CN111932665A - Hepatic vessel three-dimensional reconstruction and visualization method based on vessel tubular model - Google Patents

Hepatic vessel three-dimensional reconstruction and visualization method based on vessel tubular model Download PDF

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CN111932665A
CN111932665A CN202010544950.6A CN202010544950A CN111932665A CN 111932665 A CN111932665 A CN 111932665A CN 202010544950 A CN202010544950 A CN 202010544950A CN 111932665 A CN111932665 A CN 111932665A
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钱月晶
章增优
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Zhejiang Industry and Trade Vocational College
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Abstract

The invention provides a hepatic vessel three-dimensional reconstruction and visualization method based on a vessel tubular model, which comprises the following steps: s10, acquiring a liver CT image, and adjusting the window width and the window level to ensure that the liver CT image conforms to the gray level display range of the display device; s20, carrying out pre-processing of denoising and image enhancement on the liver CT image which accords with the gray level display range of the display device; s30, segmenting the blood vessel by utilizing a segmentation method based on a Hessian matrix and a region growing algorithm according to the preprocessed blood vessel image; s40, filling the cavity caused by the blood vessel segmentation by adopting a morphological method; s50, performing volume rendering on the blood vessel by using a triangular mesh surface rendering and ray projection algorithm according to the inherent characteristics of the hepatic blood vessel to realize three-dimensional reconstruction; s60, the three-phase image sequence is visually displayed by adopting a computer-aided liver blood vessel visualization system based on the CT dynamic enhanced image, the invention accurately and reliably segments and three-dimensionally reconstructs the liver blood vessel, and can better perform visual display to assist a doctor to determine the liver condition.

Description

Hepatic vessel three-dimensional reconstruction and visualization method based on vessel tubular model
Technical Field
The invention relates to the technical field of medical image analysis, in particular to a hepatic vessel three-dimensional reconstruction and visualization method based on a vessel tubular model.
Background
Currently, diagnosis of vascular disease relies primarily on various angiographic techniques. With the development of interventional radiology, angiography has become an important clinical diagnostic method, and plays an irreplaceable role in interventional therapy in particular. Several different angiographic imaging modalities are mainly Bi-planar X-ray (Bi-planar)/digital subtraction angiography (dsa), Magnetic Resonance Angiography (MRA), CT angiography (CTA), ultrasound angiography, and angiography techniques that combine several different medical imaging modalities. Because the blood vessel image obtained by the CT angiography technology is clear, and can provide good reference for the diagnosis and preoperative preparation of doctors, the method is mostly adopted at home and abroad for observing and diagnosing the vascular diseases.
Liver tumors typically appear in the hepatic vascular region on two-dimensional chest slices and three-dimensional CT slices. Thus, the diagnosis of liver tumors is attributed to the localization of cancer nodules in the hepatic blood vessels. Traditional liver vessel segmentation requires the surgeon to manually delineate the vessel region on each liver slice, and since there are about 200 liver slices per group, it is not only time consuming but also prone to error if the vessels are delineated manually. In order to improve the efficiency of blood vessel segmentation, it is necessary to research a liver blood vessel segmentation algorithm capable of automatically segmenting blood vessels, and then perform three-dimensional reconstruction on the segmented result, so that a surgeon can quickly locate the position of a liver tumor, thereby providing help for smoothly performing a surgical operation.
In summary, it is an urgent need of those skilled in the art to provide a hepatic vessel three-dimensional reconstruction and visualization method based on a vascular tubular model, which can accurately and reliably segment and three-dimensionally reconstruct a hepatic vessel and can better perform visualization display to assist a doctor in determining a liver condition.
Disclosure of Invention
In order to solve the above mentioned problems and needs, the present solution provides a three-dimensional reconstruction and visualization method for hepatic vessels based on a vascular tubular model, which can solve the above technical problems due to the following technical solutions.
In order to achieve the purpose, the invention provides the following technical scheme: a hepatic vessel three-dimensional reconstruction and visualization method based on a vessel tubular model comprises the following specific steps: s10, acquiring a liver CT image, and adjusting the window width and the window level to ensure that the liver CT image conforms to the gray level display range of the display device;
s20, carrying out pre-processing of denoising and image enhancement on the liver CT image which accords with the gray level display range of the display device;
s30, segmenting the blood vessel by utilizing a segmentation method based on a Hessian matrix and a region growing algorithm according to the preprocessed blood vessel image;
s40, filling the cavity caused by the blood vessel segmentation by adopting a morphological method;
s50, performing volume rendering on the blood vessel by using a triangular mesh surface rendering and ray projection algorithm according to the inherent characteristics of the hepatic blood vessel to realize three-dimensional reconstruction;
and S60, visually displaying the three-phase image sequence of the hepatic artery phase, the portal vein phase and the delayed phase by adopting a computer-aided liver blood vessel visualization system based on the CT dynamic enhanced image.
Furthermore, the obtained liver CT image is stored in a DICOM file form, and the liver CT image is made to conform to the gray level display range of the display device by adopting a method of adjusting the window width and the window level.
Further, the method for adjusting the window width and the window level specifically includes: reading DICOM image data, if bit allocation of each sample value is more than 8, storing pixel sample values of the image data by taking a word as a unit, and performing data conversion processing through high and low byte exchange, high bit interception and readjustment to display a DICOM image.
Further, the preprocessing includes noise reduction and local enhancement using a blur-based approach.
Further, the local enhancement using the blur-based method includes: first calculateAnd (3) the absolute difference between each pixel and the central pixel in the region, then, the membership function is utilized to construct a weight, and finally, the pixel values in the region are weighted and summed to obtain the enhancement result of the step. Calculating the Euclidean distance between the current pixel and the region pixel: let the region be 3 x 3, let the current pixel be (i, j), and mark the gray value as Hi,jThen the distance from the pixel in the area to the center pixel is Di,j=|Hi+p,j+qI, p, q belongs to (-1,0, 1); according to
Figure BDA0002540367510000031
k=max(D-1,-1,…,D1,1) Calculating the weight of each pixel; the output image pixel is
Figure BDA0002540367510000032
According to the formula
Figure BDA0002540367510000033
And performing edge enhancement on the output image, wherein r (I, j) ═ mean (F) × u, u is a correction parameter F (p, q) ═ I (I + p, j + q) -I (I, j), and F is the gray level difference between the pixels in the area and the central pixel.
Further, the step S30 specifically includes:
s31, inputting the blood vessel image after preprocessing, generating a pixel matrix P, initializing a space scale sigma a and enhancing a factor Umax0, spatial scale range of [ a, b]Each pixel Px,y,zCorresponding to several spatial scales sigmaiAnd a plurality of enhancement factors Ui(max);
S32: computing element Px,y,zConvolution with the second derivative of the gaussian function G (x, y, z), where,
Figure BDA0002540367510000041
s33: generating Hessian matrix H and calculating eigenvalue lambda1、λ2、λ3According to the formula Umax=max(Ui(max),P(v,σi) ) calculating an output value U of the enhancement filtermaxTo do so
Figure BDA0002540367510000042
Figure BDA0002540367510000043
Figure BDA0002540367510000044
c is half of the maximum norm value of the Hessian matrix, v is a characteristic vector, and alpha and beta are fixed constant values;
s34: iterating sigma to b and ending the scale iteration, and outputting the maximum enhanced filter output value UmaxAs the element Px,y,zAnd outputs the eigenvalue lambda of the Hessian matrix H corresponding to the output value1、λ2、λ3And a feature vector v1、v2、v3According to the obtained UmaxThe value is used to determine whether the pixel is a blood vessel.
Furthermore, a dynamic self-adaptive region growing algorithm is adopted to select a proper gray value as an initial value of the seed region to perform vessel segmentation on the enhanced image.
Furthermore, the dynamic adaptive region growing algorithm comprises the steps of selecting a CT picture from a CT sequence image enhanced by a Hessian algorithm, selecting corresponding seed points from a liver organ region, performing region growing on the seed points by using the dynamic adaptive region growing algorithm to obtain a CT picture segmentation result, storing the result by using a corresponding data structure, marking the result as a point set Q, projecting the point set Q to an adjacent next CT picture to obtain a group of projection point sets, marking the point set Q as a point set Z, and using the projection point sets as initial segmentation regions of the next CT picture; and (4) performing region growing on all points in the projection point set Z to obtain a segmentation result of an adjacent slice, recording the segmentation result as a point set Q, judging whether all CT pictures are segmented completely, and if the segmentation is completed, quitting, otherwise, continuing to segment the next CT picture.
Furthermore, the triangular mesh surface drawing realizes fracture stitching by adopting a discrete equidistant method for the convex edge, the convex points/convex mixed points of the blood vessel image, and eliminates the invalid area by utilizing interference continuity to obtain the hepatic blood vessel enclosure; the ray projection algorithm starts from each pixel of the blood vessel image space, a ray is emitted according to the sight line direction, the ray penetrates through the three-dimensional data field, whether the ray is intersected with the surrounding body or not is judged, and if the ray is not intersected with the surrounding body, the next ray is continuously searched; if the intersection exists, a plurality of equidistant sampling points are selected along the ray, cubic linear interpolation is carried out on the color values and the opacity values of 8 data points which are closest to one sampling point, the opacity value and the color value of the sampling point are solved, then the color value and the opacity value of each sampling point on each ray are synthesized from front to back or from back to front to obtain the color value of the pixel point which sends the ray, and then the final image is obtained on the screen.
The invention has the advantages that the invention can accurately and reliably segment and three-dimensionally reconstruct the liver blood vessel, and can better perform visualization display to assist doctors in determining the liver condition.
The following description of the preferred embodiments for carrying out the present invention will be made in detail with reference to the accompanying drawings so that the features and advantages of the present invention can be easily understood.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings of the embodiments of the present invention will be briefly described below. Wherein the drawings are only for purposes of illustrating some embodiments of the invention and are not to be construed as limiting the invention to all embodiments thereof.
Fig. 1 is a schematic diagram of steps of a hepatic vessel three-dimensional reconstruction and visualization method based on a vessel tubular model.
Fig. 2 is a schematic diagram illustrating specific steps for enhancing a liver blood vessel image according to the present invention.
Fig. 3 is a flowchart of the hepatic blood vessel segmentation process in this embodiment.
Fig. 4 is a schematic diagram illustrating a flow chart of a three-dimensional reconstruction process of hepatic vessels in this embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of specific embodiments of the present invention. Like reference symbols in the various drawings indicate like elements. It should be noted that the described embodiments are only some embodiments of the invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the described embodiments of the invention without any inventive step, are within the scope of protection of the invention.
The invention provides a hepatic vessel three-dimensional reconstruction and visualization method based on a vascular tubular model, which can accurately and reliably segment and three-dimensionally reconstruct hepatic vessels and can better perform visualization display to assist doctors in determining the liver condition. Since the medical image data stored in the DICOM file is usually a relative value rather than an actual display value, and the dynamic range of the data is large, the pixel depth is generally not lower than 4096 gray levels and far beyond the gray level display range of the display device, some kind of processing must be taken to map the data with large dynamic range to the gray level of the display device. The DICOM file is read by reading some data elements of the DICOM, so as to obtain necessary information and image data required for displaying the DICOM file, for example, information such as VR explicit or implicit, byte ordering format, compression format of image data and the like can be obtained by reading transmission syntax (Transfersyntax); the pixel sample value (samplespirixel) is read, with bit allocation per sample value (bitallocated), row number, column number, number of bits of the actual stored pixel (bitstored), frame number, bit depth, sign flag, window width, window level, etc. The liver CT image is generally stored in the form of a DICOM file, and since the head file of the DICOM file has one hundred formats, and reading and displaying the DICOM file has a certain difficulty, the image data needs to be adjusted to conform to the gray scale display range of the display device as mentioned in step S10.
As shown in fig. 1 to 4, a hepatic vessel three-dimensional reconstruction and visualization method based on a vessel tubular model includes the following specific steps:
s10, acquiring a liver CT image, adjusting the window width and window level to make the liver CT image conform to the gray level display range of the display device, wherein the acquired liver CT image is stored in a DICOM file form, and the liver CT image conforms to the gray level display range of the display device by adopting a method for adjusting the window width and window level, and the method for adjusting the window width and window level specifically comprises the following steps: reading DICOM image data, if bit allocation of each sample value is more than 8, storing pixel sample values of the image data by taking a word as a unit, and performing data conversion processing through high-low byte exchange, high-order interception and readjustment to display a DICOM image;
s20, carrying out pre-processing of denoising and image enhancement on the liver CT image which accords with the gray level display range of the display device;
s30, segmenting the blood vessel by utilizing a segmentation method based on a Hessian matrix and a region growing algorithm according to the preprocessed blood vessel image;
as shown in fig. 2, the hepatic blood vessel image is enhanced, in preparation for segmenting the blood vessels and liver portions,
s31, inputting the blood vessel image after preprocessing, generating a pixel matrix P, initializing a space scale sigma a and enhancing a factor Umax0, spatial scale range of [ a, b]Each pixel Px,y,zCorresponding to several spatial scales sigmaiAnd a plurality of enhancement factors Ui(max);
S32: computing element Px,y,zConvolution with the second derivative of the gaussian function G (x, y, z), where,
Figure BDA0002540367510000081
s33: generating Hessian matrix H and calculating eigenvalue lambda1、λ2、λ3According to the formula Umax=max(Ui(max),P(v,σi) ) calculating an output value U of the enhancement filtermaxTo do so
Figure BDA0002540367510000082
Figure BDA0002540367510000083
Figure BDA0002540367510000084
c is half of the maximum norm value of the Hessian matrix, v is a characteristic vector, and alpha and beta are fixed constant values;
s34: iterating sigma to b and ending the scale iteration, and outputting the maximum enhanced filter output value UmaxAs the element Px,y,zAnd outputs the eigenvalue lambda of the Hessian matrix H corresponding to the output value1、λ2、λ3And a feature vector v1、v2、v3According to the obtained UmaxValue to determine whether the pixel is a blood vessel, and UmaxThe larger the value, the greater the likelihood that the pixel is a blood vessel;
s40, filling the cavity caused by the blood vessel segmentation by adopting a morphological method;
s50, performing volume rendering on the blood vessel by using a triangular mesh surface rendering and ray projection algorithm according to the inherent characteristics of the hepatic blood vessel to realize three-dimensional reconstruction;
and S60, visually displaying the three-phase image sequence of the hepatic artery phase, the portal vein phase and the delayed phase by adopting a computer-aided liver blood vessel visualization system based on the CT dynamic enhanced image.
Due to the fact that the radius of blood vessels is greatly different from that of the main part of the liver blood vessels and the tail ends of the blood vessels, the gray values are also greatly different from that of the main part of the blood vessels and the tail ends of the blood vessels, and the geometrical structure of the blood vessels is complex, the problems are that the blood vessels are easy to be over-segmented or under-segmented. Therefore, it is important to pre-process the liver blood vessels before they are further segmented, so as to reduce noise and enhance the gray scale of the blood vessels to obtain better segmentation results, in the method, the pre-processing includes noise reduction and local enhancement based on a fuzzy method, and the local enhancement based on the fuzzy method includes: the absolute difference between each pixel and the central pixel in the region is calculated, then the membership function is used for constructing the weight, and finally the pixel values in the region are weighted and summed to obtain the enhancement result of the step. Calculating the Euclidean distance between the current pixel and the region pixel: let the region be 3 x 3, let the current pixel be (i, j), and let the gray valueIs denoted by Hi,jThen the distance from the pixel in the area to the center pixel is Di,j=|Hi+p,j+qI, p, q belongs to (-1,0, 1); according to
Figure BDA0002540367510000091
k=max(D-1,-1,…,D1,1) Calculating the weight of each pixel; the output image pixel is
Figure BDA0002540367510000092
According to the formula
Figure BDA0002540367510000093
And performing edge enhancement on the output image, wherein r (I, j) ═ mean (F) × u, u is a correction parameter F (p, q) ═ I (I + p, j + q) -I (I, j), and F is the gray level difference between the pixels in the area and the central pixel.
After a sequence blood vessel image is enhanced, a dynamic adaptive region growing algorithm is adopted to select a proper gray value as an initial value of a seed region to perform blood vessel segmentation on the enhanced image, as shown in fig. 3, the dynamic adaptive region growing algorithm comprises the steps of selecting a CT image from the CT sequence image enhanced by the Hessian algorithm, selecting corresponding seed points from a liver organ region, performing region growing on the seed points by using the dynamic adaptive region growing algorithm to obtain the result of CT image segmentation, storing the result by using a corresponding data structure, and recording the result as a point set Q, projecting the point set Q to the next adjacent CT image to obtain a group of projection point sets, and recording the point set Z as the initial segmentation region of the next CT image; and (4) performing region growing on all points in the projection point set Z to obtain a segmentation result of an adjacent slice, recording the segmentation result as a point set Q, judging whether all CT pictures are segmented completely, and if the segmentation is completed, quitting, otherwise, continuing to segment the next CT picture.
In order to allow a doctor to visually observe information such as the shape and position of a blood vessel, it is necessary to reconstruct a segmented hepatic blood vessel in three dimensions. Because the inter-layer spacing of the slices is not uniform, interpolation is needed during three-dimensional reconstruction, meanwhile, in order to improve the reconstruction precision, triangular grid surface drawing is needed to be carried out on the blood vessel, and a classical light projection algorithm is adopted to carry out volume drawing on the blood vessel, as shown in figure 4, the triangular grid surface drawing realizes fracture stitching on the convex edge and the convex point/convex mixed point of the blood vessel image by adopting a discrete equidistant method, and an invalid region is deleted by utilizing interference continuity to obtain an enclosure of the hepatic blood vessel; the ray projection algorithm starts from each pixel of the blood vessel image space, a ray is emitted according to the sight line direction, the ray penetrates through the three-dimensional data field, whether the ray is intersected with the surrounding body or not is judged, and if the ray is not intersected with the surrounding body, the next ray is continuously searched; if the intersection exists, a plurality of equidistant sampling points are selected along the ray, cubic linear interpolation is carried out on the color values and the opacity values of 8 data points which are closest to one sampling point, the opacity value and the color value of the sampling point are solved, then the color value and the opacity value of each sampling point on each ray are synthesized from front to back or from back to front to obtain the color value of the pixel point which sends the ray, and then the final image is obtained on the screen.
It should be noted that the described embodiments of the invention are only preferred ways of implementing the invention, and that all obvious modifications, which are within the scope of the invention, are all included in the present general inventive concept.

Claims (9)

1. A hepatic vessel three-dimensional reconstruction and visualization method based on a vessel tubular model is characterized by comprising the following specific steps:
s10, acquiring a liver CT image, and adjusting the window width and the window level to ensure that the liver CT image conforms to the gray level display range of the display device;
s20, carrying out pre-processing of denoising and image enhancement on the liver CT image which accords with the gray level display range of the display device;
s30, segmenting the blood vessel by utilizing a segmentation method based on a Hessian matrix and a region growing algorithm according to the preprocessed blood vessel image;
s40, filling the cavity caused by the blood vessel segmentation by adopting a morphological method;
s50, performing volume rendering on the blood vessel by using a triangular mesh surface rendering and ray projection algorithm according to the inherent characteristics of the hepatic blood vessel to realize three-dimensional reconstruction;
and S60, visually displaying the three-phase image sequence of the hepatic artery phase, the portal vein phase and the delayed phase by adopting a computer-aided liver blood vessel visualization system based on the CT dynamic enhanced image.
2. The hepatic vessel three-dimensional reconstruction and visualization method based on the vessel-like model as claimed in claim 1, wherein the acquired liver CT image is stored in a DICOM file, and the window width and the window level are adjusted to fit the liver CT image with the gray scale display range of a display device.
3. The hepatic vessel three-dimensional reconstruction and visualization method based on the vascular tubular model as claimed in claim 2, wherein the method for adjusting the window width and the window level specifically comprises: reading DICOM image data, if bit allocation of each sample value is more than 8, storing pixel sample values of the image data by taking a word as a unit, and performing data conversion processing through high and low byte exchange, high bit interception and readjustment to display a DICOM image.
4. The hepatic vessel three-dimensional reconstruction and visualization method based on the vessel-tubular model as claimed in claim 1, wherein the preprocessing comprises noise reduction and local enhancement based on fuzzy method.
5. The hepatic vessel three-dimensional reconstruction and visualization method based on the vessel-tubular model as claimed in claim 4, wherein the local enhancement based on the fuzzy method comprises: the absolute difference between each pixel and the central pixel in the region is calculated, then the membership function is used for constructing the weight, and finally the pixel values in the region are weighted and summed to obtain the enhancement result of the step. Calculating the Euclidean distance between the current pixel and the region pixel: let the region be 3 x 3, let the current pixel be (i, j), and mark the gray value as Hi,jThen the distance from the pixel in the area to the center pixel is Di,j=|Hi+p,j+qI, p, q belongs to (-1,0, 1); according to
Figure FDA0002540367500000021
Calculating the weight of each pixel; the output image pixel is
Figure FDA0002540367500000022
According to the formula
Figure FDA0002540367500000023
And performing edge enhancement on the output image, wherein r (I, j) ═ mean (F) × u, u is a correction parameter F (p, q) ═ I (I + p, j + q) -I (I, j), and F is the gray level difference between the pixels in the area and the central pixel.
6. The hepatic vessel three-dimensional reconstruction and visualization method based on the vascular tubular model as claimed in claim 1, wherein the step S30 specifically comprises:
s31, inputting the blood vessel image after preprocessing, generating a pixel matrix P, initializing a space scale sigma a and enhancing a factor Umax0, spatial scale range of [ a, b]Each pixel Px,y,zCorresponding to several spatial scales sigmaiAnd a plurality of enhancement factors Ui(max);
S32: computing element Px,y,zConvolution with the second derivative of the gaussian function G (x, y, z), where,
Figure FDA0002540367500000031
s33: generating Hessian matrix H and calculating eigenvalue lambda1、λ2、λ3According to the formula Umax=max(Ui(max),P(v,σi) ) calculating an output value U of the enhancement filtermaxTo do so
Figure FDA0002540367500000032
Figure FDA0002540367500000033
c is half of the maximum norm value of the Hessian matrix, v is a feature vector, and alpha and beta areA fixed constant value;
s34: iterating sigma to b and ending the scale iteration, and outputting the maximum enhanced filter output value UmaxAs the element Px,y,zAnd outputs the eigenvalue lambda of the Hessian matrix H corresponding to the output value1、λ2、λ3And a feature vector v1、v2、v3According to the obtained UmaxThe value is used to determine whether the pixel is a blood vessel.
7. The hepatic vessel three-dimensional reconstruction and visualization method based on the vessel tubular model as claimed in claim 6, wherein a dynamic adaptive region growing algorithm is adopted to select a proper gray value as an initial value of a seed region to perform vessel segmentation on the enhanced image.
8. The three-dimensional hepatic vessel reconstruction and visualization method based on the vascular tubular model as claimed in claim 7, wherein the dynamic adaptive region growing algorithm comprises selecting a CT image from the CT sequence image enhanced by the Hessian algorithm, selecting corresponding seed points in the liver organ region, performing region growing on the seed points by using the dynamic adaptive region growing algorithm to obtain the result of the CT image segmentation, storing the result by using a corresponding data structure, and recording the result as a point set Q, projecting the point set Q to the next adjacent CT image to obtain a group of projection point sets, and recording the group of projection point sets as a point set Z as the initial segmentation region of the next CT image; and (4) performing region growing on all points in the projection point set Z to obtain a segmentation result of an adjacent slice, recording the segmentation result as a point set Q, judging whether all CT pictures are segmented completely, and if the segmentation is completed, quitting, otherwise, continuing to segment the next CT picture.
9. The hepatic vessel three-dimensional reconstruction and visualization method based on the vessel tubular model as claimed in claim 1, wherein the triangular mesh surface rendering adopts a discrete equidistant method to realize fracture suture on the convex edge, the convex point/convex mixed point of the blood vessel image, and eliminates the invalid region by using interference coherence to obtain the surrounding body of the hepatic vessel; the ray projection algorithm starts from each pixel of the blood vessel image space, a ray is emitted according to the sight line direction, the ray penetrates through the three-dimensional data field, whether the ray is intersected with the surrounding body or not is judged, and if the ray is not intersected with the surrounding body, the next ray is continuously searched; if the intersection exists, a plurality of equidistant sampling points are selected along the ray, cubic linear interpolation is carried out on the color values and the opacity values of 8 data points which are closest to one sampling point, the opacity value and the color value of the sampling point are solved, then the color value and the opacity value of each sampling point on each ray are synthesized from front to back or from back to front to obtain the color value of the pixel point which sends the ray, and then the final image is obtained on the screen.
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CN112712586A (en) * 2020-12-22 2021-04-27 复旦大学附属中山医院 Rapid generation method of artery model
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