CN111080765B - Ray tracing volume drawing method based on gradient sampling - Google Patents
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- 230000015572 biosynthetic process Effects 0.000 claims abstract description 4
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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Abstract
The invention discloses a gradient sampling-based ray tracing volume drawing method, which aims at the performance defect of huge calculation amount of Monte Carlo ray tracing and the irrational property of sampling point distribution in the process of sampling rays by Woodcock Tracking, uses a three-dimensional Sobel operator to select 26 neighborhood voxels to calculate the volume data gradient for describing the intensity of the volume data changing in different areas, introduces gradient proportion items in Woodcock Tracking samples, and finally adds weight coefficients to the final color synthesis to ensure the unbiasedness of the algorithm.
Description
Technical Field
The invention belongs to the technical field of computer vision and three-dimensional reconstruction, relates to a Woodcock Tracking sampling method, and particularly relates to a ray tracing volume drawing method based on gradient sampling.
Background
Traditional medical imaging techniques acquire two-dimensional projection images, such as X-ray images, ultrasound images (e.g., IVUS) or tomographic images (e.g., CT images or MRI images), which are images with incomplete information descriptions, and doctors often need to view a large number of two-dimensional images for diagnosing a disease condition, which is time-consuming and labor-consuming, and position information reflected in the two-dimensional images is blurred in space, so that it is difficult to acquire clear stereoscopic perception of an organ or a focus in a three-dimensional space through the two-dimensional tomographic images, and important information such as the spatial position, size and geometric shape of the focus cannot be clearly displayed through the two-dimensional images. Under such a background, the clinical diagnosis is urgent to convert the two-dimensional tomographic image sequence into a three-dimensional image, and reconstruct the obtained two-dimensional medical image by using a computer three-dimensional reconstruction technology, so that doctors can more intuitively and comprehensively understand the medical image data, and further make accurate judgment on the illness state.
The three-dimensional reconstruction technology of the traditional medical image is divided into surface drawing and volume drawing, the basic idea of the surface drawing is that firstly, the contour line of a region of interest is extracted, then, a triangular surface patch set is constructed according to the contour line of the adjacent slice to fit the surface contour of the object. The most classical in volume rendering is a ray casting method, the basic principle of which is that a ray is emitted from each pixel point on a screen along the direction of a line of sight, when the ray passes through volume data, the ray is sampled at equal intervals along the direction of the ray, and the color value and the opacity of a sampling point are calculated by interpolation; and then synthesizing sampling points on the light rays in a sequence from front to back or from back to front, and calculating color values of pixel points on the screen corresponding to the light rays. Compared with surface drawing, the method can not only render and display surface contour information, but also display and reconstruct internal information of an object, has better drawing effect, and light projection is the most widely applied volume drawing method at present, but has a certain gap from the real illumination effect in nature, and lacks interaction among objects in volume data.
The Monte Carlo ray tracing algorithm is used for carrying out three-dimensional reconstruction on the volume data, and compared with a ray projection rendering method, the method can achieve ray reflection, refraction and diffuse reflection, so that interaction of ray information among the volume data can be achieved. The basic idea is to send out a ray from a viewpoint, continuously sample one direction according to the material property of the surface when the ray intersects with the surface of the object, send out another ray, iterate the steps until the ray strikes a light source (or escapes out of the scene), and then calculate the contribution of the ray as the color value of the pixel by using a Monte Carlo method. Monte Carlo ray tracing can achieve movie-level rendering effects, but one of the biggest drawbacks is the huge computational effort required in performance. For this reason Woodcock Tracking is used herein to sample the light, unlike the ray stepping algorithm which advances the same distance each time, the woodpack tracking algorithm simulates the actual path of the light in the medium to sample along the direction of the light, which may advance a short distance or a long distance at a time, the distribution of sampling points depending on the extinction coefficient of the volume data, i.e. areas with large extinction coefficients will obtain more sampling points. In the rendering of the monte carlo ray tracing volume, how to determine important areas and how to realize multi-sampling of the most important areas are important, the determination of the extinction coefficient is not scientific, and in practice, more sampling points should be obtained in the areas with more severe volume data changes. The three-dimensional Sobel operator is used, and the gradient of each region in the volume data is calculated by adopting 26 neighborhood voxels, so that the intensity of the change of different regions in the volume data is depicted, and then gradient proportion items are introduced in Woodcock Tracking sampling, so that fewer sampling points are rendered in a low-frequency region of the volume data, more sampling points are rendered in a high-frequency region with more intense change, and the distribution of the sampling points is more reasonable.
Disclosure of Invention
The invention aims to provide a more efficient sampling method in light sampling of Monte Carlo ray tracing, and gradient proportion items are introduced in Woodcock Tracking sampling, and gradient information is introduced according to Woodcock Tracking sampling defects, so that three-dimensional rendering has more sampling points in a high-frequency region of an image, the sampling distribution is more reasonable, and the method can effectively improve the rendering speed and the rendering quality of Monte Carlo ray tracing.
The technical scheme adopted by the invention is a ray tracing volume drawing method based on gradient sampling, wherein fig. 1 is a flow chart of the method, and fig. 2 is a schematic diagram thereof. The method comprises the steps of adopting a Monte Carlo ray tracing method to an acquired medical image sequence, firstly sending out virtual rays from a viewpoint, continuously sampling the next direction according to the regional attribute when the rays intersect with an object, sending out another ray, iterating until the rays strike a light source or escape from a scene, and then calculating contribution of the rays as color of pixels by using the Monte Carlo method; the light is sampled by adopting a woodcock Tracking sampling algorithm, and gradient proportion items are introduced on the sampling point acceptance probability, so that more sampling points exist in a high-frequency region with more severe image change.
Step 1, acquiring a medical image sequence from the Internet or a hospital, wherein a computer tomography image (CT image) is used in the method;
step 2, selecting 300 frames of continuous tomographic images with the size of 512 x 512 to form volume data;
and 3, drawing the volume data by adopting a Monte Carlo ray tracing method, wherein a rendering equation is as follows:
wherein ,represents the x position along +.>Radiation brightness emitted from direction, < >>Represents x s Along->Emergent radiation brightness->Represents x t Along->The incident radiance, s, is the depth in the medium; sigma (sigma) s (x t ) Represents x t Scattering coefficient at>Representing x to x t The transmission coefficient between describes the attenuation of light as it passes through the medium, where T r The values of (2) are:
σ t represents the extinction coefficient, which is the scattering coefficient sigma s And absorption coefficient sigma α Sum, i.e. sigma t ＝σ s +σ α The method comprises the steps of carrying out a first treatment on the surface of the Sigma in homogeneous medium t Is constant at this timex and x' represent different positions in the medium;
and 4, sampling light by adopting woodcock Tracking gradient sampling, and solving a rendering equation by using a Monte Carlo method.
Step 4.1, in the uniform medium, calculating a rendering equation by using a Monte Carlo methodItem equal to->Namely, calculating:
wherein, tfact is t j Omitting a subscript j to avoid complex formulas caused by multi-stage subscripts, and representing the distance from a j-th sampling point to the light ray starting point;
step 4.2, orderThen->Its inverse function:
step 4.3, giving a uniform random number r E [0, 1), and the value of the sampling point t is
Step 5, calculating the gradient of the volume data by a three-dimensional Sobel operator in a non-uniform medium, and calculating the acceptance probability of the light sampling points;
step 5.1, adopting a three-dimensional Sobel operator, calculating gradients by using 26 neighborhood voxels, calculating partial derivatives of each direction by using a 3X 3 template, and respectively using the templates in the x, y and z directions as follows:
after calculating the partial derivatives in each direction, the formula is:
calculating to obtain gradient value, using G (x) to replace G (x, y, z) to represent gradient of different positions in medium, using G max Representing the maximum gradient;
step 5.2, assuming uniform medium, sampling scattering points by the method of sampling uniform medium in step 4, the scattering points being used toThe probability acceptance of (2) is true, indicating that scattering occurs at x, otherwise, indicating that no scattering occurs, and that the ray is traveling along a straight line; wherein sigma max Represents the maximum extinction coefficient, delta represents the specific gravity constant, the value range is zero to positive infinity, and the larger the delta isThe more the item approaches 1,/>Representing a gradient specific gravity term; the original woodcock Tracking sampling algorithm is improved, gradient parameters G (x) and constant delta are introduced, so that the sampling distribution is more reasonable, and the sampling algorithm is as follows:
firstly, setting the maximum sampling distance as d max Let the current sampling distanceWherein the random number rand () ∈0, 1) when the sampling distance d is greater than the maximum sampling distance d max Or the random number rand () is smaller than +.>When the sampling is performed, the sampling distance is returned; otherwise, the light ray does not scatter, the light ray advances along a straight line, and the sampling distance d is increased by +.>Again judging whether the sampling distance is greater than the maximum sampling distance d max Or whether the random number rand () is smaller than +.>And the like, until the circulation condition is not met, the circulation is finished, and the sampling distance is returned.
Step 6, color synthesis, wherein a gradient proportion term is added to the original woodcock Tracking sampling algorithm, so that the unbiasedness of the algorithm is ensured, and a weight coefficient omega is introduced when the color is synthesized i ，Final synthetic colour-> wherein ci Represents a certain sample point color value and N represents the total number of sample points.
The invention adopts a ray tracing volume drawing method based on gradient sampling, so that the distribution of the ray sampling points is more reasonable, the original Woodcock Tracking sampling point distribution is only determined by the extinction coefficient, and the more the sampling points distributed in the area with larger extinction coefficient of the volume data are; according to the method, a gradient proportion term is introduced, the distribution of sampling points is improved to be determined by the extinction coefficient and the gradient, so that the distribution of the sampling points has more sampling points in a high-frequency area with severe volume data change, the high-frequency detail area of an image is emphasized to be rendered, and the rendering speed and the rendering quality of a Monte Carlo ray tracing algorithm with huge calculation amount can be effectively improved.
Drawings
FIG. 1 is a ray tracing volume rendering flow chart of gradient sampling;
FIG. 2 is a schematic view of gradient sampled ray tracing volume rendering;
FIG. 3 is a modified pre-lung rendered image;
fig. 4 is a rendered image of the lungs employing the invention.
Detailed Description
The invention is realized by adopting the following technical means:
ray tracing volume rendering based on gradient sampling. Adopting Monte Carlo ray tracing, firstly, emitting a virtual ray from a viewpoint, continuously sampling the next direction according to the regional attribute when the ray intersects with an object, emitting another ray, iterating until the ray strikes a light source or escapes from a scene, and then calculating the contribution of the ray as the color of a pixel by using a Monte Carlo method; the light is sampled by adopting a woodcock Tracking sampling algorithm, and gradient proportion items are introduced on the sampling point acceptance probability, so that more sampling points exist in a high-frequency region with more severe image change.
Step 1, acquiring a medical image sequence from the Internet or a hospital, wherein a computer tomography image (CT image) is used in the method;
step 2, selecting 300 frames of continuous tomographic images with the size of 512 x 512 to form volume data;
and 3, drawing the volume data by adopting a Monte Carlo ray tracing method, wherein a rendering equation is as follows:
wherein ,represents the x position along +.>Radiation brightness emitted from direction, < >>Represents x s Along->Emergent radiation brightness->Represents x t Along->The incident radiance, s, is the depth in the medium; sigma (sigma) s (x t ) Represents x t Scattering coefficient at>Representing x to x t The transmission coefficient between describes the attenuation of light as it passes through the medium, where T r The values of (2) are:
σ t representing extinction coefficientFor the scattering coefficient sigma s And absorption coefficient sigma α Sum, i.e. sigma t ＝σ s +σ α The method comprises the steps of carrying out a first treatment on the surface of the Sigma in homogeneous medium t Is constant at this timex and x' represent different positions in the medium;
and 4, sampling light by adopting woodcock Tracking gradient sampling, and solving a rendering equation by using a Monte Carlo method.
Step 4.1, in the uniform medium, calculating a rendering equation by using a Monte Carlo methodItem equal to->Namely, calculating:
wherein, tfact is t j Omitting a subscript j to avoid complex formulas caused by multi-stage subscripts, and representing the distance from a j-th sampling point to the light ray starting point;
step 4.2, orderThen->Its inverse function:
step 4.3, giving a uniform random number r E [0, 1), and the value of the sampling point t is
Step 5, calculating the gradient of the volume data by a three-dimensional Sobel operator in a non-uniform medium, and calculating the acceptance probability of the light sampling points;
step 5.1, adopting a three-dimensional Sobel operator, calculating gradients by using 26 neighborhood voxels, calculating partial derivatives of each direction by using a 3X 3 template, and respectively using the templates in the x, y and z directions as follows:
after calculating the partial derivatives in each direction, the formula is:
calculating to obtain gradient value, using G (x) to replace G (x, y, z) to represent gradient of different positions in medium, using G max Representing the maximum gradient;
step 5.2, assuming uniform medium, sampling scattering points by the method of sampling uniform medium in step 4, the scattering points being used toThe probability acceptance of (2) is true, indicating that scattering occurs at x, otherwise, indicating that no scattering occurs, and that the ray is traveling along a straight line; wherein sigma max Represents the maximum extinction coefficient, delta represents the specific gravity constant, the value range is zero to positive infinity, and the larger the delta isThe more the item approaches 1,/>Representing a gradient specific gravity term; the original woodcock Tracking sampling algorithm is improved, gradient parameters G (x) and constant delta are introduced, so that the sampling distribution is more reasonable, and the sampling algorithm is as follows:
firstly, setting the maximum sampling distance as d max Let the current sampling distanceWherein the random number rand () ∈0, 1) when the sampling distance d is greater than the maximum sampling distance d max Or the random number rand () is smaller than +.>When the sampling is performed, the sampling distance is returned; otherwise, the light ray does not scatter, the light ray advances along a straight line, and the sampling distance d is increased by +.>Again judging whether the sampling distance is greater than the maximum sampling distance d max Or whether the random number rand () is smaller than +.>And the like, until the circulation condition is not met, the circulation is finished, and the sampling distance is returned.
Step 6, color synthesis, wherein a gradient proportion term is added to the original woodcock Tracking sampling algorithm, so that the unbiasedness of the algorithm is ensured, and a weight coefficient omega is introduced when the color is synthesized i ，Final synthetic colour-> wherein ci Represents a certain sample point color value and N represents the total number of sample points.
FIG. 3 is a graph of a three-dimensional rendering effect of the lung before modification with a PSNR of 25.31dB; fig. 4 shows the rendering effect after the method of the present invention is adopted, the PSNR is 36.75dB, and it can be seen from the figure that the noise is less in the high frequency region with severe image variation after the method is used, and the rendering effect is better.
Claims (2)
1. A ray tracing volume rendering method based on gradient sampling, comprising the steps of:
step 1, acquiring a medical image sequence from the Internet or a hospital, and using a computer tomography image;
step 2, selecting 300 frames of continuous tomographic images with the size of 512 x 512 to form volume data;
and 3, drawing the volume data by adopting a Monte Carlo ray tracing method, wherein a rendering equation is as follows:
wherein ,represents the x position along +.>Radiation brightness emitted from direction, < >>Represents x s Along->Emergent radiation brightness->Represents x t Along->The incident radiance, s, is the depth in the medium; sigma (sigma) s (x t ) Represents x t Scattering coefficient at>Representing x to x t The transmission coefficient between them describesAttenuation of light passing through a medium, where T r The values of (2) are:
σ t represents the extinction coefficient, which is the scattering coefficient sigma s And absorption coefficient sigma α Sum, i.e. sigma t ＝σ s +σ α The method comprises the steps of carrying out a first treatment on the surface of the Sigma in homogeneous medium t Is constant at this timex and x' represent different positions in the medium;
step 4, adopting woodcock Tracking gradient sampling to sample light rays, and solving a rendering equation by using a Monte Carlo method;
step 5, calculating the gradient of the volume data by a three-dimensional Sobel operator in a non-uniform medium, and calculating the acceptance probability of the light sampling points; the three-dimensional Sobel operator is adopted, the gradient is calculated by using 26 neighborhood voxels, the partial derivative of each direction is calculated by using a 3X 3 template, and the templates in the x, y and z directions are respectively:
after calculating the partial derivatives in each direction, the formula is:
calculating to obtain gradient value, using G (x) to replace G (x, y, z) to represent gradient of different positions in medium, using G max Representing the maximum gradient;
firstly, assuming that the medium is uniform, sampling scattering points by a method for sampling the uniform medium in the same step 4The probability acceptance of (2) is true, indicating that scattering occurs at x, otherwise, indicating that no scattering occurs, and that the ray is traveling along a straight line; wherein sigma max Represents the maximum extinction coefficient, delta represents the specific gravity constant, the value range of the specific gravity constant is zero to positive infinity, and the greater delta is +.>The more the item approaches 1,/>Representing a gradient specific gravity term; the original woodcock Tracking sampling algorithm is improved, gradient parameters G (x) and constant delta are introduced, so that the sampling distribution is more reasonable, and the sampling algorithm is as follows:
firstly, setting the maximum sampling distance as d max Let the current sampling distanceWherein the random number rand () ∈0, 1) when the sampling distance d is greater than the maximum sampling distance d max Or the random number rand () is smaller than +.>When the sampling is performed, the sampling distance is returned; otherwise, it indicates that there is no issueThe light goes straight along the scattering, and the sampling distance d increases +.>Again judging whether the sampling distance is greater than the maximum sampling distance d max Or whether the random number rand () is smaller than +.>And the like, until the circulation condition is not met, the circulation is finished, and the sampling distance is returned;
step 6, color synthesis, wherein a gradient proportion term is added to the original woodcock Tracking sampling algorithm, so that the unbiasedness of the algorithm is ensured, and a weight coefficient omega is introduced when the color is synthesized i ，Final synthetic colour-> wherein ci Represents a certain sample point color value and N represents the total number of sample points.
2. The gradient sampling-based ray tracing volume rendering method of claim 1, wherein the implementation of step 4 is as follows,
step 4.1, in the uniform medium, calculating a rendering equation by using a Monte Carlo methodItem equal to->Namely, calculating:
wherein, tfact is t j Omitting a subscript j to avoid complex formulas caused by multi-stage subscripts, and representing the distance from a j-th sampling point to the light ray starting point;
step 4.2, orderThen->Its inverse function:
step 4.3, giving a uniform random number r E [0, 1), and the value of the sampling point t is
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