CN111968236A - K-D tree method-based contraposition to line fracture reduction system - Google Patents
K-D tree method-based contraposition to line fracture reduction system Download PDFInfo
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Abstract
The invention discloses a K-D tree method-based alignment and alignment fracture reduction system, which combines medical science and computer technology to perform alignment and alignment iterative splicing on fracture fragments, restore the native anatomical structure of limbs and complete the primary steps of treating fracture. The system comprises a fracture fragment three-dimensional geometric modeling module, a fracture fragment information extraction module, a fracture fragment position determining and adjusting module, a registration splicing module and a display module. Obtaining the correct position before fracture reduction through a fracture fragment information extraction module and a fracture fragment position determining and adjusting module; judging whether the fragment matching degree meets the requirement or not according to the result of the matching and splicing module; and obtaining the effect after splicing the fragments through the display module. The invention guides doctors to complete the fracture fragment reduction operation, reduces the operation risk and time consumption, avoids the interference of human factors, is not limited by time, can repeatedly carry out simulation exercise, and provides technical reference for formulating the fracture reduction operation scheme.
Description
Technical Field
The invention belongs to the field of biomedical engineering, and particularly relates to a K-D tree method-based contraposition alignment fracture reduction system.
Background
Bones are the mechanism connecting the whole limbs of the human body, and after fracture, local swelling, bone exposure, bleeding, infection, deformity and obvious pain symptoms occur. After the fracture of most patients occurs, the daily life is influenced, and the psychology of the patients is also harmed. Despite the consistent interest in research relating to fracture reduction, there are various reasons why fracture reduction may not be well-established.
The fracture reduction process mainly comprises the following steps: the position of the fracture fragment is adjusted, the bone length is recovered, the anatomical structure of the bone is restored to the original geometric form, the fracture restoration result is not good, the later fracture healing process is influenced, and therefore limb deformation and abnormal growth can be caused.
Research on fracture reduction has been ongoing, and at present, fracture reduction for treating fracture fragments mainly depends on the alignment splicing performed by the clinical experience of doctors, reduces the displacement between the fracture fragments, increases the distance between fracture surfaces of the fracture fragments, but still has many disadvantages and shortcomings:
1. only by the clinical experience of doctors, the fracture reduction operation time is long, and no more accurate fracture reduction method exists;
2. the fracture reduction is only carried out with contraposition splicing, and the study on line splicing is not carried out, thus not meeting the medical standard on the fracture reduction;
3. the fracture reduction process is complex, and the condition that one-to-many and false splicing exist in the splicing of fracture fragments is not considered.
Disclosure of Invention
The invention aims to provide a K-D tree method-based alignment-alignment fracture reduction system which is used for predicting a complex fracture reduction process so as to obtain an optimal fracture reduction operation planning scheme.
The purpose of the invention is realized by the following technical scheme: a system for contraposition and alignment fracture reduction based on a K-D tree method is characterized by comprising a fracture fragment three-dimensional geometric modeling module, a fracture fragment information extraction module, a fracture fragment position determining and adjusting module, a matching and splicing module and a display module;
the fracture fragment three-dimensional geometric modeling module is used for importing two-dimensional tomographic image data obtained by CT medical scanning into medical image processing software in a DICOM format, and establishing a three-dimensional grid geometric model representing fracture fragments after a series of image processing so as to provide a useful model for fracture reduction;
the fracture fragment information extraction module is used for extracting the geometrical information such as points, lines, surfaces and the like which can represent femoral fractures and are required by fracture reduction from the obtained fracture fragment three-dimensional grid geometrical model, and establishing an information structure body of the femoral fracture fragments to provide useful fracture fragment information for fracture reduction;
the fracture fragment position determining and adjusting module is used for positioning and evaluating the displaced femoral fracture fragments to provide accurate positions for fracture reduction;
the matching and splicing module is used for aligning femoral fracture fragments, and restoring the fracture fragments to the original anatomical structure position by finding and determining the corresponding relation between different fracture fragments, so that the fracture reduction stability is ensured;
the display module is used for observing and displaying the comminuted fracture alignment and line reduction effect and realizing the interactivity between a user and the fracture reduction system;
compared with the prior art, the invention has the beneficial effects that:
1. the K-D tree method-based alignment and alignment fracture reduction system is developed on the basis of a dialog box form under a Windows platform, the simulation of the fracture reduction process is realized through autonomous programming, the system is simple and easy to operate, and the system flow can be rapidly mastered in a short time;
2. the pair wires are spliced and added into a fracture reduction simulation system, so that the fracture reduction process can be reflected more truly, the fracture reduction result meets the medical clinical actual condition, and the splicing result is more accurate;
3. the fracture reduction process is divided into primary splicing and accurate splicing, compared with a primary splicing process, false splicing can be deleted in the primary splicing process, and the condition that fracture fragments are one-to-many before accurate splicing is avoided;
4. by constructing the fracture reduction simulation method, guidance can be provided for a doctor to designate an optimal operation scheme, so that the operation success rate is improved, the fracture reduction quality is improved, and the condition of fracture reduction deformity is reduced;
5. by constructing the fracture reduction simulation method, repeated experiments can be carried out on the established simulation model for many times, so that real biological experiments are reduced, time and resources are saved, efficiency is improved, and humanitarian disputes are avoided.
In summary, the simulation method of the present invention overcomes the disadvantages and shortcomings of the prior art.
Drawings
FIG. 1 is a schematic diagram showing the relationship between modules of the fracture reduction simulation system of the present invention;
FIG. 2 is a flow chart of a three-dimensional geometric modeling module for establishing fracture fragments;
FIG. 3 is a flow chart of a module for establishing and extracting fracture fragment information;
FIG. 4 is a flow chart of a module for establishing the determination and adjustment of the fracture fragment position;
FIG. 5 is a flow chart of building a matched tiling module;
FIG. 6 is a flow chart for establishing a preliminary splice;
FIG. 7 is a flow chart for establishing an accurate splice;
FIG. 8 is a flowchart illustrating the process of creating a K _ D tree;
fig. 9 is a flow chart of the alignment-to-alignment stitching algorithm.
Detailed Description
The first embodiment is as follows: as shown in fig. 1, the system for reduction of alignment-alignment fracture based on the K-D tree according to the present embodiment includes: the fracture fragment three-dimensional geometric modeling module, the fracture fragment information extraction module, the fracture fragment position determining and adjusting module, the matching and splicing module and the display module are sequentially connected;
the three-dimensional geometric modeling module of the fracture fragments is used for importing two-dimensional tomographic image data obtained by CT medical scanning into medical image processing software in a DICOM format, and establishing a three-dimensional grid geometric model representing the fracture fragments after a series of image processing, so that a useful model is provided for fracture reduction.
The fracture fragment information extracting module is used for extracting geometrical information such as points, lines, surfaces and the like which can represent femoral fractures and are required by fracture reduction from the obtained fracture fragment three-dimensional grid geometrical model, establishing an information structure body of the femoral fracture fragments and providing useful fracture fragment information for fracture reduction.
The module for determining and adjusting the position of the fracture fragment is used for positioning and evaluating the displaced femoral fracture fragment to provide an accurate position for fracture reduction.
The matching and splicing module is used for aligning femoral fracture fragments, and restoring the fracture fragments to the original anatomical structure position by finding and determining the corresponding relation between different fracture fragments, so that the stability of fracture restoration is ensured.
The display module is used for observing and displaying the comminuted fracture alignment and line resetting effect, and realizes the interactivity between the user and the fracture resetting system.
The second embodiment is as follows: as shown in fig. 2, in the present embodiment, the specific process of the three-dimensional geometric modeling module for fracture fragments to achieve its function is as follows:
cartilage tissues and bones are separated through a proper threshold value, the bone tissues are marked or identified by a segmentation method based on region growth, fracture fragments are extracted, then a three-dimensional grid geometric model of the fracture fragments required for reduction is obtained through the grid division and three-dimensional reconstruction processes of an MC algorithm, and optimization technologies such as smoothing, simplification or regridding and the like are carried out on the obtained three-dimensional grid geometric model, so that the characteristics of the model are improved, and the visualization effect and the manageability of the model are further improved.
Other components and connection relationships of the present embodiment are the same as those of the first embodiment.
The third concrete implementation mode: as shown in fig. 3, in the present embodiment, the specific process of the module for extracting fracture fragment information to implement its function is as follows:
a. extracting the geometric information of the three-dimensional broken bone model, and establishing an information structure body of the femoral fracture fragments, wherein the information structure body is expressed as follows:
in the formula, fracture fragment information B ═ { B ═ B1，B2，…Bn}，BiThe ith fracture fragment information in the fracture fragment information structure body; gMGeometric elements of a three-dimensional model of a fracture fragment, including the geometric shape GFSide GEPoint GP；IMFor fracture patient information, including patient name INSex ISAge IALeft and right leg bones IL；
b. Traversing the established information structure BFIS of the femoral fracture fragment to obtain a femoral fracture fragment model;
obtaining the total bounding box X of all broken bones and obtaining the point set at the lower part of the bounding box X
Finding corresponding point set from BFIS
Wherein the content of the first and second substances,
the point set of the ith broken bone in the fracture fragment information structure body is shown; b isiObtaining the ith fracture fragment information in the fracture fragment information structure body to obtain a femoral shaft fragment model Mshaft；
Acquiring the total bounding box X of all broken bones according to the left and right leg bones I in the fracture fragment information BLInformation, if ILIs the left leg bone, the point set around the minimum value of the bounding box X is obtained
If IRIs the right leg bone, the point set around the maximum value of the bounding box X is obtained
Finding corresponding point set from BFIS
Wherein the content of the first and second substances,
the point set of the ith fracture fragment in the fracture fragment information structure body; b isiObtaining the information of the ith fracture fragment in the information structure of the fracture fragments to obtain a femoral head fracture model Mhead；
c. Extracting the axis of the femur from the obtained femur fracture fragment model;
according to the femoral head bone-breaking model MheadResampling the femoral head model to obtain a three-dimensional coordinate point set S of the femoral headhead；
According to the obtained point set SheadThe sphere is fitted by the least square method, and a function H (x) of the sum of squares of the errors of the least square method is constructed as shown below0，y0，z0R) to find the center coordinates of the fitting sphere and the sphere radius, can be expressed as follows:
in the formula, xi、yi、ziSet of points SheadCoordinate value of the ith point; n is a set of points SheadThe number of middle coordinate points; x is the number of0、y0、z0To the centre P of the fitted sphere0The coordinates of (a); r is the radius of the fitting sphere;
set of points SheadCenter of sphere P of median fitting sphere0(x0，y0，z0) The far points form a femur neck three-dimensional coordinate point set SneckAccording to the set of points SneckThe function F (x ') was constructed as follows'0，y′0，z′0) Represents:
thereby obtaining the coordinate of the central point of the femoral neck as PN(x′0，y′0，z′0)xj、yj、zjSet of points SneckCoordinate value of j point; n is a set of points SneckThe number of middle coordinate points;
connection point PN(x′0，y′0，z′0) And P0(x0，y0，z0) Obtaining the femoral head axis HL;
broken bone model M according to femoral shaftshaft，Resampling the femoral shaft model to obtain a femoral shaft three-dimensional coordinate point set Sshaft；
According to the obtained point set SshaftSet points SshaftThe N points are sorted according to the sequence of Z coordinates from small to large, the points within the range of 30-60% of the maximum value of the Z coordinates are extracted, and a point set S 'is constructed'shaft(ii) a Will click set S'shaftThe points in the formula are sorted from small to large according to Z coordinates, and are sequentially divided into 15 parts, wherein each part has n coordinate points, and the formula is as follows:
calculating the center point P of each coordinate point seti(xi，yi，zi) And will point Pi(xi，yi，zi) Put in set SshaftFitting a space straight line according to a least square method to obtain a femoral shaft axis line emulsion;
d. extracting a femoral fracture surface point set;
wherein x isj、xkPoints of the information structure BFIS of femoral fracture fragments; x is the number ofkIs xjPoints in the left and right σ ranges; n is a radical ofσIs f (x)j，xk) The number of medium non-zero points; f (x)j，xk) Is a point xj、xkThe angle between the normal vectors of (a); n isj、nkIs xj、xkThe normal vector of (a); σ is xkAnd xjThe distance between the two, usually 2-4 mm;
function W (x)j) Record the point xjThe included angle of other points must be larger than the threshold value t2(ii) a If point xjSatisfy the requirement of
Then point xjTo a point on the fracture surface, otherwise not on the fracture surface.
Other components and connection relationships of this embodiment are the same as those of the first to second embodiments.
The fourth concrete implementation mode: as shown in fig. 4, in this embodiment, the specific process of determining and adjusting the position of the fracture fragment by the module to achieve its function is as follows:
e. determining an axial plane AP, a coronal plane CP and a sagittal plane SP of a femoral shaft fracture surface according to the obtained femoral shaft axial lead, and adjusting the positions of the coronal plane CP and the axial plane AP;
the axial line milk of the femoral shaft is vertical to the axial plane AP; the coronal plane CP and the sagittal plane SP are perpendicular to the axial plane AP and both pass through the axis milk of the femoral shaft; after determining the positions of the coronal plane CP and the sagittal plane SP, manually adjusting the coronal plane CP and the sagittal plane SP to the appropriate positions according to medical common knowledge;
f. calculating and adjusting the neck trunk angle and the anteversion angle of the femoral shaft;
the neck angle θ, can be expressed as follows:
in the formula, N1Is the vector of the femoral shaft axis milk; n is a radical of2Is the vector of the femoral head axis HL; theta is an included angle between the two axial lines;
front rake
Can be expressed as follows:
in the formula, N3Is a projection vector of a femoral head axis HL on an axial plane AP; n is a radical of4Is the intersection vector of the coronal plane CP and the axial plane AP;
is the included angle between the two vectors;
if the neck angle theta is in the range of 120-135 DEG and the anteversion angle
The range of 12-15 degrees meets the requirements of medical clinical specifications; otherwise, readjust the angle theta of the shaft and the anteversion angle
Until the requirements of medical clinical specifications are met.
Other components and connection relationships of this embodiment are the same as those of the first to third embodiments.
The fifth concrete implementation mode: as shown in fig. 5, in this embodiment, the specific process of the matching and splicing module to implement its function is as follows:
g. completing the initial splicing by using a central point coincidence method, as shown in FIG. 6;
in order to perform center coincidence on the femoral head and the fracture surface point set of the femoral shaft, reduce the translation dislocation between the two point sets and provide initial values of translation and rotation parameters for accurate splicing;
calculating the centroid of the set of femoral head and femoral shaft fracture surface points can be expressed as follows:
in the formula (I), the compound is shown in the specification,
fracture surface point sets of the femoral head and the femoral shaft respectively; n is the number of corresponding fracture surface point sets;
respectively as the centroids of the femoral head and femoral shaft fracture surface point sets;
the offset vector of the two centroids is recorded and can be expressed as follows:
in the formula (I), the compound is shown in the specification,
is a translation vector;
respectively as the centroids of the femoral head and femoral shaft fracture surface point sets;
the coordinates of each point in the femoral head fracture surface point set are translated by taking the femoral shaft as a reference object, and can be expressed as follows:
in the formula (I), the compound is shown in the specification,
is a fracture surface point set of femoral head;
is a translation vector;
the coordinates of the femoral head fracture surface point set after the center of gravity is formed;
h. an ICP algorithm is used for completing accurate splicing of fracture fragments of the femoral head and the femoral shaft, and the splicing is shown in figure 7;
in order to improve the accuracy of splicing, the false splicing needs to be deleted through the processes of rotation, movement and the like after the initial splicing, and the shape of the fracture fragment is finally adjusted and aligned;
using the femoral shaft as a reference object, searching by using a K _ D tree to find the corresponding closest point of the points in the femoral shaft fracture surface point set in the femoral head fracture surface point set, as shown in FIG. 8;
the Euclidean distance can be expressed as follows:
in the formula, d is the Euclidean distance between the corresponding point vectors of the femoral shaft and the femoral head; (x)1，，y1，z1)，(x2，，y2，z2) Coordinates of corresponding points of the femoral head and the femoral shaft are respectively;
solving a rotation matrix and a translation matrix;
the coordinate system of the femoral head model is OcXcYcZcThe transformed coordinate system is expressed as
Wherein d is the distance between the femoral head model and the position after restoration; omega is femoral head model winding XwThe angle of rotation; theta is the femoral head model winding YwThe angle of rotation;
for the femoral head model winding ZwThe angle of rotation; the transformation matrix R of the femoral head is three matrices
The product of (c) can be expressed as follows:
as shown in fig. 9, verifying whether the distance between the two sets of fracture surface points of the corresponding femoral head and femoral shaft is smaller than 4mm, if so, adjusting the three-dimensional spatial position of the femoral head according to the transformation matrix R of the femoral head, obtaining the information of the three-dimensional fractured model according to the adjusted spatial position coordinates of the femoral head, replacing the information structure BFIS of the femoral fracture fragment, and finishing the precise splicing; if not, returning to the step of searching the closest point by using the K _ D tree.
Other components and connection relationships of the present embodiment are the same as those of the first to fourth embodiments.
The sixth specific implementation mode: in this embodiment, the specific process of the display module to realize its function is as follows:
and connecting the output display equipment of the computer to the computer for visual interaction, so that the effect of fracture reduction can be previewed.
Other components and connection relationships of the present embodiment are the same as those of one of the first to fifth embodiments.
Claims (1)
1. An alignment-to-alignment fracture reduction system based on a K-D tree method is characterized by comprising:
the fracture fragment three-dimensional geometric modeling module (1), the fracture fragment information extraction module (2), the fracture fragment position determining and adjusting module (3), the matching and splicing module (4) and the display module (5);
the three-dimensional geometric modeling module (1) of fracture fragments is used for importing two-dimensional tomographic image data obtained by CT medical scanning into medical image processing software in a DICOM format, and establishing a three-dimensional grid geometric model representing the fracture fragments after a series of image processing so as to provide a useful model for fracture reduction;
the three-dimensional geometric modeling module (1) for the fracture fragments has the specific process of realizing the functions as follows:
cartilage tissues and bones are separated through a proper threshold value, the bone tissues are marked or identified by a segmentation method based on region growth, so that fracture fragments are extracted, then a three-dimensional grid geometric model of the fracture fragments required for reduction is obtained by adopting an MC algorithm to carry out grid division and three-dimensional reconstruction processes, and optimization technologies such as smoothing, simplification or regridding and the like are carried out on the obtained three-dimensional grid geometric model, so that the characteristics of the model are improved, and the visualization effect and the manageability of the model are further improved;
the fracture fragment information extraction module (2) is used for extracting the geometrical information such as points, lines, surfaces and the like which can represent femoral fractures and are required by fracture reduction from the obtained fracture fragment three-dimensional grid geometrical model, and establishing an information structure body of the femoral fracture fragments to provide useful fracture fragment information for fracture reduction;
the module (2) for extracting the fracture fragment information realizes the specific process of the function as follows:
a. extracting the geometric information of the three-dimensional broken bone model, and establishing an information structure body of the femoral fracture fragments, wherein the information structure body is expressed as follows:
in the formula, fracture fragment information B ═ { B ═ B1,B2,…Bn}，BiThe ith fracture fragment information in the fracture fragment information structure body; gMGeometric elements of a three-dimensional model of a fracture fragment, including the geometric shape GFSide GEPoint GP；IMFor fracture patient information, including patient name INSex ISAge IALeft and right leg bones IL；
b. Traversing the established information structure BFIS of the femoral fracture fragment to obtain a femoral fracture fragment model;
obtaining the total bounding box X of all broken bones and obtaining the point set at the lower part of the bounding box X
Finding corresponding point set from BFIS
Wherein the content of the first and second substances,
the point set of the ith broken bone in the fracture fragment information structure body is shown; b isiObtaining the ith fracture fragment information in the fracture fragment information structure body to obtain a femoral shaft fragment model Mshaft；
Acquiring the total bounding box X of all broken bones according to the left and right leg bones I in the fracture fragment information BLInformation, if ILIs the left leg bone, the point set around the minimum value of the bounding box X is obtained
If IRIs the right leg bone, the point set around the maximum value of the bounding box X is obtained
Finding corresponding point set from BFIS
Wherein the content of the first and second substances,
the point set of the ith fracture fragment in the fracture fragment information structure body; b isiObtaining the information of the ith fracture fragment in the information structure of the fracture fragments to obtain a femoral head fracture model Mhead；
c. Extracting the axis of the femur from the obtained femur fracture fragment model;
according to the femoral head bone-breaking model MheadResampling the femoral head model to obtain a three-dimensional coordinate point set S of the femoral headhead；
According to the obtained point set SheadThe sphere is fitted by the least square method, and a function H (x) of the sum of squares of the errors of the least square method is constructed as shown below0,y0,z0R) to find the center coordinates of the fitting sphere and the sphere radius, can be expressed as follows:
in the formula, xi、yi、ziSet of points SheadCoordinate value of the ith point; n is a set of points SheadThe number of middle coordinate points; x is the number of0、y0、z0To the centre P of the fitted sphere0The coordinates of (a); r is the radius of the fitting sphere;
set of points SheadCenter of sphere P of median fitting sphere0(x0,y0,z0) The far points form a femur neck three-dimensional coordinate point set SneckAccording to the set of points SneckThe function F (x ') was constructed as follows'0,y′0,z′0) Represents:
thereby obtaining the coordinate of the central point of the femoral neck as PN(x′0,y′0,z′0)xj、yj、zjSet of points SneckCoordinate value of j point; n is a set of points SneckThe number of middle coordinate points;
connection point PN(x′0,y′0,z′0) And P0(x0,y0,z0) Obtaining the femoral head axis HL;
broken bone model M according to femoral shaftshaftResampling the femoral shaft model to obtain a femoral shaft three-dimensional coordinate point set Sshaft；
According to the obtained point set SshaftSet points SshaftThe N points are sorted according to the sequence of Z coordinates from small to large, the points within the range of 30-60% of the maximum value of the Z coordinates are extracted, and a point set S 'is constructed'shaft(ii) a Will click set S'shaftThe points in the formula are sorted from small to large according to Z coordinates, and are sequentially divided into 15 parts, wherein each part has n coordinate points, and the formula is as follows:
calculating the center point P of each coordinate point seti(xi,yi,zi) And will point Pi(xi,yi,zi) Put in set SshaftFitting a space straight line according to a least square method to obtain a femoral shaft axis SL;
d. extracting a femoral fracture surface point set;
wherein x isj、xkPoints of the information structure BFIS of femoral fracture fragments; x is the number ofkIs xjPoints in the left and right σ ranges; n is a radical ofσIs f (x)j,xk) The number of medium non-zero points; f (x)j,xk) Is a point xj、xkThe angle between the normal vectors of (a); n isj、nkIs xj、xkThe normal vector of (a); σ is xkAnd xjThe distance between the two, usually 2-4 mm;
function W (x)j) Record the point xjThe included angle of other points must be larger than the threshold value t2(ii) a If point xjSatisfy the requirement of
Then point xjPoints belonging to the fracture surface, otherwise not points on the fracture surface;
the fracture fragment position determining and adjusting module (3) is used for positioning and evaluating the displaced femoral fracture fragments to provide accurate positions for fracture reduction;
the module (3) for determining and adjusting the position of the fracture fragment has the specific process of realizing the functions as follows:
e. determining an axial plane AP, a coronal plane CP and a sagittal plane SP of a femoral shaft fracture surface according to the obtained femoral shaft axial lead, and adjusting the positions of the coronal plane CP and the axial plane AP;
the axial line SL of the femoral shaft is vertical to the axial plane AP; the coronal plane CP and the sagittal plane SP are perpendicular to the axial plane AP and both pass through an axis SL of the femoral shaft; after determining the positions of the coronal plane CP and the sagittal plane SP, manually adjusting the coronal plane CP and the sagittal plane SP to the appropriate positions according to medical common knowledge;
f. calculating and adjusting the neck trunk angle and the anteversion angle of the femoral shaft;
the neck angle θ, can be expressed as follows:
in the formula, N1Is the vector of the femoral shaft axis SL; n is a radical of2Is the vector of the femoral head axis HL; theta isThe included angle between the two axial lines;
front rake
Can be expressed as follows:
in the formula, N3Is a projection vector of a femoral head axis HL on an axial plane AP; n is a radical of4Is the intersection vector of the coronal plane CP and the axial plane AP;
is the included angle between the two vectors;
if the neck angle theta is in the range of 120-135 DEG and the anteversion angle
The range of 12-15 degrees meets the requirements of medical clinical specifications; otherwise, readjust the angle theta of the shaft and the anteversion angle
Until the requirements of medical clinical specifications are met;
the matching and splicing module (4) is used for aligning femoral fracture fragments, and restoring the fracture fragments to the original anatomical structure position by finding and determining the corresponding relation among different fracture fragments, so that the stability of fracture restoration is ensured;
the matching splicing module (4) realizes the functions by the following specific processes:
g. completing primary splicing by using a central point coincidence method;
in order to perform center coincidence on the femoral head and the fracture surface point set of the femoral shaft, reduce the translation dislocation between the two point sets and provide initial values of translation and rotation parameters for accurate splicing;
calculating the centroid of the set of femoral head and femoral shaft fracture surface points can be expressed as follows:
in the formula (I), the compound is shown in the specification,
fracture surface point sets of the femoral head and the femoral shaft respectively; n is the number of corresponding fracture surface point sets;
respectively as the centroids of the femoral head and femoral shaft fracture surface point sets;
the offset vector of the two centroids is recorded and can be expressed as follows:
in the formula (I), the compound is shown in the specification,
is a translation vector;
respectively as the centroids of the femoral head and femoral shaft fracture surface point sets;
the coordinates of each point in the femoral head fracture surface point set are translated by taking the femoral shaft as a reference object, and can be expressed as follows:
in the formula (I), the compound is shown in the specification,
is a fracture surface point set of femoral head;
is a translation vector;
the coordinates of the femoral head fracture surface point set after the center of gravity is formed;
h. accurate splicing of fracture fragments of the femoral head and the femoral shaft is completed by applying an ICP (inductively coupled plasma) algorithm;
in order to improve the accuracy of splicing, the false splicing needs to be deleted through the processes of rotation, movement and the like after the initial splicing, and the shape of the fracture fragment is finally adjusted and aligned;
using the femoral shaft as a reference object, and searching and finding out the corresponding nearest point of the point in the femoral shaft fracture surface point set in the femoral head fracture surface point set by using a K _ D tree;
the Euclidean distance can be expressed as follows:
in the formula, d is the Euclidean distance between the corresponding point vectors of the femoral shaft and the femoral head; (x)1,,y1,z1)，(x2,,y2,z2) Coordinates of corresponding points of the femoral head and the femoral shaft are respectively;
solving a rotation matrix and a translation matrix;
the coordinate system of the femoral head model is OcXcYcZcThe transformed coordinate system is expressed as
Wherein d is the distance between the femoral head model and the position after restoration; omega is femoral head model winding XwThe angle of rotation; theta is the femoral head model winding YwThe angle of rotation;
for the femoral head model winding ZwThe angle of rotation; the transformation matrix R of the femoral head is three matrices Rx(ω),Ry(θ),
The product of (c) can be expressed as follows:
verifying whether the distance between the corresponding femoral head and femoral shaft fracture surface point sets is smaller than 4mm, if so, adjusting the three-dimensional space position of the femoral head according to the femoral head transformation matrix R, obtaining the information of a three-dimensional bone fracture model according to the adjusted space position coordinates of the femoral head, replacing an information structure body BFIS of femoral fracture fragments, and finishing accurate splicing; if not, returning to the step of searching the closest point by using the K _ D tree;
the display module (5) is used for observing and displaying the comminuted fracture alignment and line reduction effect and realizing the interactivity between a user and the fracture reduction system;
the display module (5) realizes the functions of the display module by the following specific processes:
and connecting the output display equipment of the computer to the computer for visual interaction, so that the effect of fracture reduction can be previewed.
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