CN1564044A - Large view field multiple solution imaging method based on reflection-retraction mechanism - Google Patents

Abstract

Elliptoid cone mirror surface and camera above the said mirror surface constitutes a reflection-refraction system. Horizontal section of the elliptoid cone mirror surface is an ellipse. The part of cambered surface with minor curvature is faced to watch center. The method includes steps: building a model in single vision point; spatial scene transformed to planar image; image plane coordinate transformed to world coordinate system, establishing horizontal viewing field and horizontal resolution as well as vertical viewing field and vertical resolution, thus, forming a transmissive projected image; computer processes the image through computer vision algorithm. Resolution of the image is higher in part with smaller curvature. Lower resolution in left and right side guarantees lager horizontal viewing field. The imaging method obtains image close to perception characteristic of human eye.

Description

Big visual field multiresolution formation method based on reflection-refraction mechanism

Technical field

The invention belongs to computer vision field, relate to imaging system in the computer vision, particularly a kind of big visual field multiresolution formation method based on reflection-refraction mechanism.

Background technology

1. foreword

Since the nineties in 20th century, the automatic driving of vehicle is the focus of automobile, information and automation field research always ^{[1] [2]}Intelligent vehicle is a Vehicular automatic driving control system that integrates multiple functions such as environment sensing, programmed decision-making, manipulation control, it also is the gordian technique in " intelligent transportation system (Intelligent Transformation System, ITS) " research at present.Intelligent vehicle can pass through active sensor (as laser radar/millimetre-wave radar) or passsive sensor (as vision sensor) perception external environment condition.Aspect realization vehicle perception external environment condition, after through exploration for many years, prove that utilizing machine vision is the most effective perceptive mode, therefore the general employing of design intelligent vehicle sensory perceptual system both at home and abroad is based on the technology path of machine vision ^[3], its basic function is by detecting the safety that track and barrier guarantee vehicle.Consider some driving behaviors: when vehicle in motion, the driver must be placed on more attention the place ahead of vehicle, fewer notice is placed on the left and right sides, even also be like this when changing or overtake other vehicles; Also to discern the barrier of the place ahead certain distance simultaneously, so that in time evade ^[4]Some studies show that during stationary vehicle, the horizontal field of view of human eye is 100 degree during speed of a motor vehicle 40km/h near 180 degree, 65 degree during 75km/h, 40 degree during 100km/h ^[5]For the traffic scene around the perception of robust ground, the vision system of intelligent vehicle preferably can have Selective Attention Mechanism as human driver, both need have higher resolution on some direction, needs a bigger visual field again.Obtain big visual field and can depend merely on dioptric system, for example fish eye lens is described with precise analytic model but fish-eye distortion is very difficult, can not provide multiresolution simultaneously; They can use the rotation camera to realize, but rotating camera are not suitable for dynamic scene, because can't catch large-scale scene simultaneously yet; Use a plurality of cameras to deal with problems to a certain extent, but with high costs, can not be applied to most of vehicles; Adopt reflection and refraction commingled system, as omnidirectional camera, but its resolution not with azimuthal variation, highest resolution does not reach the requirement of vision system security.

According to the data-searching that the applicant carried out, list of references related to the present invention has following several pieces:

[1]Steven?E.Shladover.etal.Automatic?vehicle?control?developments?in?the?PATHprogram.IEEE?Transactions?on?Vehicular?Technology，1991，Vol.40(1)：114-130。

[2]Steven?A.Nobe?et?al.An?overview?of?recent?developments?in?automated?lateraland?longitudinal?vehicle?controls.IEEE?International?conference?on?system，man?and?cybernetics，2001，Vol.5：3447-3452。

[3]Alberto?Broggi，Massimo?Bertozzi，Alessandra?fascioli，Gianni?Conte.Automatic?vehicle?guidance：The?experience?of?the?ARGO?autonomous?vehicle.World?Scientific?Publishing?Co.，1999。

[4]Xianghong?Liu.Development?of?a?vision-based?object?detection?and?recognitionsystem?for?intelligent?vehicle.Doctorial?dissertation.University?ofWisconsin-madison，2000。

[5] Zhang Dianye. the driver dynamic visual field and traffic safety fiduciary level. Southwest Jiaotong University's journal, 2000,35 (3), p:319-322 (Dianye Zhang.Dynamic visual field of driver with safety driving.Journal of Southwest Jiaotong University, 35 (3), p:319-322,2000).

[6]Simon?Baker，Shree?K.Nayar.A?theory?of?single-viewpoint?catadioptric?imageformation.International?journal?of?computer?vision?35(2)，p：175-196，1999

[7] Peng Qunsheng. the algorithm basis of computing machine photo realism graphic. Science Press .1999. Beijing.P：402-403。

[8]Shih-Schon?Lin，Bajcsy，R.True?single?view?point?cone?mirror?omni-directionalcatadioptric?system..Proceedings.Eighth?IEEE?International?Conference?on，Volume：2，7-14?July?2001，p：102-107。

Summary of the invention

At defective or deficiency that above-mentioned prior art exists, the applicant is subjected to the inspiration of omnidirectional camera, automobile rearview mirror and human eye Selective Attention Mechanism, proposes a kind of big visual field multiresolution formation method based on reflection-refraction mechanism.

Realize that the technical solution that the foregoing invention purpose is taked is, a kind of big visual field multiresolution formation method based on reflection-refraction mechanism, be characterized in, constitute a reflected refraction system by video camera and elliptical cone mirror, the position for video camera is in the top of elliptical cone mirror, the horizontal section of elliptical cone mirror is oval, makes the less that part of cambered surface of curvature towards watching the center attentively; This reflection-dioptric imaging method comprises: set up model with single view, spatial scene to the conversion of the plane of delineation, plane of delineation coordinate system to the conversion of world coordinate system, establish horizontal field of view and steps such as horizontal resolution, vertical field of view and vertical resolution, pass through above-mentioned steps, formed a width of cloth transmission projection image, this image just can be handled with common computer vision algorithms make subsequently.So just can make the resolution height of the center section of this optical system, the resolution of the left and right sides is low, has guaranteed bigger horizontal field of view simultaneously.Be the raising that cost has exchanged another part resolution for so just, thereby satisfied the automatic requirement of driving of intelligent vehicle to a certain extent resolution and visual field with the resolution that reduces a part.

Description of drawings

Fig. 1 is world coordinate system and plane of delineation coordinate system, wherein (1) reflection-dioptric system imaging synoptic diagram (2) horizontal resolution definition synoptic diagram (3) vertical field of view definition synoptic diagram (4) vertical resolution definition synoptic diagram;

Fig. 2 is the imaging point of point on the plane of delineation that is positioned on half concentric circles of ground level;

Fig. 3 is that horizontal resolution is with azimuthal Changing Pattern;

Fig. 4 be vertical field of view with azimuthal Changing Pattern, wherein dotted line is represented the coboundary, solid line is represented lower boundary;

Fig. 5 is that vertical resolution is with azimuthal Changing Pattern;

Fig. 6 is effective observation visual field of intelligent vehicle after the application multiresolution reflected refraction system

Fig. 7 is a single view multiresolution elliptical cone mirror reflection-dioptric system;

Fig. 8 is the off-the-air picture that reflection-dioptric system is gathered.

Embodiment

The present invention is described in further detail below in conjunction with technique scheme and the Figure of description that provides thereof and principle.

1. the principle of multiresolution reflected refraction system

1.1 the proof of single view constraint

As a reflection-dioptric system, wish that very it has single view [6], only in this way could determine five dimension full light functions [7], promptly from the deformation pattern of taking, produce how much correct transmission images.This is because under the constraint of single viewpoint, institute claps in the image each pixel all correspondence on certain direction, pass through the radiancy of the light of viewpoint.Because the geometric relationship of reflection-dioptric system is known, can calculated in advance go out the direction of each pixel correspondence.Therefore, just the radiation value of each pixel can be mapped on the plane apart from certain distance of viewpoint, thereby form a width of cloth transmission projection image.This image just can have been handled with common computer vision algorithms make subsequently.If for people watch, also need distortionless transmission projection image.

Among the present invention, system is had single view as one of main design object, prove that below reflection-dioptric system of being made up of elliptical cone mirror has single view (system prototype is seen Fig. 7).

Set up world coordinate system OXYZ as shown in Figure 1.Be without loss of generality, make true origin be positioned at the center of elliptic cone bottom surface ellipse, X-axis is located on the minor semi-axis of bottom surface ellipse, and Y-axis is located on the major semi-axis of bottom surface ellipse, and the Z axle is located on the center line of elliptic cone, and then the equation of elliptic cone is

$\frac{X^2}{a^2}+\frac{Y^2}{b^2}={(1-\frac{Z}{H})}^2---\left(1\right)$

A wherein, b is respectively the length of the minor semi-axis and the major semi-axis of bottom surface ellipse, and H is the height of elliptic cone.If $F(X,Y,Z)=\frac{X^2}{a^2}+\frac{Y^2}{b^2}-{(1-\frac{Z}{H})}^2=0,$ Then its partial derivative is:

$F_X(X_0,Y_0,Z_0)=\frac{{2X}_0}{a^2}=n_1$

$F_Y(X_0,Y_0,Z_0)=\frac{{2Y}_0}{b^2}=n_2---\left(2\right)$

$F_Z(X_0,Y_0,Z_0)=\frac{1}{H}(1-\frac{Z_0}{H})=n_3$

For 1 M (X on the elliptic cone ₀, Y ₀, Z ₀), its normal equation is

$\frac{X-X_0}{n_1}=\frac{Y-Y_0}{n_2}=\frac{Z-Z_0}{n_3}---\left(3\right)$

Shown in Fig. 1 (1), the center line OO ' that crosses elliptic cone makes cross section ∏ ₁, the angle on itself and XOZ plane is Φ, plane ∏ ₁Equation be

Y＝X·tgΦ (4)

Simultaneous equations (1), (4), plane ∏ ₁With the intersection O ' E of elliptic cone be (this paper only considers the situation of X 〉=0)

$X=\frac{1}{\sqrt{\frac{1}{a^2}+\frac{{\mathrm{tg}}^2\mathrm{\Φ}}{b^2}}}(1-\frac{Z}{H})---\left(5\right)$

$Y=X\·\mathrm{tg\Φ}$

Obviously this intersection is a straight line.

For any point on intersection O ' E, according to (3) and (5), its normal direction is

$n_1=\frac{2}{a^2\sqrt{\frac{1}{a^2}+\frac{{\mathrm{tg}}^2\mathrm{\Φ}}{b^2}}},n_2=\frac{2}{b^2\sqrt{\frac{1}{a^2}+\frac{{\mathrm{tg}}^2\mathrm{\Φ}}{b^2}}}\mathrm{tg\Φ},n_3=\frac{2}{H}---\left(6\right)$

Formula (6) illustrates that the normal direction of being had a few on intersection O ' E is identical, and forms a plane ∏ 2 by the elliptic cone summit.As plane ∏ ₁When crossing bottom surface long axis of ellipse or minor axis, plane ∏ 2 and plane ∏ ₁Overlap, otherwise they do not overlap.According to the reflection of light principle, all incident raies in the plane ∏ 2 through O ' E reflection after all in this plane.So just consistent with situation in [8], this situation has been proved to be in [6] has single view, so this reflection-dioptric system also is a single view.

1.2 spatial scene is to the conversion of the plane of delineation

As Fig. 1, (Z) (known quantity) must have 1 M (X at elliptic cone for X, Y for 1 W in the space ₀, Y ₀, Z ₀) (amount to be asked), make M (X ₀, Y ₀, Z ₀) normal located cross W (X, Y, Z).According to (1), (2) and (3) formula, establishment establishes an equation under having:

$\frac{X^2}{{\[a(1-\frac{Z_0}{H})+\frac{H}{a}(Z-Z_0)\]}^2}+\frac{Y^2}{{\[b(1-\frac{Z_0}{H})+\frac{H}{b}(Z-Z_0)\]}^2}=1---\left(7\right)$

$X_0=X\frac{1}{1+\frac{H}{a^2(1-\frac{Z_0}{H})}(Z-Z_0)}---\left(8\right)$

$Y_0=Y\frac{1}{1+\frac{H}{b^2(1-\frac{Z_0}{H})}(Z-Z_0)}---\left(9\right)$

If W ' (X ', Y ', Z ') be W (X, Y, virtual image Z), promptly W ' (X ', Y ', Z ') is that (X, Y is Z) with respect to M (X for W ₀, Y ₀, Z ₀) symmetric points, according to the geometrical optics principle of reflection, have

X′＝2X ₀-X

Y′＝2Y ₀-Y (10)

Z′＝2Z ₀-Z

Set up the plane of delineation coordinate system xoy shown in Fig. 1 (1), then W (X, Y, imaging point I Z) (x y) is:

$x=f\frac{X^{\′}}{Z^{\′}-H}---\left(11\right)$

$y=f\frac{-Y^{\′}}{Z^{\′}-H}$

Wherein f is a focus of camera.

In (7), because Z ₀There are not analytic solution, so applied numerical method is found the solution.

1.3 plane of delineation coordinate system is to the conversion of world coordinate system

In order to obtain the transmission projection image of people's custom, can realize by following method: at first will reflect-image mapped to of dioptric system collection is on the plane of viewpoint O ' certain distance, the photocentre of supposing a common transmission camera then is positioned on the viewpoint O ', adjust the inside and outside parameter of this transmission camera, just can generate required image.The present invention only considers point on the Z=h plane, space and the corresponding relation between the point on the plane of delineation.If 1 W in space (X, Y, h), by the some M (X on the elliptic cone ₀, Y ₀, Z ₀) virtual image point be W ' (X ', Y ', Z '), be similar to the derivation in 2.2 joints, have:

$X^{\′}=\frac{x}{f}(Z^{\′}-H)$

$Y^{\′}=-\frac{y}{f}(Z^{\′}-H)---\left(12\right)$

$Z^{\′}=2Z_0-h$

$\frac{X^{\′2}}{{\[a(1-\frac{Z_0}{H})+\frac{H}{a}(Z^{\′}-Z_0)\]}^2}+\frac{Y^{\′2}}{{\[b(1-\frac{Z_0}{H})+\frac{H}{b}(Z^{\′}-Z_0)\]}^2}=1---\left(13\right)$

Therefore:

$\frac{{\[\frac{x}{f}({2Z}_0-h-H)\]}^2}{{\[a(1-\frac{Z_0}{H})+\frac{H}{a}(Z_0-h)\]}^2}+\frac{{\[-\frac{y}{f}({2Z}_0-h-H)\]}^2}{{\[b(1-\frac{Z_0}{H})+\frac{H}{b}(Z_0-h)\]}^2}=1---\left(14\right)$

$X_0=X^{\′}\frac{1}{1+\frac{H}{a^2(1-\frac{Z_0}{H})}(Z^{\′}-Z_0)}---\left(15\right)$

$Y_0=Y^{\′}\frac{1}{1+\frac{H}{b^2(1-\frac{Z_0}{H})}(Z^{\′}-Z_0)}---\left(16\right)$

Then imaging point I (x, y) corresponding coordinates of spatial points is on the Z=h plane:

X＝2X ₀-X′

Y＝2Y ₀-Y′ (17)

Z＝h

Z in the formula (14) ₀Also use numerical methods of solving.

1.4 horizontal field of view and horizontal resolution

Obviously, horizontal field of view was up to 180 degree when this system was used for intelligent vehicle, and this section is mainly discussed resolution.Shown in Fig. 1 (2), in OXYZ coordinate system OXY plane, be that radius is justified with r, establishing has 2 W in the space ₁And W ₂, they are to the projection W on OXY plane ₁' and W ₂' all drop on the circle OW ₁' and the angle on OXZ plane be Φ, promptly with respect to the position angle of X-axis, OW ₁' and OW ₂' between angle be d Φ, their imaging points on the plane of delineation are I ₁(x ₁, y ₁) and I ₂(x ₂, y ₂), I ₁O ' and I ₂Angle between the O ' is d , and horizontal resolution is defined as follows:

W ₁The coordinate of point is (X ₁, Y ₁, h),

X ₁＝rcosΦ，Y ₁＝rsinΦ，Z ₁＝h (19)

W ₂The coordinate of point is (X ₂, Y ₂, h)

X ₂＝rcos(Φ+dΦ)，Y ₂＝rsin(Φ+dΦ)，Z ₂＝h (20)

In conjunction with formula (11), just can obtain resolution with azimuthal variation.

1.5 vertical field of view and vertical resolution

Because the reflective optical devices that uses is an elliptic cone, is not solid of revolution, so be different at its vertical field of view of different horizontal directions.If circular conical surface, then the vertical field of view of all directions is identical.Shown in Fig. 1 (3), establishing has straight line in the space, and its equation is

Y＝rsinΦ，X＝rcosΦ (21)

Respectively there is an intersection points B lower boundary and the coboundary of itself and vertical field of view _Min, B _Max, their height is respectively Z _MinAnd Z _Max, then

${\mathrm{\θ}}_{\min }=\mathrm{arctg}\frac{Z_{\min }-H}{r},{\mathrm{\θ}}_{\max }=\mathrm{arctg}\frac{Z_{\max }-H}{r},\mathrm{FOV}={\mathrm{\θ}}_{\max }-{\mathrm{\θ}}_{\max }---\left(22\right)$

Shown in Fig. 1 (4), for the W on certain position angle Φ ₁(rcos Φ, rsin Φ, Z) and W ₂(rcos Φ, rsin Φ, Z+dZ), O ' W ₁And O ' W ₂Between angle be d Θ, their imaging points on the plane of delineation are I ₁(x ₁, y ₁) and I ₂(x ₂, y ₂), I ₁O ' and I ₂Angle between the O ' is d θ, and vertical resolution is defined as follows:

${\mathrm{\ϵ}}_v=\frac{\mathrm{d\θ}}{\mathrm{d\Θ}}---\left(23\right)$

Wherein

$\mathrm{d\θ}=\arccos \frac{x_1{x}_2+y_1{y}_2+f^2}{\sqrt{(x_1^2+y_1^2+f^2)(x_2^2+y_2^2+f^2)}}$

$\mathrm{d\Φ}=\arccos \frac{{2r}^2+{(Z-H)}^2+{(Z+\mathrm{dZ}-H)}^2-{\mathrm{dZ}}^2}{2\sqrt{(r^2+{(Z-H)}^2)(r^2+{(Z+\mathrm{dZ}-H)}^2)}}$

By above-mentioned steps, formed a width of cloth transmission projection image, this image just can be handled with common computer vision algorithms make subsequently.

2. result and analysis

2.1 simulation result

Analyze for the performance to this system, the author has carried out emulation experiment, and condition is r=20m, h=0m, Φ ∈ (pi/2, pi/2), H=1.5m, a=1.5m, b=1.85m, f=6mm.Fig. 2 is one group, and to be positioned at O be half concentrically ringed imaging on the plane of delineation on the Z=0 plane in the center of circle, can find that the target of circular distribution has become oval distribution, and the spacing of middle imaging point is greater than both sides.The variation of horizontal resolution and the relation between the position angle as shown in Figure 3, the ratio of ultimate resolution and minimum resolution depends on the oval minor axis and the ratio of major axis, maximal value almost is 6 times of minimum value herein.

Relation between vertical field of view and the position angle as shown in Figure 4, what is interesting is when Φ ∈ [pi/2, pi/2) time, the maximal value of vertical field of view is identical on each horizontal direction, has only minimum value to change.This is because the minimum value θ of vertical field of view _MinDepend on the size of the imaging target surface of CCD, and maximal value θ _MaxThe ratio that depends on the minor axis a of the height H of elliptic cone and bottom surface ellipse.Vertical resolution with azimuthal variation as shown in Figure 5, its value approaches 1.This is that its imaging in vertical direction does not have distortion because for circular cone border face, and the vertical resolution of reflection-dioptric system equals the resolution of lens combination, and its value is 1.And for elliptic cone border face, as save described in 2.1 plane ∏ ₂And ∏ ₁Do not overlap, so vertical resolution approaches 1, only vertical resolution is only 1 on minor axis and long axis direction.

If the photosensitive unit of CCD chip is equally distributed, the size of target is certain, then vehicle-mounted vision system reliably around the detection and Identification scope of target as shown in Figure 6, similar with human driver's range of observation substantially, so native system is more more reasonable than other Vision Builder for Automated Inspection.

2.2 system prototype

For multiresolution and the big visual field characteristics of verifying that native system has, the author has made the reflection-dioptric system prototype of a single view multiresolution elliptical cone mirror.SONY DSR-PD150P DVCAM is used as the transmission camera, and focal length is set to 6mm, has removed light shield.The height of elliptic cone is 0.1m, and the minor axis of bottom surface ellipse is 0.1m, and major axis is 0.13m, surface coverage one deck reflectorized material.The structure of system prototype as shown in Figure 7, the deformation pattern of shooting as shown in Figure 8, therefrom as can be seen the below in the middle of image more clear than both sides.This image can be transformed to normal transmission projection image.

3. conclusion

This reflection-dioptric system manager proves bright have single view and multiresolution, has the Selective Attention Mechanism of human eye to a certain extent, by adjusting the ratio of bottom surface ellipse short shaft and major axis, can change the distribution of resolution.Utilize pinhole imaging system model and geometric optical imaging model, horizontal resolution, vertical field of view and the vertical resolution of having calculated this system respectively are with azimuthal Changing Pattern.The prototype verification that makes up based on method that the author carried theoretical analysis, in addition should new system make and safeguard simple, analysis easily, cost is low, and needed resolution of intelligent vehicle navigation and visual field but can be provided, and is better than more existing vehicle-mounted vision systems.This system can also be used for aspects such as virtual reality, teleconference, video monitor.

Claims (1)

1. big visual field multiresolution formation method based on reflection-refraction mechanism, it is characterized in that, constitute a reflected refraction system by video camera and elliptical cone mirror, the position for video camera is in the top of elliptical cone mirror, the horizontal section of elliptical cone mirror is oval, makes the less that part of cambered surface of curvature towards watching the center attentively;

This reflection-dioptric imaging method may further comprise the steps:

1) sets up model with single view

Set up world coordinate system OXYZ, make true origin be positioned at the center of elliptic cone bottom surface ellipse, X-axis is located on the minor semi-axis of bottom surface ellipse, and Y-axis is located on the major semi-axis of bottom surface ellipse, and the Z axle is located on the center line of elliptic cone, and then the equation of elliptic cone is

$\frac{X^2}{a^2}+\frac{Y^2}{b^2}={(1-\frac{Z}{H})}^2---\left(1\right)$

A wherein, b is respectively the length of the minor semi-axis and the major semi-axis of bottom surface ellipse, and H is the height of elliptic cone;

If $F(X,Y,Z)=\frac{X^2}{a^2}+\frac{Y^2}{b^2}-{(1-\frac{Z}{H})}^2=0,$ Then its partial derivative is:

$F_X(X_0,Y_0,Z_0)=\frac{{2X}_0}{a^2}=n_1$

$F_Y(X_0,Y_0,Z_0)=\frac{{2Y}_0}{b^2}=n_2---\left(2\right)$

$F_Z(X_0,Y_0,Z_0)=\frac{1}{H}(1-\frac{Z_0}{H})=n_3$

For 1 M (X on the elliptic cone ₀, Y ₀, Z ₀), its normal equation is:

$\frac{{X-X}_0}{n_1}=\frac{{Y-Y}_0}{n_2}=\frac{{Z-Z}_0}{n_3}---\left(3\right)$

The center line OO ' that crosses elliptic cone makes cross section Π ₁, the angle on itself and XOZ plane is Φ, plane Π ₁Equation be:

Y＝X·tgΦ (4)

Simultaneous equations (1), (4), the plane Π 1 and the intersection O ' E of elliptic cone are

$X=\frac{1}{\sqrt{\frac{1}{a^2}+\frac{{\mathrm{tg}}^2\mathrm{\Φ}}{b^2}}}(1-\frac{Z}{H})---\left(5\right)$

Y＝X·tgΦ

Only consider the situation of X 〉=0 in the formula, obviously this intersection is a straight line;

For any point on intersection O ' E, according to (3) and (5), its normal direction is:

$n_1=\frac{2}{a^2\sqrt{\frac{1}{a^2}+\frac{{\mathrm{tg}}^2\mathrm{\Φ}}{b^2}}},$

$n_2=\frac{2}{b^2\sqrt{\frac{1}{a^2}+\frac{{\mathrm{tg}}^2\mathrm{\Φ}}{b^2}}}\mathrm{tg\Φ},$

$n_3=\frac{2}{H}---\left(6\right)$

Formula (6) illustrates that the normal direction of being had a few on intersection O ' E is identical, and forms a plane Π 2 by the elliptic cone summit; As plane Π ₁When crossing bottom surface long axis of ellipse or minor axis, plane Π 2 and plane Π ₁Overlap, otherwise they do not overlap;

2) spatial scene is to the conversion of the plane of delineation

(X, Y Z), must have a bit (amount to be asked) M (X at elliptic cone for some known quantity W in the space ₀, Y ₀, Z ₀), make M (X ₀, Y ₀, Z ₀) normal located cross W (X, Y, Z); According to (1), (2) and (3), establishment establishes an equation under having:

$\frac{X^2}{[a(1-\frac{Z_0}{H})+\frac{H}{a}\left({Z-Z}_0\right){]}^2}+\frac{Y^2}{[b(1-\frac{Z_0}{H})+\frac{H}{b}\left({Z-Z}_0\right){]}^2}=1---\left(7\right)$

$X_0=X\frac{1}{1+\frac{H}{a^2(1-\frac{Z_0}{H})}\left({Z-Z}_0\right)}---\left(8\right)$

$Y_0=Y\frac{1}{1+\frac{H}{b^2(1-\frac{Z_0}{H})}\left({Z-Z}_0\right)}---\left(9\right)$

If W ' (X ', Y ', Z ') be W (X, Y, virtual image Z), promptly W ' (X ', Y ', Z ') is that (X, Y is Z) with respect to M (X for W ₀, Y ₀, Z ₀) symmetric points, according to the geometrical optics principle of reflection, have:

X′＝2X ₀-X

Y′＝2Y ₀-Y (10)

Z′＝2Z ₀-Z

Set up plane of delineation coordinate system xoy, then W (X, Y, imaging point I Z) (x y) is:

$x=f\frac{X^{\′}}{Z^{\′}-H}---\left(11\right)$

$y=f\frac{-Y^{\′}}{Z^{\′}-H}$

Wherein f is a focus of camera;

In (7), because Z ₀There are not analytic solution, so applied numerical method is found the solution;

3) plane of delineation coordinate system is to the conversion of world coordinate system

At first will reflect-image mapped to that dioptric system is gathered is on the plane of viewpoint O ' certain distance, the photocentre of supposing a common transmission camera then is positioned on the viewpoint O ', adjust the inside and outside parameter of this transmission camera, just can generate required image; Only consider point on the Z=h plane, space and the corresponding relation between the point on the plane of delineation; If 1 W in space (X, Y, h), by the some M (X on the elliptic cone ₀, Y ₀, Z ₀) virtual image point be W ' (X ', Y ', Z '), have

$X^{\′}=\frac{x}{f}(Z^{\′}-H)$

$Y^{\′}=-\frac{y}{f}(Z^{\′}-H)---\left(12\right)$

Z′＝2Z ₀-h

$\frac{X^{\′2}}{[a(1-\frac{Z_0}{H})+\frac{H}{a}(Z^{\′}-Z_0){]}^2}+\frac{Y^{\′2}}{[b(1-\frac{Z_0}{H})+\frac{H}{b}(Z^{\′}-Z_0){]}^2}=1---\left(13\right)$

Therefore

$\frac{[\frac{x}{f}(2Z_0-h-H){]}^2}{[a(1-\frac{Z_0}{H})+\frac{H}{a}(Z_0-h){]}^2}+\frac{[-\frac{y}{f}({2Z}_0-h-H){]}^2}{[b(1-\frac{Z_0}{H})+\frac{H}{b}(Z_0-h){]}^2}=1---\left(14\right)$

$X_0=X^{\′}\frac{1}{1+\frac{H}{a^2(1-\frac{Z_0}{H})}(Z^{\′}-Z_0)}---\left(15\right)$

$Y_0=Y^{\′}\frac{1}{1+\frac{H}{b^2(1-\frac{Z_0}{H})}(Z^{\′}-Z_0)}---\left(16\right)$

Then imaging point I (x, y) corresponding coordinates of spatial points is on the Z=h plane:

X＝2X ₀-X′

Y＝2Y ₀-Y′ (17)

Z＝h

Z in the formula (14) ₀Also use numerical methods of solving;

4) establish horizontal field of view and horizontal resolution

In OXYZ coordinate system OXY plane, be that radius is justified with r, establishing has 2 W in the space ₁And W ₂, they are to the projection W on OXY plane ₁' and W ₂' all drop on the circle OW ₁' and the angle on OXZ plane be Φ, promptly with respect to the position angle of X-axis, OW ₁' and OW ₂' between angle be d Φ, their imaging points on the plane of delineation are I ₁(x ₁, y ₁) and I ₂(x ₂, y ₂), I ₁O ' and I ₂Angle between the O ' is d , and horizontal resolution is defined as follows:

Wherein:

W ₁The coordinate of point is (X ₁, Y ₁, h)

X ₁＝rcosΦ，Y ₁＝rsinΦ，Z ₁＝h (19)

W ₂The coordinate of point is (X ₂, Y ₂, h)

X ₂＝rcos(Φ+dΦ)，Y ₂＝rsin(Φ+dΦ)，Z ₂＝h (20)

In conjunction with formula (11), just can obtain resolution with azimuthal variation;

5) vertical field of view and vertical resolution

Because the reflective optical devices that uses is an elliptic cone, is not solid of revolution, so be different at its vertical field of view of different horizontal directions; If circular conical surface, then the vertical field of view of all directions is identical; Vertical field of view is defined as follows:

If straight line is arranged in the space, its equation is

Y＝rsinΦ，X＝rcosΦ (21)

Respectively there is an intersection points B lower boundary and the coboundary of itself and vertical field of view _Min, B _Max, their height is respectively Z _MinAnd Z _Max, then

${\mathrm{\θ}}_{\min }=\mathrm{arctg}\frac{Z_{\min }-H}{r},{\mathrm{\θ}}_{\max }=\mathrm{arctg}\frac{Z_{\max }-H}{r},\mathrm{FOV}={\mathrm{\θ}}_{\max }-{\mathrm{\θ}}_{\min }---\left(22\right)$

For the W on certain position angle Φ ₁(rcos Φ, rsin Φ, Z) and W ₂(rcos Φ, rsin Φ, Z+dZ), O ' W ₁And O ' W ₂Between angle be d Θ, their imaging points on the plane of delineation are I ₁(x ₁, y ₁) and I ₂(x ₂, y ₂), I ₁O ' and I ₂Angle between the O ' is d θ, and vertical resolution is defined as follows:

${\mathrm{\ϵ}}_v=\frac{\mathrm{d\θ}}{\mathrm{d\Θ}}---\left(23\right)$

Wherein

$\mathrm{d\θ}=\arccos \frac{x_1{x}_2+y_1{y}_2+f^2}{\sqrt{(x_1^2+y_1^2+f^2)(x_2^2+y_2^2+f^2)}}$

$\mathrm{d\Φ}=\arccos \frac{{2r}^2+{(Z-H)}^2+{(Z+\mathrm{dZ}-H)}^2-{\mathrm{dZ}}^2}{2\sqrt{(r^2+{(Z-H)}^2)(r^2+{(Z+\mathrm{dZ}-H)}^2)}}$

By above-mentioned steps, formed a width of cloth transmission projection image, this image just can be handled with common computer vision algorithms make subsequently.

Images