Characteristics of a good academic paper
Taking the medical academic paper as an example, a good medical paper has the following characteristics: A good medical SCI paper is born, both a good selection of topics, good design, and specific implementation and serious summary, the author must grasp each link, to be serious, rigorous and strict. Some people temporarily want to write a paper, usually there is no topic selection, no design, no material, not to mention the accumulation, how can you temporarily write a paper? Therefore, medical SCI paper writing must pay attention to accumulation!
According to the medical paper source classification:
Divided into two categories of original (including thesis, treatise and short report) and edited (including textbooks, reference books, monographs, literature, reviews, lectures, special talks, symposiums, etc.);
According to the purpose of the paper writing classification: academic papers and dissertations;
According to the nature of the medical disciplines and subjects The four categories are: basic medicine, clinical medicine, preventive medicine, rehabilitation medicine, etc.
According to the research content of the dissertation is divided into: experimental research paper, survey research paper, experimental research paper, data analysis paper, experience paper five categories;
According to the genre of the dissertation is divided into: dissertation, literature, synthesis, review, lectures, technology and methodology, case reports, and medical popularization of the paper etc. Therefore, the authors must choose the form of expression of the paper according to the content of their own research work and research materials.
Every experiment or clinical observation should be closely planned and followed. In the application of strict operation and related procedures, not to mention the arbitrary change of their own research design and argumentation. Experts often see many authors writing articles, often used, may, probably, estimated, or data without statistics said that there is a clear effect, these words are not rigorous.
Academic papers on medicine
Application of algorithms in three-dimensional reconstruction of medical images
Abstract:
The technology of three-dimensional reconstruction of medical images can be traced back to the early 1970s. Due to objective reasons such as the expensive price of medical imaging equipment that integrates the 3D reconstruction platform, the domestic medical image 3D visualization and diagnosis started late, and it was only in the 1990s that certain colleges and universities began to carry out research at all levels [1]. With the development of computer technology, in just a few years, three-dimensional reconstruction technology has become an important means of exploring the mysteries of life, as well as disease diagnosis, surgical planning.
1 Common medical three-dimensional reconstruction material
Electronic computed tomographyComputed tomography, CT for short, is a novel new diagnostic technology that combines electronic computers and X-rays. Its main feature is that it has a high density resolution, which is 10 to 20 times higher than that of ordinary X-ray photographs [2].CT can accurately measure the small differences in radiation attenuation characteristics between different tissues in a certain plane and display them as digital images, which can distinguish the different densities of various soft tissues in extremely fine detail and thus form a contrast. For example, cranial radiographs cannot distinguish between brain tissue and cerebrospinal fluid, but CT can not only show the ventricular system, but also distinguish the gray matter and white matter of the brain parenchyma.CT, if the contrast agent is introduced to enhance the contrast, the resolution is even higher, which can broaden the diagnostic scope of the disease, and improve the diagnosis of the correct rate.
Magnetic Resonance Imaging (MRI) is a type of tomography that uses the phenomenon of magnetic resonance to obtain electromagnetic signals from the human body and reconstruct information about the body. 1946 saw the independent discovery of MRI by Flelix Bloch of Stanford University and Edward Purcell of Harvard. In 1946, Flelix Bloch of Stanford University and Edward Purcell of Harvard University independently discovered the phenomenon of magnetic **** vibration, and in 1972 Paul Lauterbur developed a method of spatial encoding of magnetic **** vibration signals, which can reconstruct images of the human body. Magnetic **** vibration imaging has some **** in common with other tomographic techniques, for example, they can show the distribution of certain physical quantities (e.g., density) in space. At the same time, magnetic **** vibration imaging also has its own characteristics, can get any direction of the tomographic image, three-dimensional body image, and even can get the space? Four-dimensional image of the spectral distribution.
At present, the three-dimensional reconstruction of medical images are mainly surface drawing, body drawing, as well as by the object surface of the two-dimensional grayscale image reconstruction of its three-dimensional geometric shape method, or known as the dark and light to restore the shape of the method and so on.
2 Marching Cubes Algorithm Fundamentals
The Marching Cubes [3] algorithm for moving cubes is a method for constructing equivalent surfaces proposed by Lorensen et al. in 1987, which has been in use until now, and it is a representative of the technique of extraction of equivalent surfaces within the voxel cell [4]. An isosurface is defined as the set of all points in a mesh space consisting of all points with a sampling value equal to a given value. The essence of the algorithm is to view a series of two-dimensional sliced data as a three-dimensional data field, from which material with a certain domain value is extracted and connected into triangular facets in some topological form.
An isosurface is the set of all voxel points in space that have some identical value, and the values of the voxel points are taken as the result of trilinear interpolation of eight points from V0 to V7 in the voxel region. It can be expressed as follows: c is a constant. f(f) is the equivalent surface in the voxel data f. The calculation formula can be expressed as:
(1)
Where ?0,?1,? ,?7 are constants determined by the values of the eight fixed points V0~V7.
In the MC algorithm, it is assumed that the original data is a discrete three-dimensional spatial regular data field as shown in Figure 1. Images produced by tomography (CT) and magnetic **** vibration imaging (MRI), which are used for medical diagnostics, fall into this category.
The basic idea of the MC algorithm is to process the voxels in the data field one by one, as shown in Figure 2, classify the voxels that intersect with the isosurfaces, and use interpolation to calculate the intersections of the isosurfaces with the prisms of the voxels (V0~V7). According to the relative position of each vertex in the voxel to the isosurface, the intersection points of the isosurface and the cube edges are connected in a certain way to generate the isosurface, which serves as an approximation representation of the isosurface within that cube. After calculating the relevant parameters about the isosurfaces within the body data field, the isosurfaces are drawn using the surface drawing function provided by commonly used graphics software packages or hardware [5].
Isosurfaces are generally drawn using a binarization method, where the value of the point (0 or 1) is determined by comparing it to a given threshold value, with a vertex density value < 1 for a domain value Outside, and 0 for a vertex density value ? domain value Inside is 0. Each vertex of V0~V7 has 2 states Outside and Inside, so there are 256 combinatorial states for 8 vertices***, and 15 triangular configurations based on complementary symmetry as well as rotational symmetry***. When searching according to the index during reconstruction, each index is divided into three parts: index, rotation, and triangular model.The main process of Marching Cubes algorithm is as follows:
(1) Read the three-dimensional discrete regular data field into memory hierarchically.
(2) Scan the two layers of data and construct voxels one by one, 8 corner points in each voxel are taken from two adjacent layers; the 8 fixed points can be defined as (i, j, k), (i+1, j, k), (i+1, j+1, k), (i+1, j, k+1 ), (i+1, j+1, k+1 ), (i, j+1, k+1 ), (i, j+1, k+ 1), (i, j+1, k), (i, j , k+1) (as shown in Figure 3).
(3) Compare the function value of each corner point of the voxel with the given equivalent face value c, and construct a state table for the voxel based on the comparison.
(4) Based on the state table, derive the boundary voxel that will have an intersection with the equivalent surface.
(5) Calculate the intersection of the voxel's prismatic edges with the equivariant surface by linear interpolation.
(6) Using the center difference method, find the normal vector at each corner point of the voxel, and then by linear interpolation, find the normal at each vertex of the triangular face piece.
(7) Draw the isosurface image based on the coordinates and normal vectors of each vertex on each triangular surface piece.
3 Judgment of space equivalence points and the intersection of the equivalence surface and the boundary of the voxel
Take a discrete mesh prism, set the two nodes on the prism as Mi (xi, yi, zi, qi) and Mj (xj, yj, zj, qj); take the equivalence of the quantum value of the value of the C, when the satisfaction of the (q-c)(q-c) ?0 (the equivalence of the point of the determination of the conditional equation) then Mi and Mj Take the equivalence point Mo between the two points, and set the coordinates of the equivalence point Mo as (xo, yo, zo), and the formula (2) can be obtained from the two points of Mi and Mj according to the linear interpolation:
(2)
In the formula, k=(qi-c)(qj-c)?0. According to the equivalence surface judgment condition formula (1) and the formula of the equivalence point coordinate formula (2), it can be searched and judged according to the structural discretization information for the mesh prongs, and thereby Find all the equivalent points of the structure in the specified domain. After the equivalence points are found, they can be connected into triangles or polygons to form part of the equivalence surface.
4 Calculating the normal vector of an isosurface
In order to display an isosurface image using the graphics hardware, the normal vector of the isosurface of a triangular slice must be given, and an appropriate lighting model must be chosen for rendering to produce a realistic image. For each point on the isosurface, its gradient component along the tangent direction of the surface should be zero, so the direction of the gradient vector along that point also represents the normal direction of the isosurface at that point. Equivalent faces are often manifolds with different densities of matter, and thus their gradient vector values are not zero, i.e., Equation (3):
(3)
It is time-consuming to compute the normals of the triangular facets directly, and in order to eliminate discontinuous variations in lightness and darkness between the triangular facets, it is sufficient to give the normal at each vertex of the triangular facet and to plot each triangular facet using Gouraud's model. Here we use the center interpolation method to calculate the gradient at each corner point of each voxel. In the case of triangles, the normal vector of each triangular face piece is calculated, then the normal vector of each vertex is obtained using the normal vector of the triangular face, and finally the normal vector of a point on the triangular face is obtained by interpolating the three normal vectors of the three vertices of the triangle. There are simple ways to compute the normal vectors of the vertices for the isosurfaces. Considering that the direction of the gradient of an isosurface is perpendicular to the tangent line of the isosurface, the perpendicular line of the isosurface can be replaced by the gradient vector. In the three-dimensional case, the gradient direction of the contour plane is the normal direction of the contour plane. As a result, Equation (4) can be obtained:
(4)
5 Optimization of Marching Cubes - Mesh Model Simplification Algorithms
A series of results have been achieved for mesh model simplification algorithms. Most of the current simplification algorithms consider the change in the geometric position of the model before and after edge folding as the cost of folding, thus reducing the number of polygons to achieve the goal of improving computational efficiency. The purpose of the grid simplification algorithm is to improve the efficiency under the premise of guaranteeing the image accuracy as much as possible. Therefore, the principle of selecting the coordinate points is as close as possible to the original grid, generally there are two subset selection method and optimization selection method [6] subset selection method that is, simply choose the one with smaller cost among the two endpoints of the edge, and the optimization selection method is to select the point v with the smallest quadratic error as the folding point, which corresponds to the quadratic error measure is, while the quadratic error of the point v is the quadratic equation, and to find the minimum of it is to find the minimum of the The point at which the equation has zero partial derivation with respect to x, y, and z. The x, y, and z solved are the new vertex coordinates. This process is equivalent to solving the matrix equation of equation (5).
(5)
Measure of the cost of folding
The calculation of the cost of folding is divided into two steps. The first step: when calculating the quadratic error sidelobe of each vertex, the mean value of the quadratic error measure of each vertex is calculated based on Garland's standard quadratic error measure, while taking into account the influence of the area of the surrounding triangles; the second step: when calculating the cost of folding an edge, the length of the edge and the degree of change in the triangle morphology induced by the folding of the edge are used as the weighting factors.
The specific calculation method is as follows: in three-dimensional space, the plane P can be expressed as ax + by + cz + d = 0, can also be expressed as PTv = 0. Where P = [a, b, c]T is the unit normal vector of the plane P, and there, d is a constant. The square of the distance from any point v=[x, y, z, 1]T in the model space to that plane is the equation (6):
(6)
The quadratic error of any point v=[x, y, z, 1]T in the lattice model ? (v) is defined as the sum of squares from that vertex to the planes associated with that fixed point, which can be expressed as equation (7):
(7)
where planes(v) denotes a set consisting of all triangular planes containing the fixed point v, called the set of planes associated with the vertex v. The quadratic error of each point in the mesh model in the initial state is 0. Equation (8) can be obtained after deformation of the above equation.
(8)
where kp is the quadratic error measure of the plane P.
(9)
It is called the quadratic matrix of v=[x, y, z, 1]T.
Called the quadratic error of point v. When edge folding is performed, an additional rule (Garland et al., 1987) can be used to obtain the quadratic error measure at point v. The value of the quadratic error at that vertex is, that is, the cost of folding that edge.
6 Mesh Simplification Algorithms for Medical 3D Reconstruction
Mesh algorithms are generally applied to speed up 3D reconstruction, but mesh-only algorithms lack practical value. The loss of accuracy is unacceptable compared to its high speed of plotting. Therefore, the mesh simplification algorithm is further optimized? A mesh simplification algorithm based on body drawing.
Body mapping is the process of displaying all the substances (skin, bones, muscles, etc.) in a slice in one image. However, a lot of triangulated surface drawing is pointless in cases where only the bones need to be viewed. Ignoring those unnecessary triangles can effectively increase the speed of reconstruction while maintaining accuracy.
7 Conclusion
The MC algorithm, which determines the polygons of voxels by comparing the thresholds, often has the unavoidable disadvantage of being slow in the face of large volumes of data, but now various targeted improvements have given it greater potential for development, so that the MC algorithm is not just a mere algorithm, it is closer to ? Voxel? It is closer to the concept of "voxel". Many of the popular 3D reconstruction algorithms are based on MC and are modified in order to obtain the specific 3D model needed. Algorithms such as wavelet transform based medical image fusion algorithms, tomographic medical image interpolation algorithms, etc. are mainly designed to make data such as CT easily segmented by thresholds in MC algorithms. Now, the use of OpenGL, VTK and other image function libraries has made 3D image modeling easy to expect the application of 3D reconstruction technology in medicine will have greater development.
References:
[1] Pu Chao,Zhang Yumin. Algorithm and application of three-dimensional processing of medical images[J]. Military Automation,2004.6:210~212
[2] Luo Shuqian,Zhou Gohong,Shi Jiaoying. Simplified modeling of polyhedra based on triangle removal criterion[J]. Journal of Computing,2008.2:135~138
[3] Nielson GM.Dual Marching Cubes.IEEE Visualization 2004.
[4] Tian J, Bao Shanglian, Zhou Mingquan. Medical Image Processing and Analysis[M]. Electronic Industry Press 2003.
[5] Jin Tianhong,Liu Zhenzhai. Research on three-dimensional reconstruction of medical images[J]. Medical and Health Equipment,2008.2:34
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