CN104408719A - Three-collinear-feature-point monocular vision space positioning method - Google Patents

Abstract

The invention relates to a three-collinear-feature-point monocular vision space positioning method, and belongs to the field of machine vision. A camera system is positioned in a central perspective model during working; three collinear points are selected as feature points; one of the three collinear points serves as a center point; a relational expression between space coordinates of the feature points and projection coordinates is determined according to a perspective projection relation; and images, which are shot by a camera, of the feature points serve as the projection coordinates. According to the position relation, the length and the projection coordinates of the feature points, the determined relational expression is resolved, a coordinate position of three-dimensional space of the feature points is obtained, and the feature points are positioned. The positioning method can be implemented by algebraic operation, iterative operation is avoided, and the space positioning precision and the space positioning efficiency are improved.

Description

A kind of conllinear three unique point monocular vision space-location method

Technical field

The present invention relates to a kind of conllinear three unique point monocular vision space-location method, belong to technical field of machine vision.

Background technology

Monocular vision location is exactly only complete positioning work with a video camera.It has be simple and easy to and applied widely etc. specific, without the need to solving optimal distance in stereoscopic vision between two video cameras and Feature Points Matching problem, also can not produce very large distortion as omnibearing vision sensor.

In machine vision research field, under monocular vision condition, how to complete solving of position and attitude become an important research direction, monocular vision location technology is applied to many aspects, such as: camera calibration, robot localization, visual servo, target following and monitoring etc.

The researchist of various countries proposes the problem that a variety of algorithm solves monocular vision location, and the unique point wherein related to has coplanar also to be had non-coplanar, and the quantity of required unique point is also different, and algorithm adopts the algorithm of iterative approach mostly, and counting yield is low.

Summary of the invention

The object of the invention is a kind of conllinear three unique point monocular vision space-location method, with solve existing monocular vision space-location method adopt iterative approach algorithm cause counting yield low and not accurate enough problem.

Technical scheme of the present invention is: a kind of conllinear three unique point monocular vision space-location method, and it is characterized in that, this localization method comprises the following steps:

1) choose three collinear point as unique point, and one of them point is mid point;

2) the above-mentioned volume coordinate of three unique points and the relational expression of projection coordinate is determined according to projection projection relation;

3) use the image of located camera shooting unique point as projection coordinate, according to the position relationship between three unique points, length and projection coordinate to step 2) determined relational expression resolves, obtain the three dimensional space coordinate position of unique point, realize the location to unique point.

Described step 2) in determined relational expression be:

$z_a=f\frac{x_a}{{\mathrm{xu}}_a}$

$z_b=f\frac{x_b}{{\mathrm{xu}}_b}$

$z=f\frac{x}{\mathrm{xu}}$

$z_a=f\frac{y_a}{{\mathrm{yu}}_a}$

$z_b=f\frac{y_b}{{\mathrm{yu}}_b}$

$z=f\frac{y}{\mathrm{yu}}$

Wherein (x _a, y _a, z _a), (x _b, y _b, z _b) and (x, y, z) be respectively the volume coordinate of three unique point A, B and C, C is the mid point between AB, (xu _a, yu _a), (xu _b, yu _b) and (xu, yu) be respectively three unique point A, B and C projection coordinates on focal plane, focal length used when f is the projection coordinate of shooting unique point.

Described step 3) in located camera be operated in perspective projection model.

Described step 3) process carrying out resolving is as follows:

A) according to being wherein that the feature of mid point is to step 2) determined relational expression carries out abbreviation,

z+Δz-a ₁*x-a ₁*Δx＝0

z-Δz-a ₂*x+a ₂*Δx＝0

z-a ₃*x＝0

z+Δz-b ₁*y-b ₁*Δy＝0

z-Δz-b ₂*y+a ₂*Δy＝0

z-b ₃*y＝0

Wherein, a ₁=f/xu _a, a ₂=f/xu _b, a ₃=f/xu, b ₁=f/yu _a, b ₂=f/yu _b, b ₃=f/yu, Δ x=x _a-x=x-x _b, Δ y=y _a-y=y-y _b, Δ z=z _a-z=z-z _b, the focal length of f for adopting when video camera is taken, (xu _a, yu _a), (xu _b, yu _b), (xu, yu) unique point coordinate of arriving for video camera captured in real-time, a ₁, a ₂, a ₃, b ₁, b ₂, b ₃can calculate in real time;

B) result after abbreviation is carried out derive further and can obtain:

Δx＝z/c ₁

Δy＝z/c ₂

Δz＝z/c ₃

Wherein c ₁=(a ₁-a ₂) * a ₃/ (2a ₃-a ₁-a ₂), c ₂=(b ₁-b ₂) * b ₃/ (2b ₃-b ₁-b ₂) c ₃=(a ₁-a ₂) * a ₃/ (a ₁* a ₃+ a ₂* a ₃-2a ₁* a ₂);

C) length between any two unique points is brought into step B) relational expression of deriving and step 2) relational expression determined, the volume coordinate (x, y, z) solving unique point C is:

$x=\frac{\mathrm{xu}*z}{f}$

$y=\frac{\mathrm{yu}*z}{f}$

$z=\frac{L}{\sqrt{\frac{1}{{c_1}^2}+\frac{1}{{c_2}^2}+\frac{1}{{c_3}^2}}}$

Wherein L is the length of AC;

D) according to three unique point conllinear and one of them feature being mid point and step C) the middle point coordinate that calculates solves the volume coordinate of other two unique points, thus realizes the space orientation to three collinear feature points.

The invention has the beneficial effects as follows: the present invention will determine located camera system works in perspective model, by choosing three collinear point as unique point, and be wherein mid point, according to the relational expression of perspective projection relation determination unique point volume coordinate and projection coordinate, use the image of video camera shooting unique point as projection coordinate, according to the position relationship between unique point, length and projection coordinate, determined relational expression is resolved, thus obtain the three dimensional space coordinate position of unique point, realize the location to unique point.Localization method of the present invention adopts algebraic operation to complete, and avoids interative computation, improves sterically defined precision and efficiency.

Accompanying drawing explanation

Fig. 1 is perspective projection model coordinate system schematic diagram;

Fig. 2 is unique point spatial relationship schematic diagram.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is further described.

The object of this invention is to provide a kind of monocular vision space-location method of conllinear three unique point, to complete resolving of unique point locus fast and accurately.The present invention supposes that located camera system works is in perspective projection model.

1. choose 3 collinear point as unique point, be designated as A (x respectively _a, y _a, z _a), B (x _b, y _b, z _b) and C (x, y, z), A, B are respectively two end points, and C is the mid point of AB line, and the length of AC is L.

2. according to the relation of perspective projection relation determination unique point volume coordinate and projection coordinate.

As shown in Figure 1, camera coordinates is [Xc, Yc, Zc], and image coordinate is [xu, yu], according to perspective projection equation, then has:

$x_u=f\frac{x_c}{z_c}$

$y_u=f\frac{y_c}{z_c}$

Namely the x coordinate of subpoint is only relevant with z coordinate to the x coordinate of imaging focal length, unique point, and the y coordinate of subpoint is only relevant with z coordinate to the y coordinate of imaging focal length, unique point.

Video camera captured in real-time to three unique point coordinates be respectively A ' (xu _a, yu _a), B ' (xu _b, yu _b), C ' (xu, yu), focal length used during shooting is f.According to the pass between perspective projection relation determination unique point volume coordinate and projection coordinate be:

$z_a=f\frac{x_a}{{\mathrm{xu}}_a}---1-1$

$z_b=f\frac{x_b}{{\mathrm{xu}}_b}---1-2$

$z=f\frac{x}{\mathrm{xu}}---1-3$

$z_a=f\frac{y_a}{{\mathrm{yu}}_a}---1-4$

$z_b=f\frac{y_b}{{\mathrm{xu}}_b}---1-5$

$z=f\frac{y}{\mathrm{yu}}---1-6$

3., according to the position relationship between three unique points, C is the mid point of A, B, known:

x _a＝x+Δx 2-1

x _b＝x-Δx 2-2

y _a＝y+Δy 2-3

y _b＝y-Δy 2-4

z _a＝z+Δz 2-5

z _b＝z-Δz 2-6

4. according to the relation of locus coordinate between three unique points, the relational expression between determined unique point volume coordinate and projection coordinate is changed to:

$z+\mathrm{\Δz}=f\frac{x+\mathrm{\Δx}}{{\mathrm{xu}}_a}---3-1$

$z-\mathrm{\Δz}=f\frac{x-\mathrm{\Δx}}{{\mathrm{xu}}_b}---3-2$

$z=f\frac{x}{\mathrm{xu}}---3-3$

$z+\mathrm{\Δz}=f\frac{y+\mathrm{\Δy}}{{\mathrm{yu}}_a}---3-4$

$z-\mathrm{\Δz}=f\frac{y-\mathrm{\Δy}}{{\mathrm{yu}}_b}---3-5$

$z=f\frac{y}{\mathrm{yu}}---3-6$

5. formula is reduced to further:

z+Δz-a ₁*x-a ₁*Δx＝0 4-1

z-Δz-a ₂*x+a ₂*Δx＝0 4-2

z-a ₃*x＝0 4-3

z+Δz-b ₁*y-b ₁*Δy＝0 4-4

z-Δz-b ₂*y+a ₂*Δy＝0 4-5

z-b ₃*y＝0 4-6

Wherein:

a ₁＝f/xu _a

a ₂＝f/xu _b

a ₃＝f/xu

b ₁＝f/yu _a

b ₂＝f/yu _b

b ₃＝f/yu

F is known focal length, (xu _a, yu _a), (xu _b, yu _b), (xu, yu) unique point coordinate of arriving for video camera captured in real-time, therefore, a ₁, a ₂, a ₃, b ₁, b ₂, b ₃also can calculate in real time (being the equal of a known number).

6. derive further can obtain obtaining formula in step 5:

Δx＝z/c ₁5-1

Δy＝z/c ₂5-2

Δz＝z/c ₃5-3

Wherein:

c ₁＝(a ₁-a ₂)*a ₃/(2a ₃-a ₁-a ₂)

c ₂＝(b ₁-b ₂)*b ₃/(2b ₃-b ₁-b ₂)

c ₃＝(a ₁-a ₂)*a ₃/(a ₁*a ₃+a ₂*a ₃-2a ₁*a ₂)

7. due to the information dropout in projection process, only cannot obtain the spatial coordinate location of unique point with above-listed formula, therefore need extra and information is assisted.

By the prior demarcation to unique point, the length of known AC is L, then have:

$L=\sqrt{{\mathrm{\Δx}}^2+{\mathrm{\Δy}}^2+{\mathrm{\Δz}}^2}---5-4$

Formula 5-1,5-2,5-3 are substituted into 5-4 can obtain:

$z=\frac{L}{\sqrt{\frac{1}{{c_1}^2}+\frac{1}{{c_2}^2}+\frac{1}{{c_3}^2}}}---5-5$

The z solved by 5-5 substitutes in formula 1-3 and 1-6 can try to achieve x, y,

$x=\frac{\mathrm{xu}*z}{f}---5-6$

$y=\frac{\mathrm{yu}*z}{f}---5-7$

So far the volume coordinate (x, y, z) of mid point C is obtained.

The z solved by 5-5 substitutes in formula 5-1,5-2 and 5-3 can try to achieve Δ x, Δ y, Δ z, and the value of Δ x, Δ y, Δ z is substituted into the volume coordinate coordinate A (x that formula 2-1 to 2-6 can try to achieve A, B _a, y _a, z _a), B (x _b, y _b, z _b).

Claims (4)

1. a conllinear three unique point monocular vision space-location method, it is characterized in that, this localization method comprises the following steps:

1) choose three collinear point as unique point, and one of them point is mid point;

2) the above-mentioned volume coordinate of three unique points and the relational expression of projection coordinate is determined according to projection projection relation;

3) use the image of located camera shooting unique point as projection coordinate, according to the position relationship between three unique points, length and projection coordinate to step 2) determined relational expression resolves, obtain the three dimensional space coordinate position of unique point, realize the location to unique point.

2. conllinear three unique point monocular vision space-location method according to claim 1, is characterized in that, described step 2) in determined relational expression be:

$z_a=f\frac{x_a}{{\mathrm{xu}}_a}$

$z_b=f\frac{x_b}{{\mathrm{xu}}_b}$

$z=f\frac{x}{\mathrm{xu}}$

$z_a=f\frac{y_a}{{\mathrm{yu}}_a}$

$z_b=f\frac{y_b}{{\mathrm{yu}}_b}$

$z=f\frac{y}{\mathrm{yu}}$

Wherein (x _a, y _a, z _a), (x _b, y _b, z _b) and (x, y, z) be respectively the volume coordinate of three unique point A, B and C, C is the mid point between AB, (xu _a, yu _a), (xu _b, yu _b) and (xu, yu) be respectively three unique point A, B and C projection coordinates on focal plane, focal length used when f is the projection coordinate of shooting unique point.

3. conllinear three unique point monocular vision space-location method according to claim 1, is characterized in that, described step 3) in located camera be operated in perspective projection model.

4. conllinear three unique point monocular vision space-location method according to claim 2, is characterized in that, described step 3) process carrying out resolving is as follows:

A) according to being wherein that the feature of mid point is to step 2) determined relational expression carries out abbreviation,

z+Δz-a ₁*x-a ₁*Δx＝0

z-Δz-a ₂*x+a ₂*Δx＝0

z-a ₃*x＝0

z+Δz-b ₁*y-b ₁*Δy＝0

z-Δz-b ₂*y+a ₂*Δy＝0

z-b ₃*y＝0

Wherein, a ₁=f/xu _a, a ₂=f/xu _b, a ₃=f/xu, b ₁=f/yu _a, b ₂=f/yu _b, b ₃=f/yu, Δ x=x _a-x=x-x _b, Δ y=y _a-y=y-y _b, Δ z=z _a-z=z-z _b, the focal length of f for adopting when video camera is taken, (xu _a, yu _a), (xu _b, yu _b), (xu, yu) unique point coordinate of arriving for video camera captured in real-time, a ₁, a ₂, a ₃, b ₁, b ₂, b ₃can calculate in real time;

B) result after abbreviation is carried out derive further and can obtain:

Δx＝z/c ₁

Δy＝z/c ₂

Δz＝z/c ₃

Wherein c ₁=(a ₁-a ₂) * a ₃/ (2a ₃-a ₁-a ₂), c ₂=(b ₁-b ₂) * b ₃/ (2b ₃-b ₁-b ₂) c ₃=(a ₁-a ₂) * a ₃/ (a ₁* a ₃+ a ₂* a ₃-2a ₁* a ₂);

C) length between any two unique points is brought into step B) relational expression of deriving and step 2) relational expression determined, the volume coordinate (x, y, z) solving unique point C is:

$x=\frac{\mathrm{xu}*z}{f}$

$y=\frac{\mathrm{yu}*z}{f}$

$z=\frac{L}{\sqrt{\frac{1}{{c_1}^2}+\frac{1}{{c_2}^2}+\frac{1}{{c_3}^2}}}$

Wherein L is the length of AC;

D) according to three unique point conllinear and one of them feature being mid point and step C) the middle point coordinate that calculates solves the volume coordinate of other two unique points, thus realizes the space orientation to three collinear feature points.