CN101866485B - Brain cortex surface maximum principal direction field diffusion method for three-dimensional brain magnetic resonance image - Google Patents

Abstract

The invention relates to a three-dimensional brain magnetic resonance image brain cortex surface maximum principal direction field diffusion method, which has the technical scheme that the method comprises the following steps: carrying out pretreatment and brain cortex surface reconstruction on three-dimensional brain magnetic resonance images; calculating the principal curvature, the principal direction and the differential coefficient of the principal curvature of a peak on the brain cortex surface; using an alpha-expansion graph cut method for minimizing an energy function to carry out diffusion on the maximum principal direction field; and projecting the diffused maximum principal direction field into a tangent plane. The invention has the advantages that: 1. the method sets the weights of smooth items and data items in different regions on the brain cortex surface into different values, so the inherent geometrical structure and discontinuity in the maximum principal direction field can be perfectly maintained; and 2. the principal direction field diffusion is regarded as an energy minimization problem which is converted into a diffusion marking problem, and the alpha-expansion graph cut method can be used for effectively working out the strong local optimum solution of the energy function.

Description

The three-dimensional brain magnetic resonance image brain cortex surface maximum principal direction field diffusion method

Technical field

The present invention relates to a kind of three-dimensional brain magnetic resonance image brain cortex surface maximum principal direction field diffusion method; Utilize alpha-expansion figure to cut maximum principal direction field diffusion method on the brain cortex surface of three-dimensional brain magnetic resonance image of (graph cuts) method, belong to field of medical image processing.

Background technology

The brain cortex surface that comes out from three-dimensional brain magnetic resonance image reconstruct is the two-dimentional flow pattern that is embedded in three-dimensional, extremely curling and fold.Analysis based on brain cortex surface is very suitable for portrayal and analyzes corticocerebral essential structure, for example curvature, geodesic distance, skin thickness etc.The field of direction on the brain cortex surface comprises important information, and for example, maximum principal direction field and minimum principal direction field indicate principal curvatures to reach minimum and maximum direction respectively.But; Principal direction field on the reliable calculating brain cortex surface also is not easy; For example; The common noise of principal direction field that is calculated in smooth cortical surface zone is big and unreliable, because little in the variation of flat site curvature on all directions, small noise just possibly have a strong impact on the principal direction field that is calculated.Therefore, brain cortex surface is analyzed, must be implemented principal direction field diffusion, its objective is the noise in the level and smooth principal direction field, keep geometry and uncontinuity main in the principal direction field simultaneously in order to utilize principal direction field.Brain ditch that principal direction field after the disperse can be used for following the tracks of based on the flow field or gyrus basin are cut apart with the cortex fold morphology analysis of direction guiding etc.

Maximum principal direction field diffusion method on the present existing brain cortex surface is regarded this problem as an energy minimization problem, and this energy function comprises a data item and a level and smooth item.Data item is used to make the maximum principal direction field after the disperse similar as far as possible with the maximum principal direction field of original calculation, and level and smooth item is used to make the maximum principal direction field after the disperse to change smoothly.This energy function is found the solution through variational method or gradient decline mode.Maximum principal direction field diffusion method on the existing brain cortex surface has following major defect: the weight in one of which, different cortical surface zone is made as identical, causes the maximum principal direction field of disperse too level and smooth in brain ditch bottom and gyrus top.Two, present energy minimization method is trapped in inferior local optimum easily.

Summary of the invention

The technical matters that solves

Weak point for fear of existing method; The present invention proposes a kind of three-dimensional brain magnetic resonance image brain cortex surface maximum principal direction field diffusion method, is applicable to maximum principal direction field diffusion on the brain cortex surface that human three-dimensional brain magnetic resonance image reconstructs, that represented by triangle.

Technical scheme

Basic thought of the present invention is: with the maximum principal direction field diffusion problem formulation on the brain cortex surface is an energy minimization problem; And then be converted into a discrete markers problem; Promptly give the maximum principal direction that a mark is represented disperse to each summit on the brain cortex surface; This discrete markers problem can utilize alpha-expansion figure segmentation method effectively to find the solution, because the figure segmentation method can guarantee to obtain the strong local optimum of the energy function of some type.

Maximum principal direction field diffusion method on a kind of brain cortex surface of three-dimensional brain magnetic resonance image is characterized in that step is following:

Step 1 pair three-dimensional brain magnetic resonance image carries out pre-service and brain cortex surface is rebuild: utilize the distorted pattern method to remove skull; Utilize method for registering to remove non-cerebral tissue; Utilize gauss hybrid models and markov random file method that image is carried out tissue segmentation; Obtain the image that white matter, grey matter and three kinds of types of organizations of celiolymph represent; Utilization is carried out topology based on the method for figure to the white matter image and is proofreaied and correct the brain cortex surface that utilizes the reconstruction of Marching Cubes method to be represented by triangle;

Step 2 is calculated the derivative of principal curvatures, principal direction and the principal curvatures on summit on the brain cortex surface: utilize finite difference method to calculate the derivative of principal curvatures, principal direction and the principal curvatures on summit on the brain cortex surface; When the maximum principal curvatures on each summit the derivative of maximum principal direction be on the occasion of the time, change the maximum principal direction on this summit into reverse direction;

Step 3 pair maximum principal direction field carries out disperse: utilize alpha-expansion figure segmentation method minimization of energy function

$E=\underset{(x,y)\∈N}{\mathrm{\Σ}}{V}_{x,y}(l_x,l_y)+\underset{x\∈S}{\mathrm{\Σ}}{D}_x\left(l_x\right)$

Wherein,

X and y are the apex coordinate on the brain cortex surface, and p (x) is the original maximum principal direction in summit x place; (x, y) ∈ N representes that x and y are the set of adjacent vertex, S is the set on all summits on the brain cortex surface; || || be 2 norms; Be the maximum principal direction of summit x disperse, l _xBe the maximum principal direction of summit x disperse sign and l in solution space _x∈ L;

Be the maximum principal direction of summit y disperse, l _yBe the maximum principal direction of summit y disperse sign and l in solution space _y∈ L;

Described L={l ¹, l ²..., l ⁿBe the solution space Θ={ v of the maximum principal direction field of discrete disperse ¹, v ²..., v ⁿSign, n=n wherein _θ* (n _φ-2)+2; n _θFor the number of discrete angle in the x-y plane is 12～36; n _φFor the number of discrete angle in the z direction of principal axis is 9～18;

V among the said solution space Θ ¹=(0,0,1), v ⁿ=(0,0 ,-1);

v ⁱ＝(cos(((i-2)％n _θ)·2π/n _θ)sin((1+(i-2)/n _θ)·π/n _φ)，sin(((i-2)％nθ)·2π/n _θ)sin((1+(i-2)/n _θ)·π/n _φ)，cos((1+(i-2)/n _θ)·π/n _φ))，，1＜i＜n；

Said g (x)=exp (λ | c (x) |), said g (y)=exp (λ | c (y) |), said h (x)=1-g (x), wherein λ is that weight parameter is 5.0～10.0, c () is maximum principal curvatures;

Utilize alpha-expansion figure segmentation method to find the solution, obtain the maximum principal direction field of disperse;

Step 4 projects to the maximum principal direction field of disperse in the section on each summit.

Beneficial effect

The three-dimensional brain magnetic resonance image brain cortex surface maximum principal direction field diffusion method that the present invention proposes; Make that the feasibility of maximum principal direction field diffusion method is embodied on the three-dimensional brain magnetic resonance image deutocerebrum cortical surface: at first; Along with the precision of MR imaging apparatus improves constantly with the preprocess method of three-dimensional brain magnetic resonance image further ripely, it is relatively easy to obtain the brain cortex surface that geometry is accurate, topological structure is correct; Simultaneously, regard maximum principal direction field diffusion as an energy minimization problem, and convert a discrete markers problem into, it is feasible that utilization figure segmentation method is effectively found the solution this discrete markers problem.

The present invention has the following advantages with respect to other method: 1, this method level and smooth and weight of data item of zones of different on brain cortex surface is made as differently, can better keep geometry and uncontinuity intrinsic in the maximum principal direction field like this; 2, regard maximum principal direction field diffusion as an energy minimization problem, and convert a discrete markers problem into, utilization figure segmentation method can effectively be found the solution the strong local optimum of this energy function.

Description of drawings

Fig. 1: maximum principal direction field diffusion on the three-dimensional brain magnetic resonance image brain cortex surface of the embodiment of the invention,

(a) shown maximum principal curvatures on the embodiment image deutocerebrum cortical surface,

(b) shown the maximum principal direction field on the deutocerebrum cortical surface of rectangular area among Fig. 1 (a),

(c) shown the maximum principal direction field of the disperse on the brain cortex surface corresponding among Fig. 1 (b);

Fig. 2: an example of the lip-deep maximum principal direction field diffusion of emulation,

(a) shown the lip-deep desirable maximum principal direction field of three-dimensional brain magnetic resonance image emulation,

(b) shown the maximum principal direction field of three-dimensional brain magnetic resonance image simulator and noise,

(c) shown the maximum principal direction of three-dimensional brain magnetic resonance image emulation disperse;

Fig. 3: before the maximum principal direction field diffusion on the three-dimensional brain magnetic resonance image brain cortex surface with disperse after the consistance comparative example,

(a) consistance of the maximum principal direction field on the three-dimensional brain magnetic resonance image brain cortex surface among the demonstration embodiment

(b) show among the embodiment consistance of the maximum principal direction field of disperse on the three-dimensional brain magnetic resonance image brain cortex surface;

Fig. 4: before the maximum principal direction field diffusion on this instance brain cortex surface with disperse after conforming distribution histogram;

Fig. 5: before the maximum principal direction field diffusion on 12 brain cortex surfaces with disperse after the comparison of average homogeneity property;

Embodiment

Combine embodiment, accompanying drawing that the present invention is further described at present:

Propose according to the present invention based on the maximum principal direction field diffusion method on the brain cortex surface of figure segmentation method, we have realized the prototype system of this method with C Plus Plus.The source of view data is: normal person's three-dimensional brain magnetic resonance image in the reality.

Concrete implementation step is following:

1. pre-service and brain cortex surface are rebuild:

Utilize the distorted pattern method to remove skull; Utilize method for registering to remove non-cerebral tissue; Utilize gauss hybrid models and markov random file method that image is carried out tissue segmentation; Obtain the image that white matter, grey matter and three kinds of types of organizations of celiolymph represent, utilize based on the method for figure the white matter image is carried out the topology correction, utilize Marching Cubes method to rebuild the brain cortex surface of representing by triangle;

2. the derivative of principal curvatures, principal direction and the principal curvatures on summit on the calculating brain cortex surface:

Utilize finite difference method to calculate the derivative of principal curvatures, principal direction and the principal curvatures on summit on the brain cortex surface; The maximum principal curvatures of checking each summit the derivative of maximum principal direction whether be on the occasion of; If be on the occasion of, the maximum principal direction on this summit of then overturning is a reverse direction; Fig. 1 (a) has shown the maximum principal curvatures on the routine brain cortex surface; Fig. 1 (b) has shown the maximum principal direction field on the deutocerebrum cortical surface of rectangular area among Fig. 1 (a).

3. maximum principal direction field is carried out disperse:

The disperse of maximum principal direction field can be expressed as following energy function on the brain cortex surface

$E=\underset{(x,y)\∈N}{\mathrm{\Σ}}(g\left(x\right)+g\left(y\right))\left|\right|v\left(x\right)-v\left(y\right)\left|\right|+\underset{x\∈S}{\mathrm{\Σ}}h\left(x\right)\left|\right|v\left(x\right)-p\left(x\right)\left|\right|$

Wherein, v (x)=(u (x), v (x), w (x)) is the maximum principal direction of summit x place disperse, and v (y) is the maximum principal direction of summit y place disperse, and p (x) is the original maximum principal direction in x place, summit.(x, y) ∈ N representes that x and y are the set of adjacent vertex, S representes the set on all summits on the brain cortex surface.|| || represent 2 norms.G (x)=exp (λ | c (x) |), g (y)=exp (λ | c (y) |), h (x)=1-g (x), wherein λ is that weight parameter is 8.0, c () is maximum principal curvatures.The zone of bends on brain cortex surface, corresponding to brain ditch bottom and gyrus crown areas, the absolute value of this c of place () is bigger, and maximum principal direction field can calculate relatively reliably; And the noise of the maximum principal direction field that calculates in smooth zone is bigger, and is more unreliable.So g () is made as bottom the brain ditch and the value of gyrus bizet is less, and h () is bigger in the value of brain ditch bottom and gyrus bizet.

is data item, is used to make the maximum principal direction field of disperse similar as far as possible with original maximum principal direction field.

is level and smooth, is used to make the maximum principal direction field smooth change of disperse.Can find out that at brain ditch bottom and gyrus bizet, the weight of data item is bigger, forces the maximum principal direction field of disperse similar with original maximum principal direction field; In smooth cortex zone, level and smooth weight is bigger, forces the level and smooth variation of maximum principal direction field of disperse.In order maximum master side to be asked a disperse is converted into a discrete markers problem, v (x) is expressed as v (x)=(cos θ sin φ, sin θ sin φ, cos φ), wherein θ ∈ [0,2 π), φ ∈ [0, π].Make θ=i2 π/n _θ, i ∈ [0, n _θ-1], n _θThe number of discrete angle is made as 12 among the expression θ.Make φ=j π/n _φ, j ∈ [0, n _φ], n _φThe number of discrete angle is made as 9 among the expression φ.Make L={l ¹, l ²..., l ⁿThe solution space Θ={ v of maximum principal direction field of the discrete disperse of expression ¹, v ²..., v ⁿ, n=n wherein _θ* (n _φ-2)+2.Above energy function can be converted into:

$E=\underset{(x,y)\∈N}{\mathrm{\Σ}}{V}_{x,y}(l_x,l_y)+\underset{x\∈S}{\mathrm{\Σ}}{D}_x\left(l_x\right)$

Wherein,

utilizes alpha-expansion figure segmentation method effectively to find the solution this energy function.

Step 4 projects to the maximum principal direction field of disperse in the section.

Fig. 1 (c) has shown the maximum principal direction field of the disperse on the brain cortex surface corresponding among Fig. 1 (b).

Effect for maximum principal direction field diffusion method on the quantitative test brain cortex surface is applied to this method on the surface of an emulation.Can accurate Analysis on the surface of emulation calculate the desirable maximum principal direction on each summit, then random noise is added in the position on each summit, and utilize finite difference method to calculate to add the maximum principal direction on each summit behind the noise.Fig. 2 (a) and (b) with (c) shown the lip-deep desirable maximum principal direction field of emulation, the maximum principal direction field of noise and the maximum principal direction of disperse respectively.Average angle through maximum principal direction field, the maximum principal direction field that adds noise and desirable maximum principal direction field after the following formula calculating disperse is poor:

$\mathrm{AngleDiff}=\frac{1}{{\mathrm{\&Sigma;}}_{x\&Element;\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HSA00000156048100021.png,HSA00000156048100022.png"\; state="\{\{state\}\}">S</figure-callout>}}1}\underset{x\&Element;S}{\mathrm{\&Sigma;}}\arccos \&lang;p\left(x\right)\&CenterDot;v\left(x\right)\&rang;$

Wherein, p (x) representes desirable maximum principal direction, the maximum principal direction of v (x) expression disperse or the maximum principal direction of interpolation noise.Adding the maximum principal direction field of noise and the average angle difference of desirable maximum principal direction field is 67.7 degree, and the average angle difference of maximum principal direction field after the disperse and desirable maximum principal direction field is 6.3 degree, shows that this method has reached good disperse result.

This method is applied on 12 normal persons' the brain cortex surface.The definition consistance is estimated the disperse result:

$\mathrm{Coh}\left(x\right)=\frac{1}{{\mathrm{\&Sigma;}}_{(x,y)\&Element;\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="HSA00000156048100021.png,HSA00000156048100022.png"\; state="\{\{state\}\}">N</figure-callout>}}1}\underset{(x,y)\&Element;N}{\mathrm{\&Sigma;}}v\left(x\right)\&CenterDot;v\left(y\right)$

Wherein, the direction of v (x) expression summit x, (x, y) ∈ N representes the adjacent vertex set.Big consistance value shows that the field of direction is more level and smooth and consistent.Therefore, this value can reflect the disperse result to a certain extent.Fig. 3 (a) and (b) show the consistance of the maximum principal direction field of maximum principal direction field and disperse on the routine brain cortex surface respectively.In the ideal case, in the maximum principal direction field of disperse, consistance should approach 1.0 in smooth cortex zone, and consistance approaches 0 at gyrus bizet and brain ditch bottom.Can find out significantly, compare that in the maximum principal direction field of disperse, consistance has increased in smooth cortex zone, and well keep in brain ditch bottom and gyrus crown areas with original maximum principal direction field.Calculated conforming distribution histogram on the brain cortex surface simultaneously, as shown in Figure 4, can find out that than original maximum principal direction field, consistance obviously increases in the maximum principal direction field of disperse.Fig. 5 has shown that on 12 brain cortex surfaces the variation of average homogeneity property before maximum principal direction field diffusion and after the disperse can find out that average homogeneity property significantly increases, and shown the validity of this method.

Claims (1)

1. maximum principal direction field diffusion method on the brain cortex surface of a three-dimensional brain magnetic resonance image is characterized in that step is following:

Step 1 pair three-dimensional brain magnetic resonance image carries out pre-service and brain cortex surface is rebuild: utilize the distorted pattern method to remove skull; Utilize method for registering to remove non-cerebral tissue; Utilize gauss hybrid models and markov random file method that image is carried out tissue segmentation; Obtain the image that white matter, grey matter and three kinds of types of organizations of celiolymph represent; Utilization is carried out topology based on the method for figure to the white matter image and is proofreaied and correct the brain cortex surface that utilizes the reconstruction of Marching Cubes method to be represented by triangle;

Step 2 is calculated the derivative of principal curvatures, principal direction and the principal curvatures on summit on the brain cortex surface: utilize finite difference method to calculate the derivative of principal curvatures, principal direction and the principal curvatures on summit on the brain cortex surface; When the maximum principal curvatures on each summit the derivative of maximum principal direction be on the occasion of the time, change the maximum principal direction on this summit into reverse direction;

Step 3 pair maximum principal direction field carries out disperse: utilize alpha-expansion figure segmentation method minimization of energy function

$E=\underset{(x,y)\&Element;N}{\mathrm{\&Sigma;}}{V}_{x,y}(l_x,l_y)+\underset{x\&Element;S}{\mathrm{\&Sigma;}}{D}_x\left(l_x\right)$

Wherein,

X and y are the apex coordinate on the brain cortex surface, and p (x) is the original maximum principal direction in summit x place; (x, y) ∈ N representes that x and y are the set of adjacent vertex, S is the set on all summits on the brain cortex surface; || || be 2 norms;

Be the maximum principal direction of summit x disperse, l _xBe the maximum principal direction of summit x disperse sign and l in solution space _x∈ L;

Be the maximum principal direction of summit y disperse, l _yBe the maximum principal direction of summit y disperse sign and l in solution space _y∈ L;

Described L={l ¹, l ²..., l ⁿBe the solution space Θ={ v of the maximum principal direction field of discrete disperse ¹, v ²..., v ⁿSign, n=n wherein _θ* (n _φ-2)+2; n _θFor the number of discrete angle in the x-y plane is 12～36; n _φFor the number of discrete angle in the z direction of principal axis is 9～18;

V among the said solution space Θ ¹=(0,0,1), v ⁿ=(0,0 ,-1);

v ⁱ＝(cos(((i-2)％n _θ)·2π/n _θ)sin((1+(i-2)/n _θ)·π/n _φ)，sin(((i-2)％n _θ)·2π/n _θ)sin((1+(i-2)/n _θ)·π/n _φ)，cos((1+(i-2)/n _θ)·π/n _φ))，1＜i＜n；

Said g (x)=exp (λ | c (x) |), said g (y)=exp (λ | c (y) |), said h (x)=1-g (x), wherein λ is that weight parameter is 5.0～10.0, c () is maximum principal curvatures;

Utilize alpha-expansion figure segmentation method to find the solution, obtain the maximum principal direction field of disperse;

Step 4 projects to the maximum principal direction field of disperse in the section on each summit.

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