CN103948431B - A kind of tracer method for designing being applied to surgical navigational gauge point error indicator - Google Patents

Abstract

The invention discloses a kind of tracer method for designing being applied to surgical navigational gauge point error indicator, comprising: the internal and external parameter and the certainty annuity coordinate system that obtain binocular optical navigation system; Define a discrete space point set; According to pinhole imaging system principle, spatial discrete points is projected on the imaging surface of left and right cameras, calculate theoretical sub-pix point coordinates; Centered by theoretical sub-pix point, determine a range of error, on left and right cameras imaging surface each get at random point in above-mentioned range of error several, the spatial point coordinate of these pairing pixels is rebuild according to the Epipolar geometry principle of binocular vision, and calculate the distance of these spatial point and former spatial point, using the space relative error magnitudes of the average of these distances as former spatial point; By visual for the space relative error distribution of operating theater instruments position.The present invention can instruct surgeon's operation apparatus in the region that space relative error is less to navigate, to improve the precision of surgical navigational.

Description

A kind of tracer method for designing being applied to surgical navigational gauge point error indicator

Technical field

The present invention relates to computer assisted surgery research field, specifically a kind of tracer method for designing being applied to surgical navigational gauge point error indicator.

Background technology

In recent years, optical operation navigation technology obtains to be promoted fast, gradually in the operations such as neurosurgery, Oral and Maxillofacial Surgery, orthopaedics.In optical operation navigation system, marker tracking location is the core content of surgical navigational, and its method for tracking and positioning and precision directly determine the precision of surgical navigational, range of application and practicality.

The precision of surgical navigational is not only correlated with the precision of marker tracking method, the position of also putting with optical positioning system is relevant, although the precision of marker tracking method is higher, but the relative position as operating theater instruments and optical positioning system is not be in best tracing area, then can greatly reduce final navigation accuracy, make surgical effect and preoperative planning deviation comparatively large, even cause operative failure.Its reason is that gauge point error distribution in available field of view is uneven, and diverse location equidistant with navigation system, error distribution is also different, and this depends mainly on orientation and the resolution of gauge point on image of video camera shot mark point.Therefore, need analyzing and positioning systematic error to distribute, and make it visual.Preoperative according to error map spectrum, adjustment optical positioning system position, makes the zone of action of operation tool be positioned at error comparatively zonule, to improve the precision of surgical navigational.

Therefore, design a kind of tracer method for designing being applied to surgical navigational gauge point error indicator and have very large necessity for the precision improving navigation.

Summary of the invention

It is uneven for the present invention is directed to gauge point error distribution in available field of view, diverse location equidistant with navigation system, error distribution is also this different problem, a kind of tracer method for designing being applied to surgical navigational gauge point error indicator is provided, the method can Positioning System Error distribute, and make it visual, thus instruct doctor's operation apparatus to navigate in space error comparatively zonule, improve the precision of surgical navigational.

Object of the present invention is realized by following technical scheme: a kind of tracer method for designing being applied to surgical navigational gauge point error indicator, the method is the space relative error distribution calculating surgical navigational binocular optical navigation system available field of view, then by visual for the space relative error distribution of operating theater instruments position.

Concrete, the method for the space relative error distribution of described calculating surgical navigational binocular optical navigation system available field of view is:

(1) internal and external parameter of binocular optical navigation system is obtained;

(2) system coordinate system of binocular optical navigation system is determined;

(3) the discrete space point set of a distribution in cuboid is defined;

(4) according to pinhole imaging system principle, spatial discrete points is projected on the imaging surface of left and right cameras, calculate theoretical sub-pix point coordinates;

(5) centered by theoretical sub-pix point, determine a circular or square range of error, on left and right cameras imaging surface each get at random point in above-mentioned range of error several, wherein left and right cameras get count identical, the spatial point coordinate of these pairing pixels is rebuild according to the Epipolar geometry principle of binocular vision, and calculate the distance of these spatial point and former spatial point, using the space relative error magnitudes of the average of these distances as former spatial point.

Concrete, in described step (1), the internal and external parameter of binocular optical navigation system obtains by demarcating left and right cameras, or given by manufacturer.

Concrete, in described step (2), the system coordinate system of binocular optical navigation system is defined as follows: with the line of two video camera photocentres for X-axis, and their mid point is initial point, and it is X-axis positive direction that initial point points to right video camera photocentre; Y-axis was defined as initial point and perpendicular to the Z axis of left and right cameras coordinate system, was positive direction above initial point pointing space; Use right-hand rule determination Z axis, the shooting direction pointing to left and right cameras is Z axis positive direction.

Concrete, in described step (3), the wide height of described cuboid is long parallel with the X, Y, Z axis of system coordinate system respectively, and system Z axis crosses the central point on two sides before and after cuboid.

Concrete, in described step (4), the step calculating theoretical sub-pix point coordinates is:

(4-1), under establishing system coordinate system, P point coordinates is (X _w, Y _w, Z _w), the actual coordinate of this point coordinates in camera coordinate system is (X _c, Y _c, Z _c), the corresponding coordinate of sub-pix point coordinates namely in image coordinate system be (u, v), P point transforms to the formula of camera coordinate system from system coordinate system:

$\left[\begin{array}{c}{X}_c\\ Y_c\\ Z_c\end{array}\right]=R\left[\begin{array}{c}{X}_w\\ Y_w\\ Z_w\end{array}\right]+T$

Here R is the orthogonal matrix of 3 × 3, and T is the vector of 3 × 1, and R, T are the external parameter of video camera;

(4-2) by coordinate (X _c, Y _c, Z _c) be normalized to (X _c/ Z _c, Y _c/ Z _c, 1), (X _c/ Z _c, Y _c/ Z _c, 1) with the coordinate of theoretical linear model (X ' _c/ Z ' _c, Y ' _c/ Z ' _c, 1) and there is following relation:

$\left[\begin{array}{c}{X}_c^{\′}/Z_c^{\′}\\ Y_c^{\′}/Z_c^{\′}\\ 1\end{array}\right]=(1+k_1{r}^2+k_2{r}^4+k_5{r}^6)\left[\begin{array}{c}{X}_c/Z_c\\ Y_c/Z_c\\ 1\end{array}\right]+\left[\begin{array}{c}2k_3\mathrm{xy}+k_4(r^2+2x^2)\\ k_3(r^2+2y^2)+2k_4\mathrm{xy}\\ 1\end{array}\right]\text{;}$

Wherein x=X _c/ Z _c, y=Y _c/ Z _c, r ²=x ²+ y ², k ₁, k ₂, k ₃, k ₄, k ₅for 5 components of camera lens distortion factor matrix k;

(4-3) obtain by pinhole imaging system linear model P point to transform to image coordinate system coordinate transform formula from camera coordinate system:

$\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=A\left[\begin{array}{c}{X}_c^{\′}/Z_c^{\′}\\ Y_c^{\′}/Z_c^{\′}\\ 1\end{array}\right];$

Here $A=\left[\begin{array}{ccc}{f}_x& s& u_0\\ 0& f_y& v_0\\ 0& 0& 1\end{array}\right]$ For the internal matrix of video camera, s is the obliquity factor of video camera, i.e. the angle of imaging plane two vertical axis, f _x=f/d _x, f _y=f/d _y, f is the focal length of video camera, and d _x, d _ybe the physical size of each pixel on x-axis, y-axis direction on image respectively, be all known parameters, by video camera, producer provides; u ₀, v ₀the image coordinate system initial point o in units of physical length _icoordinate under the image coordinate system in units of pixel.

Concrete, in described step (5), the computational process of space relative error magnitudes is as follows:

(5-1) centered by theoretical sub-pix point, a circular or square range of error is determined, each some P got at random in above-mentioned range of error on left and right cameras imaging surface _li(i=1,2 ..., N), P _ri(i=1,2 ..., N), by P _liand P _rimatch one to one, form N ²plant combination;

(5-2) according to the formula in step (4-2), (4-3), the actual camera coordinate (X that each pixel described in step (5-1) is corresponding is obtained _c/ Z _c, Y _c/ Z _c, 1): P _iput under left camera coordinate system vector meets following relation:

Wherein t _lifor arbitrary value, make B _li=[X _lic/ Z _lic, Y _lic/ Z _lic, 1] and T, then have in like manner can obtain, under right camera coordinate system vector meets following relation:

From O under system coordinate system _lpoint is to P _lithe vector of point for:

${\stackrel{\→}{P}}_{\mathrm{lgi}}=R_{\mathrm{lgi}}{B}_{\mathrm{li}}{t}_{\mathrm{li}}+T_{\mathrm{lgi}}$

In like manner, under system coordinate system from O _rpoint is to P _rithe vector of point for:

${\stackrel{\→}{P}}_{\mathrm{rgi}}=R_{\mathrm{rgi}}{B}_{\mathrm{ri}}{t}_{\mathrm{ri}}+T_{\mathrm{rgi}}$

Solving equation group $\left\{\begin{array}{c}{\stackrel{\→}{P}}_{\mathrm{lgi}}=R_{\mathrm{lgi}}{B}_{\mathrm{li}}{t}_{\mathrm{li}}+T_{\mathrm{lgi}}\\ {\stackrel{\→}{P}}_{\mathrm{rgi}}=R_{\mathrm{rgi}}{B}_{\mathrm{ri}}{t}_{\mathrm{ri}}+T_{\mathrm{rgi}}\end{array}\right.$ Namely P is tried to achieve _ithe coordinate of point under system coordinate system;

(5-3) N is obtained ²individual spatial point, after the coordinate under system coordinate system, calculates this N ²individual spatial point and former coordinate points distance average, as the relative error magnitudes of former spatial point.

Concrete, the described space relative error distribution visualization method by operating theater instruments position is: define a gray scale or color-bar, for each error amount gives a kind of gray scale or colour, build three-dimensional relative error distribution gray scale or color atlas, according to the distance of luminous point and binocular optical navigation system, two dimensional gray or color atlas and operating theater instruments luminous point position are shown.

Compared with prior art, tool has the following advantages and beneficial effect in the present invention:

The space relative error location mode of calculating surgical navigational binocular vision system available field of view proposed by the invention, can by visual for the space relative error distribution of operating theater instruments position, surgeon's operation apparatus in the region that space relative error is less is instructed to navigate, to improve the precision of surgical navigational.

Accompanying drawing explanation

Fig. 1 is the definition of system coordinate system in the inventive method and the spatial point imaging schematic diagram in left and right cameras.

Fig. 2 is the design sketch being rectangle distribution discrete space point in the inventive method.

Fig. 3 is national forest park in Xiaokeng schematic diagram.

Fig. 4 is centered by theoretical sub-pix point, determines the schematic diagram of a square range of error.

Fig. 5 is discrete space point visual field relative error distribution collection of illustrative plates schematic diagram.

Fig. 6 is the tracer design sketch of display two-dimensional field of view relative error distribution collection of illustrative plates and luminous point position.

Detailed description of the invention

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited thereto.

Embodiment 1

The present embodiment is a kind of tracer method for designing being applied to surgical navigational gauge point error indicator, adopts the tracer of this method design, can improve the precision of surgical navigational further.

This tracer, by the discrete space point set of definition one about the distribution in cuboid of binocular optical navigation system Z axis symmetry, determines the spatial point scope of spike.Computer memory point is at the theoretical sub-pix point coordinates of left and right cameras imaging surface, and reject theoretical sub-pix point and be positioned at the extraneous spatial point of imaging surface, then 8 pixels that theoretical sub-pix point is adjacent are got, rebuild their spatial point, get the average of these spatial point and former spatial point distance, as the space relative error magnitudes of former spatial point, then a gray scale or color-bar is defined, for each error amount gives a kind of gray scale or colour, according to the distance of luminous point and binocular optical navigation system, two dimensional gray or color atlas and luminous point position are shown.Concrete steps are as follows:

First, the internal and external parameter of binocular optical navigation system is obtained.The internal and external parameter of binocular optical navigation system is the call parameter of solution room point theoretical sub-pix point coordinates and reverse spatial point coordinate on left and right cameras imaging surface, general binocular optical navigation system obtains by demarcating left and right cameras, and the binocular optical navigation system of business is then by manufacturer's this parameter given.In the present invention, the binocular optical navigation system of use is the near infrared binocular optical positioning system through demarcating.

Determine the system coordinate system of binocular optical navigation system.Spatial discrete points position is conveniently determined in the definition of system coordinate system, and with the line of two video camera photocentres for X-axis, their mid point is initial point, and it is X-axis positive direction that initial point points to right video camera photocentre; Y-axis was defined as initial point and perpendicular to the Z axis of left and right cameras coordinate system, was positive direction above initial point pointing space; Use right-hand rule determination Z axis, the shooting direction pointing to left and right cameras is Z axis positive direction.As shown in Figure 1, (the X in figure _w, Y _w, Z _w, O _w) be system coordinate system, (X _l, Y _l, Z _l, O _l) be left camera coordinate system, (X _r, Y _r, Z _r, O _r) be right camera coordinate system, I _l, I _rleft and right imaging plane respectively, the some p that left camera coordinates is fastened _lwith the some p that right camera coordinates is fastened _rp in system coordinate system _wpoint imaging, to polar plane Π by O _l, p _l, e _ldetermine for 3, wherein e _l, e _rphotocentre line O _lo _rrespectively with I _l, I _rintersection point.Define the discrete space point set of a distribution in cuboid.The present embodiment, in system coordinate system Z axis positive direction z=300mm place's definition first spatial discrete points face, discrete point zone is 1200mm in the degree of depth of Z-direction, and namely last spatial discrete points face is positioned at z=1500mm place, the wide W=800mm in face, high H=800mm.The wide height that edge discrete point line is formed is long parallel with the X, Y, Z axis of system respectively, and system Z axis crosses the central point on two sides before and after cuboid.Spatial discrete points distributes with fixed interval dx=5mm, dy=5mm, dz=5mm, and makes discrete point about Z axis symmetric arrays on XYZ axle.As shown in Figure 2.

According to pinhole imaging system principle, spatial discrete points projected on the imaging surface of left and right cameras, calculate theoretical sub-pix point coordinates, its schematic diagram as shown in Figure 3.In the process calculated, relate to three coordinate systems, be respectively system coordinate system, camera coordinate system and image coordinate system, about the definition of system coordinate system, describe above, the definition of make a brief explanation here camera coordinate system and image coordinate system.In figure 3, O _crepresent the photocentre of video camera, X _c, Y _cparallel with the plane of delineation respectively, Z _cperpendicular to the plane of delineation, and be the optical axis of video camera, then O _cand X _c, Y _c, Z _ccoordinate axes forms camera coordinate system jointly.Image coordinate is two-dimensional coordinate system, in units of pixel, with the image upper left corner for initial point, usually carrys out the coordinate of each pixel in representative digit image with (u, v), also represents line number and columns in this pixel place array simultaneously.Computational process is as follows: in figure 3, and under system coordinate system, P point coordinates is (X _w, Y _w, Z _w), in camera coordinate system, coordinate is (X _c, Y _c, Z _c), there is a spin matrix R and translation vector T between system coordinate system and camera coordinate system, their pass is:

$\left[\begin{array}{c}{X}_c\\ Y_c\\ Z_c\end{array}\right]=R\left[\begin{array}{c}{X}_w\\ Y_w\\ Z_w\end{array}\right]+T$

Here R is the orthogonal matrix of 3 × 3, and T is the vector of 3 × 1, and they are external parameters of video camera.National forest park in Xiaokeng is an ideal model, in the imaging system of reality, there is lens distortion, can not meet this linear relationship completely, introduces nonlinear model here to obtain sub-pix point coordinates exactly in the process therefore converted.By the camera coordinates (X of linear model _c, Y _c, Z _c) be normalized to (X _c/ Z _c, Y _c/ Z _c, 1), be subject to the impact of camera lens radial direction and tangential distortion, actual camera coordinates (X _c/ Z _c, Y _c/ Z _c, 1) with the coordinate of linear model (X ' _c/ Z ' _c, Y ' _c/ Z ' _c, 1) and there is following relation:.

$\left[\begin{array}{c}{X}_c^{\′}/Z_c^{\′}\\ Y_c^{\′}/Z_c^{\′}\\ 1\end{array}\right]=(1+k_1{r}^2+k_2{r}^4+k_5{r}^6)\left[\begin{array}{c}{X}_c/Z_c\\ Y_c/Z_c\\ 1\end{array}\right]+\left[\begin{array}{c}2k_3\mathrm{xy}+k_4(r^2+2x^2)\\ k_3(r^2+2y^2)+2k_4\mathrm{xy}\\ 1\end{array}\right]\text{;}$

Wherein x=X _c/ Z _c, y=Y _c/ Z _c, r ²=x ²+ y ², k ₁, k ₂, k ₃, k ₄, k ₅for 5 components of distortion factor k matrix.The pixel coordinate of definition sub-pix point is (u, v), can obtain by pinhole imaging system linear model P point to transform to image coordinate system coordinate transform formula from camera coordinate system:

$\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=A\left[\begin{array}{c}{X}_c^{\′}/Z_c^{\′}\\ Y_c^{\′}/Z_c^{\′}\\ 1\end{array}\right]$

Here $A=\left[\begin{array}{ccc}{f}_x& s& u_0\\ 0& f_y& v_0\\ 0& 0& 1\end{array}\right]$ For the internal matrix of video camera, s is the obliquity factor of video camera, i.e. the angle of imaging plane two vertical axis, f _x=f/d _x, f _y=f/d _y, f is the focal length of video camera, and d _x, d _ybe the physical size of each pixel on x-axis, y-axis direction on image respectively, their value is all known parameters, and by video camera, producer provides.

Calculate theoretical sub-pix point pixel coordinate (u, v) of spatial point, centered by theoretical sub-pix point, get minimum square region, namely get the region that 8 pixel adjacent with theoretical sub-pix point forms, as shown in Figure 4.For each 8 of the pixel of the error of calculation in left and right cameras, respectively get a point and to partner the spatial point coordinate reconstructing and project this two pixel, totally 64 kinds of combinations, then calculate they and the former spatial point distance average relative error magnitudes as former spatial point.Computational process is as follows: the theoretical subpixel coordinates supposing P point is (u, v), and the internal matrix of video camera is A, so P point normalization camera coordinates (X ' _c/ Z ' _c, Y ' _c/ Z ' _c, 1) and theoretical subpixel coordinates between meet following equation:

$\left[\begin{array}{c}{X}_c^{\′}/Z_c^{\′}\\ Y_c^{\′}/Z_c^{\′}\\ 1\end{array}\right]=A^{-1}\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]$

Consider the impact of camera lens radial direction and tangential distortion, at actual camera coordinate (X _c/ Z _c, Y _c/ Z _c, 1) and desirable normalization coordinate (X ' _c/ Z ' _c, Y ' _c/ Z ' _c, 1) corresponding relation as follows.

$\left[\begin{array}{c}{X}_c^{\′}/Z_c^{\′}\\ Y_c^{\′}/Z_c^{\′}\\ 1\end{array}\right]=(1+k_1{r}^2+k_2{r}^4+k_5{r}^6)\left[\begin{array}{c}{X}_c/Z_c\\ Y_c/Z_c\\ 1\end{array}\right]+\left[\begin{array}{c}2k_3\mathrm{xy}+k_4(r^2+2x^2)\\ k_3(r^2+2y^2)+2k_4\mathrm{xy}\end{array}\right]$

Actual camera coordinate (X can be calculated by formula above _c/ Z _c, Y _c/ Z _c, 1), therefore P _iput under left camera coordinate system vector meets following relation:

Wherein t _lifor arbitrary value, make B _li=[X _lic/ Z _lic, Y _lic/ Z _lic, 1] ^t, then have in like manner can obtain, under right camera coordinate system vector meets following relation:

From O under system coordinate system _lpoint is to P _lithe vector of point for:

${\stackrel{\→}{P}}_{\mathrm{lgi}}=R_{\mathrm{lgi}}{B}_{\mathrm{li}}{t}_{\mathrm{li}}+T_{\mathrm{lgi}}$

In like manner, under system coordinate system from O _rpoint is to P _rithe vector of point for:

${\stackrel{\→}{P}}_{\mathrm{rgi}}=R_{\mathrm{rgi}}{B}_{\mathrm{ri}}{t}_{\mathrm{ri}}+T_{\mathrm{rgi}}$

Solving equation group $\left\{\begin{array}{c}{\stackrel{\→}{P}}_{\mathrm{lgi}}=R_{\mathrm{lgi}}{B}_{\mathrm{li}}{t}_{\mathrm{li}}+T_{\mathrm{lgi}}\\ {\stackrel{\→}{P}}_{\mathrm{rgi}}=R_{\mathrm{rgi}}{B}_{\mathrm{ri}}{t}_{\mathrm{ri}}+T_{\mathrm{rgi}}\end{array}\right.$ P can be tried to achieve _ithe coordinate of point under system.

Obtain 64 spatial point after the coordinate under system, calculate these 64 spatial point and former coordinate points distance average, as the relative error magnitudes of former spatial point.

Then according to scope definition gray scale or the color-bar of error amount, for all spatial point error amounts give a kind of gray scale or color, a solid space gray scale or color atlas is formed, as shown in Figure 5.Calculate the average of all luminous point Z axis in operating theater instruments, by the position display of the system XOY face two dimensional gray or color atlas and luminous point that are in this position out, as shown in Figure 6, in figure, A represents the position of three luminous points, B represents adding and average of three luminous point Z axis coordinates, thus help doctor to optimize the Camera composition of binocular optical navigation system in surgical navigational in the preoperative, and operation apparatus navigates in the region that space relative error is less in operation process.

Above-described embodiment is the present invention's preferably embodiment; but embodiments of the present invention are not restricted to the described embodiments; change, the modification done under other any does not deviate from spirit of the present invention and principle, substitute, combine, simplify; all should be the substitute mode of equivalence, be included within protection scope of the present invention.

Claims (7)

1. one kind is applied to the tracer method for designing of surgical navigational gauge point error indicator, it is characterized in that, the method is the space relative error distribution calculating surgical navigational binocular optical navigation system available field of view, then by visual for the space relative error distribution of operating theater instruments position;

The method of the space relative error distribution of described calculating surgical navigational binocular optical navigation system available field of view is:

(1) internal and external parameter of binocular optical navigation system is obtained;

(2) system coordinate system of binocular optical navigation system is determined;

(3) the discrete space point set of a distribution in cuboid is defined;

(4) according to pinhole imaging system principle, spatial discrete points is projected on the imaging surface of left and right cameras, calculate theoretical sub-pix point coordinates;

(5) centered by theoretical sub-pix point, determine a circular or square range of error, on left and right cameras imaging surface each get at random point in above-mentioned range of error several, wherein left and right cameras get count identical, the spatial point coordinate of these pairing pixels is rebuild according to the Epipolar geometry principle of binocular vision, and calculate the distance of these spatial point and former spatial point, using the space relative error magnitudes of the average of these distances as former spatial point.

2. the tracer method for designing being applied to surgical navigational gauge point error indicator according to claim 1, it is characterized in that, in described step (1), the internal and external parameter of binocular optical navigation system obtains by demarcating left and right cameras, or given by manufacturer.

3. the tracer method for designing being applied to surgical navigational gauge point error indicator according to claim 1, it is characterized in that, in described step (2), the system coordinate system of binocular optical navigation system is defined as follows: with the line of two video camera photocentres for X-axis, their mid point is initial point, and it is X-axis positive direction that initial point points to right video camera photocentre; Y-axis was defined as initial point and perpendicular to the Z axis of left and right cameras coordinate system, was positive direction above initial point pointing space; Use right-hand rule determination Z axis, the shooting direction pointing to left and right cameras is Z axis positive direction.

4. the tracer method for designing being applied to surgical navigational gauge point error indicator according to claim 1, it is characterized in that, in described step (3), the wide height of described cuboid is long parallel with the X, Y, Z axis of system coordinate system respectively, and system Z axis crosses the central point on two sides before and after cuboid.

5. the tracer method for designing being applied to surgical navigational gauge point error indicator according to claim 3, is characterized in that, in described step (4), the step calculating theoretical sub-pix point coordinates is:

(4-1), under establishing system coordinate system, P point coordinates is (X _w, Y _w, Z _w), the actual coordinate of this point coordinates in camera coordinate system is (X _c, Y _c, Z _c), the corresponding coordinate of sub-pix point coordinates namely in image coordinate system is (u, v), and P point transforms to the formula of camera coordinate system from system coordinate system:

$\left[\begin{array}{c}{X}_c\\ Y_c\\ Z_c\end{array}\right]=R\left[\begin{array}{c}{X}_w\\ Y_w\\ Z_w\end{array}\right]+T$

Here R is the orthogonal matrix of 3 × 3, and T is the vector of 3 × 1, and R, T are the external parameter of video camera;

(4-2) by coordinate (X _c, Y _c, Z _c) be normalized to (X _c/ Z _c, Y _c/ Z _c, 1), (X _c/ Z _c, Y _c/ Z _c, 1) with the coordinate of theoretical linear model (X ' _c/ Z ' _c, Y ' _c/ Z ' _c, 1) and there is following relation:

$\left[\begin{array}{c}{X}_c^{\′}/Z_c^{\′}\\ Y_c^{\′}/Z_c^{\′}\\ 1\end{array}\right]=(1+k_1{r}^2+k_2{r}^4+k_5{r}^6)\left[\begin{array}{c}{X}_c/Z_c\\ Y_c/Z_c\\ 1\end{array}\right]+\left[\begin{array}{c}2k_{3}xy+k_4(r^2+2x^2)\\ k_3(r^2+2y^2)+2k_{4}xy\\ 1\end{array}\right];$

Wherein x=X _c/ Z _c, y=Y _c/ Z _c, r ²=x ²+ y ², k ₁, k ₂, k ₃, k ₄, k ₅for 5 components of camera lens distortion factor matrix k;

(4-3) obtain by pinhole imaging system linear model P point to transform to image coordinate system coordinate transform formula from camera coordinate system:

$\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=A\left[\begin{array}{c}{X}_c^{\′}/Z_c^{\′}\\ Y_c^{\′}/Z_c^{\′}\\ 1\end{array}\right];$

Here $A=\left[\begin{array}{ccc}{f}_x& s& u_0\\ 0& f_y& v_0\\ 0& 0& 1\end{array}\right]$ For the internal matrix of video camera, s is the obliquity factor of video camera, i.e. the angle of imaging plane two vertical axis, f _x=f/d _x, f _y=f/d _y, f is the focal length of video camera, d _x, d _ybe the physical size of each pixel on x-axis, y-axis direction on image respectively, be all known parameters, by video camera, producer provides; u ₀, v ₀the image coordinate system initial point o in units of physical length _icoordinate under the image coordinate system in units of pixel.

6. the tracer method for designing being applied to surgical navigational gauge point error indicator according to claim 5, is characterized in that, in described step (5), the computational process of space relative error magnitudes is as follows:

(5-1) centered by theoretical sub-pix point, a circular or square range of error is determined, each some P got at random in above-mentioned range of error on left and right cameras imaging surface _li(i=1,2 ..., N), P _ri(i=1,2 ..., N), by P _liand P _rimatch one to one, form N ²plant combination;

(5-2) according to the formula in step (4-2), (4-3), the actual camera coordinate (X that each pixel described in step (5-1) is corresponding is obtained _c/ Z _c, Y _c/ Z _c, 1): P _iput under left camera coordinate system vector meets following relation:

Wherein t _lifor arbitrary value, make B _li=[X _lic/ Z _lic, Y _lic/ Z _lic, 1] ^t, then have in like manner can obtain, under right camera coordinate system vector meets following relation:

From O under system coordinate system _lpoint is to P _lithe vector of point for:

${\stackrel{\→}{P}}_{lgi}=R_{lgi}{B}_{li}{t}_{li}+T_{lgi}$

In like manner, under system coordinate system from O _rpoint is to P _rithe vector of point for:

Solving equation group $\left\{\begin{array}{c}{\stackrel{\→}{P}}_{lgi}=R_{lgi}{B}_{li}{t}_{li}+T_{lgi}\\ {\stackrel{\→}{P}}_{rgi}=R_{rgi}{B}_{ri}{t}_{ri}+T_{rgi}\end{array}\right.$ Namely P is tried to achieve _ithe coordinate of point under system coordinate system;

(5-3) N is obtained ²individual spatial point, after the coordinate under system coordinate system, calculates this N ²individual spatial point and former coordinate points distance average, as the relative error magnitudes of former spatial point.

7. the tracer method for designing being applied to surgical navigational gauge point error indicator according to claim 1, it is characterized in that, the described space relative error distribution visualization method by operating theater instruments position is: define a gray scale or color-bar, for each error amount gives a kind of gray scale or colour, build three-dimensional relative error distribution gray scale or color atlas, according to the distance of luminous point and binocular optical navigation system, two dimensional gray or color atlas and operating theater instruments luminous point position are shown.