follows that using finite difference calculus discrete Iteration is obtained to the gradient descent flow of energy function J (u):
ωjlIt can be calculated by the formula of S53, enable dt are as follows:
J has traversed ∑ηIn all mesh point；
S55: given to stop iterative steps k.
2. a kind of industrial part 3-D image smooth surface method based on Cone-Beam CT according to claim 1, feature Be: in step s3, the 3-D image that the data for projection that the basis obtains rebuilds industrial part using FDK algorithm is specific Include: S31: data for projection is weighted；S32: one-dimensional filtering is carried out to the data for projection after weighting in conjunction with ramp filter； S33: three-dimensional weighted back projection is carried out to the filter result of step S32；
Specific algorithm is as follows:
1) data for projection that planar array detector actual acquisition arrives is p (β, a, b), then after data for projection weighting are as follows:
Wherein, β indicates the angle of central ray and y-axis, and a, b respectively represent horizontal position and vertical position on planar array detector Coordinate, R indicate radiographic source to the distance of rotation center；
2) one-dimensional filtering is carried out to the data for projection p ' (β, a, b) after weighting
Wherein " * " represents convolution operator,Q is integration variable；
3) by the data for projection after convolutionThe data for projection being converted on dummy detector The then reconstruction formula at point (x, y, z) to be reconstructed are as follows:
The wherein three-dimensional coordinate of (x, y, z) expression point to be reconstructed, image grayscale of f (x, y, the z) expression at (x, y, z), U (x, Y, β)=R+xcos β+ysin β,Indicate corresponding ray on dummy detector Horizontal position coordinate,Indicate vertical position of the corresponding ray on dummy detector Set coordinate.
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CN101393145A (en) * 2008-10-22 2009-03-25 重庆大学 Cone beam double-helix CT Scanning and imaging method for large sized object
WO2011042821A1 (en) * 2009-10-06 2011-04-14 Koninklijke Philips Electronics, N.V. Method for artifact reduction in cone-beam ct images

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