CN103473805B - The method of three-dimensional reconstruction hepatic model volume is measured based on improved confinement growth algorithm - Google Patents

Abstract

The invention discloses a kind of method measuring three-dimensional reconstruction hepatic model volume based on improved confinement growth algorithm, use quasi Monte Carlo method choose the Seed Points in traditional algorithm of region growing and grow criterion and improve, and by the Region growing segmentation method after improvement, segmentation is carried out to abdominal CT images and extract liver area; Utilize the bianry image split to carry out three-dimensional reconstruction obtain only having the three-dimensional reconstruction hepatic model of surface mesh and close model; The square enclosure box of rule is set, the most bottom surface of bounding box is set to projection plane, calculate the pentahedron volume that tri patch reconstruction model with positive and negative direction method vector and its projection on a projection plane surround, the algebraic sum finally calculating all pentahedron volumes is exactly the volume of hepatic model.The present invention can show liver morphology preferably thus effectively carry out cubing to three-dimensional reconstruction hepatic model, and can the liver volume of measure portion, has higher measuring accuracy.

Description

The method of three-dimensional reconstruction hepatic model volume is measured based on improved confinement growth algorithm

Technical field

The present invention relates to a kind of method measuring three-dimensional reconstruction hepatic model volume based on improved confinement growth algorithm, relate to medical image process and Computer Applied Technology two technical fields, mainly according to the processing power of computing machine, abdominal CT images is split, then carry out three-dimensional reconstruction and realize cubing.

Background technology

Because China belongs to liver diseases hotspot, in the process for the treatment of liver diseases, doctor needs to obtain liver volume data relatively accurately usually.Liver volume is measured not only can quantitative evaluation liver size, can also indirectly reflect liver function situation, there is extensive and important clinical value, all significant in assessment cirrhosis Hepatic Functional Reserve, liver neoplasm operation selection, Post operation evaluation and liver transfer operation, the accuracy that therefore preoperative liver volume is measured directly affects the selection of operation plan.

Because liver is erose organ, for a long time, most liver volume measuring method is for two dimensional image, integral and calculating volume is carried out by the area asking for liver area in image series, but this method is merely able to estimate liver volume according to formula, and its measurement precision need further raising.

Three-dimensional reconstruction hepatic model has good formation, and doctor just can carry out liver morphology analysis, and the cubing accuracy of Three-dimension Reconstruction Model is that doctors are confessed.

Through finding existing technology retrieval, Chinese patent literature CN102663819A, publication date 2012-09-12, describe " the liver volume measuring method based on ultrasonoscopy and three-dimensional model ", although the method has carried out cubing to the liver of three-dimensional reconstruction, but its core concept carries out liver segmentation for X-Y scheme, calculate the product of the area sum of all liver sections and the spacing of adjacent two sections, using the volume of result of calculation as liver.Asking for tomography area is in the method that each section is divided into multiple triangle, obtains the area of section by asking multiple leg-of-mutton area sum.This method needs just can more close to actual value by less for the area of triangle subdivision the liver area area adding up out, and therefore the process of subdivision compares wastes time and energy, and the error of computed tomography area is larger.In addition, the method carries out liver volume measurement for two dimensional image, and the measurement result of the method not tap into row measurement result to the integrated straight of three-dimensional liver reconstitution model more satisfactory.

In " research based on the volume of intracranial hematoma measuring method of CT image " that " medical equipment information " 22 volumes 12 in 2007 are interim, doctor Li Qiang and Wu Juan employ integral method measuring in volume of hematoma, every layer of hemotoncus of sequence C T image is all split, then ask for hemotoncus region area in every one deck according to pixel size and quantity, finally calculate the volume of hemotoncus according to the product of areas of thickness and every layer.Standardization liver volume measuring method is refer in University Of Qingdao Zhao Jing Master's thesis " CT three-dimensional reconstruction and the application of Future liver volume in children's's liver tumor operation ":

(1) standardization liver volume=706.2 × body surface area+2.4;

(2) children's's 30kg body surface area (m ²)=body weight (kg) × 0.035+0.1;

(3) children's's 30kg body surface area (m ²body weight)=[(kg)-30] × 0.02+1.05.

By the calculating of standard liver volume, roughly can understand the liver volume size of normal person, but the liver volume that illness occurs then can not obtain with this formulae discovery.These two sections of articles are similar with " the liver volume measuring method based on ultrasonoscopy and three-dimensional model ", all indirectly carry out cubing for two dimensional image, not needing Region dividing unlike " research based on the volume of intracranial hematoma measuring method of CT image " middle calculating region area is several triangles, but pixels whole in region of adding up out after calculating each pixel size and, finally carry out integration cube.

In document " Stereology:anoveltechniqueforrapidassessmentoflivervolum e " (InsightsImaging (2012) 3:387 – 393), author proposes the area that a kind of method based on stereology measures liver area on two dimensional image, by being several square nets single image Region dividing, then add up the number of grid that liver area comprises, and then carry out cubing by integral formula.And at document " Validationstudyofafast; accurate; andprecisebraintumorvolumemeasurement " (Computermethodsandprogramsinbiomedicine, (2013)), author is carrying out in cubing to brain tumor, first obtaining splitting image by improving Level Set Method, then image area being calculated, trying to achieve gross tumor volume finally by integration.And at document " CTlivervolumetryusingthree-dimensionalimagedatainlivingd onorlivertransplantation:Effectsofslicethicknessonvolume calculation " (LiverTranspl.2011December; 17 (12): 1427 – 1436.) in, author for central bay different image layer spacing apart from size on the impact of cubing, and in this article the computing method of volume still for two dimensional image, calculate liver area area by number of pixels and pixel size in statistics liver area, then carry out integration and ask liver volume.

Ask for volume method in medical science involved in above-mentioned document all indirectly to measure for two dimensional image, there is certain Subjective Factors, and said method is all carry out cubing for whole object, local measurement can not be carried out, be subject to certain restrictions, and its measurement precision need further raising.

Summary of the invention

The technical issues that need to address of the present invention are just the defect overcoming prior art, a kind of method measuring three-dimensional reconstruction hepatic model volume based on improved confinement growth algorithm is provided, the inventive method directly carries out cubing for Three-dimension Reconstruction Model, and can directly measure model regional area, in measurement precision, also there is good effect.

For solving the problem, the present invention adopts following technical scheme:

The invention provides a kind of method measuring three-dimensional reconstruction hepatic model volume based on improved confinement growth algorithm, described method comprises the following steps:

1), CT Image semantic classification;

2), area-of-interest is set, Quasi-Monte-Carlo method choice Seed Points;

3), liver area is split;

4), post processing of image is split;

5), liver three-dimensional reconstruction;

6), bounding box is set, and to tri patch normal vector consistency adjustment;

7), tri patch projection, ask pentahedron volume cumulative sum, obtain volume data.

Be specially: first use quasi Monte Carlo method choose the Seed Points in traditional algorithm of region growing and grow criterion and improve, and by the Region growing segmentation method after improvement, segmentation carried out to abdominal CT images and extract liver area; Secondly utilize the bianry image split to carry out three-dimensional reconstruction obtain only having the three-dimensional reconstruction hepatic model of surface mesh and close model; The square enclosure box of rule is finally set, the most bottom surface of bounding box is set to projection plane, calculate the pentahedron volume that tri patch reconstruction model with positive and negative direction method vector and its projection on a projection plane surround, the algebraic sum finally calculating all pentahedron volumes is exactly the volume of hepatic model.

Concrete steps are:

The first step: use nonlinear mapping technique to improve the contrast of liver area in abdominal CT images, comparatively large rectangle region, i.e. a region of interest ROI are alternatively set in liver area;

Second step: use quasi Monte Carlo method to distribute in ROI random point, then carries out screening suitable Seed Points;

3rd step: region growing adopts four neighborhood methods to grow, is set growing criterion by the gray-scale value of pixel and the change of Grad, and first use Robert operator calculates the average gradient value in area-of-interest when algorithm of region growing judges whether some pixels meet growth conditions, if this grey scale pixel value meet as shown in the formula, so this pixel is included in growth district, otherwise judges next pixel.

$G_{\mathrm{ave}}-a\stackrel{\&OverBar;}{\&dtri;T}<G_i<G_{\mathrm{ave}}+a\stackrel{\&OverBar;}{\&dtri;T}$

Wherein, a is regulation and control parameter;

4th step: use the algorithm of region growing improved to carry out segmentation to continuous print abdominal CT images and obtain liver area, then carry out aftertreatment and obtain continuous liver area bianry image;

Post-processing step comprises: the filling according to morphological method, image being carried out to cavity, canny operator is used to obtain good liver contour images, then with flood-fill algorithm, liver contour images is filled, finally obtain that there is the liver image compared with smooth contoured;

Then classical MarchingCube algorithm is used to carry out surface rendering reconstruction to the liver image of these segmentations, because this method carries out cubing for the Three-dimension Reconstruction Model closed, so some surface hole defects spatially can be there are in the model after rebuilding, need the model after to reconstruction to carry out the repairing of surface hole defect, so just can obtain the hepatic model only with surperficial triangle gridding closed;

5th step: first, arrange a regular rectangle bounding box according to this reconstruction hepatic model volume coordinate distance, and the most bottom surface of bounding box is set to projection plane Z, its normal vector is N.Six faces of this bounding box can change the size of bounding box by man-machine interactively, so that carry out the measurement of liver local volume.

Secondly, because process of reconstruction intermediate cam dough sheet normal vector direction is not unified, inconsistent inside and outside direction.So need the surperficial tri patch traveling through whole hepatic model, unification adjustment is carried out to the normal vector of tri patch.：

1), an initial tri patch Δ ABC normal vector n is obtained,

2), the normal vector n of the tri patch that traversal is adjacent with Δ ABC _iif, n*n _i<0, then n _icontrary with n direction, so just change normal vector n _idirection, consistent with n direction; If n*n _i>0, then n _iidentical with n direction, proceed traversal adjustment;

3), the tri patch after normal vector unification is classified: first kind tri patch is that the normal vector inner product of its normal vector and projection plane Z is greater than 0; Equations of The Second Kind tri patch is that the normal vector inner product of its normal vector and projection plane Z is less than 0; 3rd class tri patch is that the normal vector inner product of its normal vector and projection plane Z equals 0.

6th step: by coming alternately bounding box to intercept internal model, carry out the cubing of regional area;

7th step: calculate liver volume, forms pentahedron by tri patch is projected on projecting plane, calculates that sorted pentahedron volume is cumulative asks poor.

The present invention proposes a kind of volume measuring method of CT 3-dimensional reconstruction liver, the method is partitioned into liver area by carrying out improvement to traditional region growing method, then obtain three-dimensional reconstruction hepatic model, finally by projection volume algebraic sum, liver volume is calculated.The present invention not only carries out cubing to liver and has higher calculating accuracy, but also can also measure local liver volume.

Innovative point of the present invention has:

1. the present invention is split liver image by using the algorithm of region growing of Seed Points selection course and the region growing criterion improved.Quasi Monte Carlo method is adopted to come liver area image selected seed point first, the method can carry out statistical computation according to the random point be distributed in liver area to liver area Pixel Information, then selects suitable Seed Points and makes the region growing criterion meeting this area information.

2. in medical science, the cubing of histoorgan is all measured for whole object, and also for how carrying out regional liver cubing designs in the present invention.By using MarchingCube algorithm to carry out three-dimensional reconstruction to the liver image after segmentation, and the regular square bounding box of an applicable reconstruction model size is set.Owing to can carry out to bounding box the size that man-machine interactively operation changes bounding box, therefore can intercept partial liver by bounding box, then carry out local measurement.

3. medically measuring great majority to liver volume is carry out integral and calculating for two dimensional image to carry out measurement volumes indirectly, the present invention directly carries out cubing to the hepatic model of three-dimensional reconstruction, and directly carries out cubing to three-dimensional reconstruction hepatic model and have more accurate measurement result.Core of the present invention is the use of the liver volume that pentahedron volume that the tri patch with positive and negative direction method vector and its projection on a projection plane surround sues for peace to ask for three-dimensional reconstruction.MarchingCube algorithm is used to carry out to liver image the three-dimensional reconstruction hepatic model that three-dimensional reconstruction is only had surperficial triangle gridding in the present invention, after unification adjustment is carried out to tri patch normal vector, tri patch is classified, the normal vector inner product of tri patch normal vector and projection plane is divided into be greater than 0, be less than 0 and equal 0 three kinds, the third situation volume projection is 0, therefore ignores.Finally the first two kind tri patch is projected on the projection plane arranged and obtain pentahedron, then pentahedron is split into three tetrahedrons, by asking three tetrahedral volumes and obtaining this pentahedron volume.Finally the pentahedron volume of three groups of tri patch projections is carried out cumulative read group total and obtain final three-dimensional reconstruction hepatic model volume.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention.

Fig. 2 selects ROI and the schematic diagram of the random point that distributes in liver area, and wherein white portion is the area-of-interest arranged, and the point in white portion is the random point of low difference distribution.

Fig. 3 is through over-segmentation and carries out the liver bianry image of aftertreatment.

Fig. 4 is three-dimensional reconstruction liver Local map, and this part is through the partial liver obtained after bounding box intercepts, and this model is the liver partial model only with surperficial triangle gridding.

Fig. 5 is reconstruction model cubing principle schematic, and Y represents reconstruction model, and arrow n represents tri patch normal vector direction on model, and y represents the projection of Y on projection plane Z, and N represents that view plane normal measures.

Fig. 6 is pentahedron composition schematic diagram, pentahedron P ₁p ₂p ₃q ₁q ₂q ₃can subdivision be three tetrahedrons, be respectively: P ₁q ₁q ₂q ₃, P ₁p ₂p ₃q ₂with P ₁p ₃q ₂q ₃.Three tetrahedron volumes and be exactly pentahedral volume are asked by formula 6.

Embodiment

As shown in Figure 1, the invention provides a kind of method measuring three-dimensional reconstruction hepatic model volume based on improved confinement growth algorithm, described method comprises the following steps:

1), CT Image semantic classification;

2), area-of-interest is set, Quasi-Monte-Carlo method choice Seed Points;

3), liver area is split;

4), post processing of image is split;

5), liver three-dimensional reconstruction;

6), bounding box is set, and to tri patch normal vector consistency adjustment;

7), tri patch projection, ask pentahedron volume cumulative sum, obtain volume data.

Concrete steps are:

The first step: use nonlinear mapping technique to improve the contrast of liver area in abdominal CT images, a comparatively large rectangle region is alternatively set in liver area, i.e. area-of-interest (ROI), as shown in Figure 2.

The present invention selects nonlinear mapping technique to process abdomen images, and it is by the gray-scale value g of input image pixels (x, y) _in(x, y) is converted to the gray-scale value g of output image by mapping function F (x, y) _out(x, y).Use Sigmoids function to realize this process, Sigmoids function as shown in Equation (1):

$P^{\&prime;}=(\mathrm{Max}-\mathrm{Min})\&CenterDot;\frac{1}{1+e^{-\frac{p-\mathrm{\&beta;}}{\mathrm{\&alpha;}}}}+\mathrm{Min}---\left(1\right)$

Wherein, P is the gray-scale value of input pixel, and P ' is the gray-scale value of output pixel, and Min and Max is minimum value and the maximal value of output image gray scale.α is the regulation and control parameter of input gray level scope, and β is around the gray scale in center range.This process can improve picture contrast.Due to the adhesion of liver peripheral region many muscle and the mucous membrane of abdominal CT, be difficult to effectively differentiate by naked eyes, after Nonlinear Mapping, abdomen images contrast can be improved preferably, make liver area profile can become clear, be conducive to the subsequent singulation of liver.

Then a regular square ROI is set on the liver area of abdominal CT images by the mode of man-machine interactively, this region area is maximally included in liver area, is so more conducive to statistics liver area Pixel Information to select Seed Points and to arrange growth criterion;

Second step: use quasi Monte Carlo method to distribute in ROI random point, then screen suitable Seed Points.

The random point of the low difference distribution that can be distributed in ROI by use quasi Monte Carlo method, the relatively uniform point of this process need distribution can statistical picture information exactly, uses Halton algorithm realize quasi Monte Carlo method and generate equally distributed low difference random point in the present invention.Because each random point is corresponding with liver area pixel respectively, the half-tone information in liver area therefore can be added up by the pixel corresponding to these random points.And these random points are by being used to the Seed Points in algorithm of region growing after screening, be conducive to like this reducing impact that artificial selected seed point brings (such as the artificial Seed Points selected is a noise spot, or grey scale pixel value corresponding to the Seed Points selected and liver area gray average difference is excessive etc. that factor all can have an impact to the effect of algorithm of region growing).

Seed Points screening is as shown in formula 2,3:

$G_{\mathrm{ave}}=\frac{1}{M-m}\underset{i=1}{\overset{M-m}{\mathrm{\&Sigma;}}}{G}_i---\left(2\right)$

$\frac{|G_j-G_{\mathrm{ave}}|}{G_{\mathrm{ave}}}\&le;u---\left(3\right)$

Wherein: G _ipixel P corresponding to random point _igray-scale value, G _avefor whole pixel grey scale average corresponding to random point in the ROI that comes out.M is the quantity of the random point of the low difference distribution that quasi Monte Carlo method generates.M is singular point quantity, and singular point refers to the small holes to occurring in pretreated CT image for liver region, and some random points correspond to these small holes, so grey scale pixel value is 0 corresponding to this point, therefore these some needs are excluded.U is numeric ratio, is used for controlling suitable Seed Points quantity;

3rd step: select suitable growth criterion to be committed step in algorithm of region growing, the present invention is set growing criterion by the gray-scale value of pixel and the change of Grad.First use Robert operator calculates the average gradient value in area-of-interest when algorithm of region growing judges whether some pixels meet growth conditions, if this grey scale pixel value meets formula 4, so this pixel is included in growth district, otherwise judges next pixel.

$G_{\mathrm{ave}}-a\stackrel{\&OverBar;}{\&dtri;T}<G_i<G_{\mathrm{ave}}+a\stackrel{\&OverBar;}{\&dtri;T}---\left(4\right)$

Wherein, a is regulation and control parameter;

4th step: use the algorithm of region growing improved to carry out segmentation to continuous print abdominal CT images and obtain liver area, then carry out aftertreatment and obtain continuous liver area bianry image.Post-processing step comprises: the filling according to morphological method, image being carried out to cavity; Use canny operator to obtain good liver contour images, then with flood-fill algorithm, liver contour images is filled, finally obtain that there is the liver image compared with smooth contoured, as shown in Figure 3;

Then classical MarchingCube algorithm is used to carry out surface rendering reconstruction to the liver image of these segmentations, cubing is carried out owing to the present invention be directed to closed Three-dimension Reconstruction Model, so some surface hole defects spatially can be there are in the model after rebuilding, so need the model after to reconstruction to carry out the repairing of surface hole defect, so just can obtain the hepatic model only with surperficial triangle gridding closed, as shown in Figure 4;

5th step: first, arrange a regular rectangle bounding box according to this reconstruction hepatic model volume coordinate distance, and the most bottom surface of bounding box is set to projection plane Z, its normal vector is N.Six faces of this bounding box can change the size of bounding box by man-machine interactively, so that carry out the measurement of liver local volume.

Secondly, because process of reconstruction intermediate cam dough sheet normal vector direction is not unified, inconsistent inside and outside direction.So need the surperficial tri patch traveling through whole hepatic model, unification adjustment is carried out to the normal vector of tri patch.First choose a tri patch Δ ABC, its normal vector is n, as initial normal vector.Then the normal vector n of the tri patch that traversal is adjacent with Δ ABC _iif, n*n _i<0, then n _icontrary with n direction, so just change normal vector n _idirection, consistent with n direction; If n*n _i>0, then n _iidentical with n direction, proceed traversal adjustment.Finally, the tri patch after normal vector unification is classified: first kind tri patch is that the normal vector inner product of its normal vector and projection plane Z is greater than 0; Equations of The Second Kind tri patch is that the normal vector inner product of its normal vector and projection plane Z is less than 0; 3rd class tri patch is that the normal vector inner product of its normal vector and projection plane Z equals 0;

6th step: because the bounding box around reconstruction model can change size by man-machine interactively, therefore, by coming alternately bounding box to intercept reconstruction model, obtaining liver partial model, so just can carry out the cubing of local to hepatic model.Because six coordinate ranges of face in space coordinates of bounding box are confirmable, and in time intercepting partial liver model alternately to the face of bounding box, in mutual process, the coordinate in bounding box six faces also can change in space coordinates.When carrying out liver local measurement, need to judge which tri patch is within the scope of bounding box, because only have the tri patch of the regional liver model after intercepting in the scope of bounding box.Judge that the method for tri patch whether within the scope of bounding box is: traversal tri patch, judge whether the coordinate of tri patch three points is all in bounding box coordinate range, if the coordinate of tri patch point is not in bounding box coordinate range, then illustrate that this triangle is crossing with bounding box or outside bounding box coordinate range, so this tri patch is just left in the basket and does not calculate; Otherwise tri patch is projected on the Z of projecting plane, carries out volume computing according to the 7th step;

7th step: liver volume is calculated: forming a pentahedron by tri patch being projected on projecting plane, calculating sorted pentahedron volume cumulative sum, then ask difference to calculate.

First-selected needs projects to tri patch Δ ABC tri-point coordinate of traversal on plane Z respectively, obtains projected triangle Δ abc.Now Δ ABC and Δ abc forms a pentahedron, then carries out subdivision to this pentahedron, obtains three tetrahedrons (as shown in Figure 6).Finally calculate each tetrahedral volume according to formula 5:

$V\left(P_1{Q}_1{Q}_2{Q}_3\right)=\frac{1}{6}*\left|\begin{array}{cccc}1& 1& 1& 1\\ x_1& x_2& x_3& x_4\\ y_1& y_2& y_3& y_4\\ z_1& z_2& z_3& z_4\end{array}\right|---\left(5\right)$

Wherein (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂) (x ₃, y ₃, z ₃) (x ₄, y ₄, z ₄) be respectively tetrahedron P ₁q ₁q ₂q ₃four point coordinate, then cumulative three tetrahedral volumes and be exactly pentahedron volume after projecting.

Last in the process of overall hepatic model volume computing point two class situations: a kind of is that the normal vector inner product of tri patch normal vector and projection plane Z is greater than 0, and the pentahedron volume cumulative sum after these tri patchs project is V ₁; Another kind of tri patch is that the normal vector inner product of its normal vector and projection plane Z is less than 0, and the pentahedron volume cumulative sum after the projection of these tri patchs is V ₂.The projection of tri patch on projection plane Z that normal vector inner product due to normal vector and projection plane Z equals 0 is straight line, and its volume is 0, so ignore.Finally obtain the volume of three-dimensional reconstruction hepatic model as shown in Equation (6).

V _liver=| V ₁-V ₂| (6)

Last it is noted that obviously, above-described embodiment is only for example of the present invention is clearly described, and the restriction not to embodiment.For those of ordinary skill in the field, can also make other changes in different forms on the basis of the above description.Here exhaustive without the need to also giving all embodiments.And thus the apparent change of amplifying out or variation be still among protection scope of the present invention.

Claims (2)

1. measure a method for three-dimensional reconstruction hepatic model volume based on improved confinement growth algorithm, it is characterized in that, described method comprises the following steps:

1), CT Image semantic classification;

2), arrange area-of-interest, quasi Monte Carlo method selects Seed Points;

3), liver area is split;

4), post processing of image is split;

5), liver three-dimensional reconstruction;

6), bounding box is set, and to tri patch normal vector consistency adjustment;

7), tri patch projection, ask pentahedron volume cumulative sum, obtain volume data;

Be specially: first use quasi Monte Carlo method choose the Seed Points in traditional algorithm of region growing and grow criterion and improve, and by the Region growing segmentation method after improvement, segmentation carried out to abdominal CT images and extract liver area; Secondly utilize the bianry image split to carry out three-dimensional reconstruction obtain only having the three-dimensional reconstruction hepatic model of surface mesh and close model; The square enclosure box of rule is finally set, the most bottom surface of bounding box is set to projection plane, calculate the pentahedron volume that tri patch reconstruction model with positive and negative direction method vector and its projection on a projection plane surround, the algebraic sum finally calculating all pentahedron volumes is exactly the volume of hepatic model.

2. measure the method for three-dimensional reconstruction hepatic model volume as claimed in claim 1 based on improved confinement growth algorithm, it is characterized in that, concrete steps are:

The first step: use nonlinear mapping technique to improve the contrast of liver area in abdominal CT images, rectangular area, i.e. a region of interest ROI are alternatively set in liver area;

Second step: use quasi Monte Carlo method to distribute in ROI random point, then screen suitable Seed Points;

The random point of the low difference distribution that distributed in ROI by use quasi Monte Carlo method, uses Halton algorithm realize quasi Monte Carlo method and generate equally distributed low difference random point;

Seed Points screening is as formula (1), (2):

$G_{ave}=\frac{1}{M-m}\underset{i=1}{\overset{M-m}{\&Sigma;}}{G}_i---\left(1\right)$

$\frac{|G_j-G_{ave}|}{G_{ave}}\&le;v---\left(2\right)$

Wherein: G _ipixel P corresponding to random point _igray-scale value, G _avefor whole pixel grey scale average corresponding to random point in the ROI that comes out; M is the quantity of the random point of the low difference distribution that quasi Monte Carlo method generates; M is singular point quantity, and singular point refers to the small holes to occurring in pretreated CT image for liver region, and some random points correspond to these small holes, so grey scale pixel value is 0 corresponding to this point, therefore these some needs are excluded; U is numeric ratio, is used for controlling suitable Seed Points quantity;

3rd step: region growing adopts four neighborhood methods to grow, is set growing criterion by the gray-scale value of pixel and the change of Grad, and first use Robert operator calculates the average gradient value in area-of-interest when algorithm of region growing judges whether some pixels meet growth conditions, if this grey scale pixel value meets following formula, so this pixel is included in growth district, otherwise judges next pixel;

$G_{ave}-a\stackrel{\&OverBar;}{\&dtri;T}<G_i<G_{ave}+a\stackrel{\&OverBar;}{\&dtri;T}$

Wherein, a is regulation and control parameter;

4th step: use the algorithm of region growing improved to carry out segmentation to continuous print abdominal CT images and obtain liver area, then carry out aftertreatment and obtain continuous liver area bianry image;

Post-processing step comprises: the filling according to morphological method, image being carried out to cavity, canny operator is used to obtain good liver contour images, then with flood-fill algorithm, liver contour images is filled, finally obtain that there is the liver image compared with smooth contoured;

Then classical MarchingCube algorithm is used to carry out surface rendering reconstruction to the liver image of these segmentations, because this method carries out cubing for the Three-dimension Reconstruction Model closed, so some surface hole defects spatially can be there are in the model after rebuilding, need the model after to reconstruction to carry out the repairing of surface hole defect, so just can obtain the hepatic model only with surperficial triangle gridding closed;

5th step: first, arrange a regular rectangle bounding box according to this reconstruction hepatic model volume coordinate distance, and the most bottom surface of bounding box is set to projection plane Z, its normal vector is N; Six faces of this bounding box can change the size of bounding box by man-machine interactively, so that carry out the measurement of liver local volume;

Secondly, because process of reconstruction intermediate cam dough sheet normal vector direction is not unified, inconsistent inside and outside direction; So need the surperficial tri patch traveling through whole hepatic model, unification adjustment is carried out to the normal vector of tri patch:

1), an initial tri patch Δ ABC normal vector n is obtained, as initial normal vector;

2), the normal vector n of the tri patch that traversal is adjacent with Δ ABC _iif, n*n _i<0, then n _icontrary with n direction, so just change normal vector n _idirection, consistent with n direction; If n*n _i>0, then n _iidentical with n direction, proceed traversal adjustment;

3), the tri patch after normal vector unification is classified: first kind tri patch is that the normal vector inner product of its normal vector and projection plane Z is greater than 0; Equations of The Second Kind tri patch is that the normal vector inner product of its normal vector and projection plane Z is less than 0; 3rd class tri patch is that the normal vector inner product of its normal vector and projection plane Z equals 0;

6th step: by coming alternately bounding box to intercept internal model, carry out the cubing of regional area;

7th step: calculate liver volume, forming a pentahedron by tri patch being projected on projecting plane, calculating sorted pentahedron volume cumulative sum, then ask difference to calculate.