CN110801203A - Human cranial nerve fiber tracking method based on local features - Google Patents

Human cranial nerve fiber tracking method based on local features Download PDF

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CN110801203A
CN110801203A CN201911043684.2A CN201911043684A CN110801203A CN 110801203 A CN110801203 A CN 110801203A CN 201911043684 A CN201911043684 A CN 201911043684A CN 110801203 A CN110801203 A CN 110801203A
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毕重科
朱林
李欣昕
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Abstract

The invention discloses a human brain nerve fiber tracking method based on local features, which is used for solving the problem that the periphery of a singular point cannot be correctly tracked in the human brain nerve fiber tracking process. The method mainly comprises the following steps: the method comprises the following steps of firstly, finding all grids with singular points from a human brain tensor field by using a singular point positioning method; step two, judging whether the midpoint of the grid falls on four quadrant angle bisectors or the center, if so, removing the side corresponding to the tensor with smaller anisotropy during the interpolation of the feature vector, and otherwise, removing the side with the farthest distance; thirdly, tensor field interpolation is carried out, the characteristic value of the midpoint of the grid is calculated by utilizing a scalar bilinear interpolation method, and the characteristic vector of the midpoint of the grid is calculated by utilizing tensor interpolation; and step four, rendering an interpolation result. The human brain nerve fiber tracking method can accurately find singular points in the human brain tensor field and overcome the problem of inaccurate tracking around the singular points, thereby improving the tracking accuracy.

Description

Human cranial nerve fiber tracking method based on local features
Technical Field
The invention relates to the technical field of human cranial nerve fiber tracking, in particular to a method for solving the problem that the periphery of a singular point cannot be correctly tracked in the human cranial nerve fiber tracking process.
Background
There are many nerve fibers in the human brain, and these intricate neurons are interwoven together to form a network. The network of neurons controls different levels of consciousness, movement, sleep, etc., for example, the human brain coordinates our perception, thinking and movement through its neuronal activity. Therefore, the tracking of the human brain nerve fibers can help human brain researchers draw detailed human brain nerve circuit diagrams, and further promotes the cognition of neuroscientists on the human brain. However, the human brain nerve fiber tracking is not ideal because of the large quantity, complexity and randomness of movement of the human brain nerve fiber.
At present, the tracking of human cranial nerve fibers mainly adopts methods such as electric probes, chemical reagents, genetic modification, tensor field interpolation and the like. Mathematically, the human brain can be represented as a diffusion tensor field, and the neurons are tensors in the tensor field, so that the tracking of the human brain nerve fibers is the tracking of flow lines in the tensor field. In general, a motion trajectory can be accurately tracked by a tensor field interpolation method, but when there is a tensor point (singular point) where the anisotropy is zero, the brownian motion has almost no direction around the singular point. It is difficult for the prior art to accurately track around singular points.
Therefore, there is a need for a method for neuroscientists to accurately find singular points in the human brain tensor field and to overcome the problem of inaccurate tracking around the singular points.
Disclosure of Invention
Aiming at the prior art, the invention provides a human cranial nerve fiber tracking method based on local characteristics, which solves the problem that the periphery of a singular point cannot be accurately tracked in the prior human cranial nerve fiber tracking technology.
In order to solve the technical problem, the invention provides a human cranial nerve fiber tracking method based on local features, which comprises the following steps:
the method comprises the following steps of firstly, finding all grids with singular points from a human brain tensor field by using a singular point positioning method;
step two, judging whether singular points in the grid are located on four quadrant angle bisectors or centers, if so, removing the edges corresponding to the smaller tensor of the anisotropic FA during the interpolation of the eigenvector, and otherwise, removing the edges with the farthest distance;
thirdly, tensor field interpolation, namely calculating an eigenvalue lambda of an interpolation point in the grid by using a scalar bilinear interpolation method, and calculating an eigenvector e of the interpolation point in the grid by using tensor interpolation;
and step four, rendering an interpolation result.
Further, in the first step of the method of the present invention, the singular point positioning method comprises the following steps:
the method comprises the steps of firstly determining the main direction of four vertexes of a grid, determining the eigenvector corresponding to the maximum eigenvalue as the tensor main direction, then judging whether cos α of the tensor rotation angle of any two adjacent vertexes is smaller than zero, and finally calculating the number n of cos α smaller than zero, wherein if n is an odd number, singular points exist in the grid, otherwise, singular points do not exist.
In step two of the method of the present invention, the expression of the anisotropy FA is as follows:
Figure BDA0002253544300000021
wherein the content of the first and second substances,
Figure BDA0002253544300000022
λ1，λ2，λ3is the eigenvalue of the matrix.
In the third step of the method of the present invention, the eigenvalue λ of the interpolation point in the grid is expressed as follows:
Figure BDA0002253544300000023
wherein the content of the first and second substances,
Figure BDA0002253544300000024
andis R1And R2Eigenvalues of the two tensor points.
In the third step of the method of the invention, the feature vector e of the interpolation point in the grid is expressed as follows:
wherein the coefficient SyIs composed of
Figure BDA0002253544300000027
Figure BDA0002253544300000028
Are each R1And R2The feature vectors of the two points are,
Figure BDA0002253544300000029
is a rotation matrix.
Compared with the prior art, the invention has the beneficial effects that:
first, the present invention provides a singular point locating method in step one, by which all grids with singular points can be accurately found in the human brain tensor field.
Secondly, the invention provides a method for eliminating the interference of singular points in the tensor field to the tracking in the step two, and the problem that the singular points can not be accurately tracked around is solved.
Thirdly, during the interpolation of the tensor field in the third step, the eigenvalue and the eigenvector are respectively interpolated, and as a result, the anisotropy of the tensor field is kept as much as possible.
In conclusion, the invention provides a method for solving the problem that the periphery of a singular point cannot be correctly tracked in the process of tracking the human cranial nerve fibers. The method improves the accuracy of tracking the human cranial nerve fibers and further promotes the cognition of human cranial nerve circuits by human cranial researchers.
Drawings
FIG. 1 is a flow chart of the human cranial nerve fiber tracking method based on local features according to the present invention.
FIG. 2 is a schematic diagram of locating singular points in the present invention.
Figure 3 is a schematic diagram of tensor field interpolation in the present invention.
FIG. 4 is a partial code diagram of eigenvalue interpolation in the present invention.
FIG. 5 is a partial code diagram of feature vector interpolation in the present invention.
FIG. 6 is a diagram of the present invention in which a point falls on a first bisector of the quadrant angle, and the left part of the code is removed by comparing the anisotropy magnitudes of the corresponding two vertex tensors.
FIG. 7 is a graph showing the tracking effect of the present invention in the vicinity of the triple singular point.
FIG. 8 is a graph showing the tracking effect of the present invention in the vicinity of the wedge singularity.
Detailed Description
The invention will be further described with reference to the following figures and specific examples, which are not intended to limit the invention in any way.
The invention provides a human brain nerve fiber tracking method based on local features, which mainly comprises the following steps: finding all grids with singular points from a human brain tensor field by using a singular point positioning method; judging whether singular points in the grid fall on four quadrant angle bisectors or centers, if so, removing the side corresponding to the smaller tensor of the anisotropy FA during the interpolation of the eigenvector, and otherwise, removing the side with the farthest distance; tensor field interpolation, namely calculating an eigenvalue lambda of an interpolation point in a grid by utilizing a scalar bilinear interpolation method, and calculating an eigenvector e of the interpolation point in the grid by utilizing tensor interpolation; and rendering an interpolation result, accurately tracking the nerve fibers near the singular point in the human brain tensor field, and simultaneously distributing the nerve fibers around the singular point in a uniform and accurate distribution mode.
As shown in fig. 1, the specific process is as follows:
step 101, finding all grids with singular points from a human brain volume field by using a singular point positioning method;
in data representation, a singular point is a tensor with zero anisotropy, which has two or more equal eigenvalues. For one tensor, the eigenvector e generally represents the direction of the tensor, and its magnitude is represented by the eigenvalue λ, so the eigenvector corresponding to the largest eigenvalue is the principal direction of the tensor. Since brownian motion has almost no direction of motion around a singular point, it is difficult to accurately track around the singular point.
The singular point positioning method comprises the following steps of firstly determining the principal direction of four vertexes of a grid, wherein an eigenvector corresponding to the maximum eigenvalue is the principal direction of a tensor, then judging whether cos α of the tensor rotation angle of any two adjacent vertexes is smaller than zero, finally calculating the number n of cos α smaller than zero, if n is an odd number, singular points exist in the grid, and if not, no singular points exist.
FIG. 2 is a diagram illustrating singular point positioning in the present invention, wherein four vertices of each rectangle are four tensor samples, and the directions of arrows are principal directions of tensors, and cos α of principal direction rotation angles of two vertex tensors corresponding to thick edges in the diagram is less than zero.
Step 102, judging whether singular points in the grid are located on four quadrant angle bisectors or centers, if so, executing step 103, and removing edges corresponding to the smaller anisotropy FA tensor during feature vector interpolation; otherwise, step 104 is performed to remove the edge farthest away.
Anisotropy is an important indicator of the study of the tensor field. At present, various anisotropy calculation methods exist, such as anisotropy index, fractional anisotropy, relative anisotropy and volume fraction, etc., however, the present invention calculates tensor anisotropy using the fractional anisotropy calculation method. The calculation formula of the anisotropy FA, i.e.
Figure BDA0002253544300000041
Wherein the content of the first and second substances,
Figure BDA0002253544300000042
λ1，λ2，λ3is the eigenvalue of the matrix.
There is a subtle difference in the comparison of anisotropy when the tensor points in the grid fall on the four quadrant bisector and center. When the tensor point falls on the four-quadrant angular bisector, comparing the anisotropy of the tensors corresponding to the two vertexes; when the tensor point falls on the center, the sum of the two tensor anisotropies for each edge should be calculated and then the magnitudes are compared. FIG. 6 is a partial code diagram of the invention with dots falling on the first quadrant bisector and the left removed by comparing the magnitude of anisotropy.
And 105, carrying out tensor field interpolation, calculating an eigenvalue lambda of an interpolation point in the grid by using a scalar bilinear interpolation method, and calculating an eigenvector e of the interpolation point in the grid by using tensor interpolation.
In order to preserve anisotropy of the tensor field as much as possible, the tensor field interpolation separates eigenvalues and eigenvectors, and calculates by a scalar bilinear interpolation method as shown in fig. 4 and a tensor interpolation method as shown in fig. 5, respectively. The eigenvalues λ of the interpolation points, R as shown in FIG. 31And R2Are two dots, R1Characteristic value of point
Figure BDA0002253544300000043
Namely, it is
Figure BDA0002253544300000044
Then R2Characteristic value of point
Figure BDA0002253544300000045
Namely, it is
Figure BDA0002253544300000046
The characteristic value λ of the point P, i.e.
The feature vector of the interpolation point is e. As shown in FIG. 3, first R1Feature vector of pointsNamely, it is
Then R2Feature vector of points
Figure BDA0002253544300000052
Namely, it is
Figure BDA0002253544300000053
Then the feature vector e of point P, i.e.
Figure BDA0002253544300000054
Wherein
Figure BDA0002253544300000055
For a rotation matrix, coefficient SxAnd SyAre respectively as
Figure BDA0002253544300000056
Figure BDA0002253544300000057
And step 106, rendering an interpolation result.
Two types of singular points mainly exist in a human brain tensor field, which are a trisection (Trisector) and a wedge (wedge), respectively, and the streamline is difficult to accurately track near the two types of singular points by using a plurality of existing tracking technologies, and the tracking results always have the problems of infinite closeness, intersection and the like. To verify the effectiveness of our proposed local feature-based human cranial nerve fiber tracking method, we chose to track around these two singular points separately. Fig. 7 and 8 are graphs of the tracking effect in the vicinity of the triple point and the wedge singularity, respectively. The points circled by the boxes in the figure are seed points, i.e. the starting points of the tracing of each streamline. Obviously, the streamline traced by each seed point is uniformly distributed near the singular point, and the problems of infinite proximity, intersection and the like do not occur.
While the present invention has been described with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments, which are illustrative only and not restrictive, and various modifications which do not depart from the spirit of the present invention and which are intended to be covered by the claims of the present invention may be made by those skilled in the art.

Claims (5)

1. A human brain nerve fiber tracking method based on local features is characterized by comprising the following steps:
the method comprises the following steps of firstly, finding all grids with singular points from a human brain tensor field by using a singular point positioning method;
step two, judging whether singular points in the grid are located on four quadrant angle bisectors or centers, if so, removing the edges corresponding to the smaller tensor of the anisotropic FA during the interpolation of the eigenvector, and otherwise, removing the edges with the farthest distance;
thirdly, tensor field interpolation, namely calculating an eigenvalue lambda of an interpolation point in the grid by using a scalar bilinear interpolation method, and calculating an eigenvector e of the interpolation point in the grid by using tensor interpolation;
and step four, rendering an interpolation result.
2. The method for tracking human cranial nerve fibers based on local features of claim 1, wherein in the first step, the singular point locating method comprises the following steps:
the method comprises the steps of firstly determining the main direction of four vertexes of a grid, determining the eigenvector corresponding to the maximum eigenvalue as the tensor main direction, then judging whether cos α of the tensor rotation angle of any two adjacent vertexes is smaller than zero, and finally calculating the number n of cos α smaller than zero, wherein if n is an odd number, singular points exist in the grid, otherwise, singular points do not exist.
3. The method for tracking human cranial nerve fibers according to claim 1, wherein in the second step, the expression of anisotropy (FA) is as follows:
Figure FDA0002253544290000011
wherein the content of the first and second substances,
Figure FDA0002253544290000012
λ1，λ2，λ3is the eigenvalue of the matrix.
4. The method for tracking human brain nerve fibers based on local features according to claim 1, wherein in the third step, the feature value λ of the interpolation points in the grid is expressed as follows:
Figure FDA0002253544290000013
wherein the content of the first and second substances,
Figure FDA0002253544290000014
and
Figure FDA0002253544290000015
are each R1And R2Eigenvalues of the two tensor points.
5. The method for tracking human brain nerve fibers based on local features according to claim 1, wherein in the third step, the feature vector e of the interpolation points in the grid is represented as follows:
Figure FDA0002253544290000016
wherein the coefficient SyIs composed of
Figure FDA0002253544290000021
Figure FDA0002253544290000022
Are each R1And R2The feature vectors of the two points are,is a rotation matrix.
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