CN102663742A - Determination method of rotary stereo visual rotation axis based on quadratic curve fitting - Google Patents

Determination method of rotary stereo visual rotation axis based on quadratic curve fitting Download PDF

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Publication number
CN102663742A
CN102663742A CN2012100785794A CN201210078579A CN102663742A CN 102663742 A CN102663742 A CN 102663742A CN 2012100785794 A CN2012100785794 A CN 2012100785794A CN 201210078579 A CN201210078579 A CN 201210078579A CN 102663742 A CN102663742 A CN 102663742A
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China
Prior art keywords
point
turning axle
image
projection
rotation axis
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CN2012100785794A
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Chinese (zh)
Inventor
陈胜勇
刘大伟
汪晓妍
刘盛
王万良
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Zhejiang University of Technology ZJUT
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Zhejiang University of Technology ZJUT
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Priority to CN2012100785794A priority Critical patent/CN102663742A/en
Publication of CN102663742A publication Critical patent/CN102663742A/en
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Abstract

A determination method of a rotary stereo visual rotation axis based on quadratic curve fitting comprises the following steps: (1) Acquiring point tracking on an image; (2) After several discrete points on a projection image of a spatial circle formed through rotating the point are acquired, fitting and acquiring a corresponding quadratic curve according to the discrete points; (3) Calculating the image of an infinitely straight line; (4) Taking the projection of the spatial circle formed through rotating the point in space as the quadratic curve Ci, wherein a corresponding center oi satisfies the following formula: oi=Cil endlessness and the center is the projection of the point on the rotation axis; (5) After the central point of the quadratic curve is acquired, reconstructing the central point so as to obtain a spatial point on the rotation axis; (6) according to the point on the rotation axis, fitting and acquiring the rotary stereo visual rotation axis. The invention provides the determination method of the rotary stereo visual rotation axis based on the quadratic curve fitting. By using method, calculating can be simplified, precision can be increased and practicability is good.

Description

Definite method based on the rotating stereovision turning axle of conic fitting
Technical field
The present invention relates to fields such as computer vision, Flame Image Process, graphics, how much, mathematics, especially a kind of method of rotating stereovision.
Background technology
Turning axle commonly used at present confirms that method is a discrete point coordinate position on the left track when perhaps some put the rotation on universal stage through the demarcation thing; Obtain space tracking by discrete point then, after calculate the character calculating turning axle of confirming that the center of circle is perhaps intersected through Surface Method vector and turning axle.The technological deficiency that existing definite method exists: calculation of complex, precision is lower, practicality is relatively poor.
Summary of the invention
For the deficiency that calculation of complex, precision are lower, practicality is relatively poor of definite method of overcoming existing rotating stereovision turning axle, the present invention provides a kind of and simplifies calculating, promote precision, have the definite method based on the rotating stereovision turning axle of conic fitting of good practicality.
The technical solution adopted for the present invention to solve the technical problems is:
A kind of definite method of the rotating stereovision turning axle based on conic fitting, definite method of said rotating stereovision turning axle may further comprise the steps:
(1) obtains the tracking of putting on the image;
(2) after some discrete points on the projected image that has obtained the formed space circle of certain some rotation, obtain corresponding quafric curve according to said discrete point match, the equation of quafric curve is:
ax 2+by 2+cx+dy+e＝0
Wherein a, b, c, d and e are the coefficients of quafric curve, are written as matrix form to be:
x 2 y 2 x y 1 a b c d e = 0 As n discrete point, then matrix of coefficients is n * 5 matrixes, goes out quafric curve with least square fitting;
(3) ask the image of line at infinity: focoid are on line at infinity, and the space focoid are [1,0, ± i, 0] T, after the projection matrix projection, can form two points is c iAnd c j, obtain the image l of line at infinity by these two points ∞=c i* c j
(4) make space point rotate formed space circle and be projected as quafric curve C i, its corresponding center o then i=c il ∞, promptly be the projection of certain point on the turning axle;
(5) after obtaining the central point of quafric curve, rebuild said central point and promptly obtain the spatial point on the turning axle;
Get wherein two width of cloth images and promptly can rebuild certain point on the turning axle, suppose that certain unknown point is X on the turning axle w, its projection calculates through said method and is o i, the projection matrix that wherein two width of cloth images are corresponding is P 1And P 2, then obtain by linear camera model:
o i＝P 1X w
o i＝P 2X w
Get a spatial point on the turning axle by top solution of equation;
(6) according to the point on the turning axle, match obtains the rotating stereovision turning axle.
Further, in the said step (3), be the image of line at infinity with respect to the hachure that disappears that the limit of some imaging planes simulates this Plane of rotation through every other image.
Beneficial effect of the present invention mainly shows: simplify calculating, promote precision, have good practicality.
Description of drawings
Fig. 1 is the synoptic diagram of each limit of relative first width of cloth image.
Fig. 2 is the parameter synoptic diagram of discrete point rotational trajectory.
Fig. 3 is the synoptic diagram of line at infinity.
Fig. 4 is the turning axle synoptic diagram of rebuilding.
Embodiment
Below in conjunction with accompanying drawing the present invention is further described.
With reference to Fig. 1～Fig. 4, a kind of definite method of the rotating stereovision turning axle based on conic fitting, definite method of said rotating stereovision turning axle may further comprise the steps:
(1) obtains the tracking of putting on the image;
(2) after some discrete points on the projected image that has obtained the formed space circle of certain some rotation, obtain corresponding quafric curve according to said discrete point match, the equation of quafric curve is:
ax 2+by 2+cx+dy+e＝0
Wherein a, b, c, d and e are the coefficients of quafric curve, are written as matrix form to be:
x 2 y 2 x y 1 a b c d e = 0 As n discrete point, then matrix of coefficients is n * 5 matrixes, goes out quafric curve with least square fitting;
(3) ask the image of line at infinity: focoid are on line at infinity, and the space focoid are [1,0, ± i, 0] T, after the projection matrix projection, can form two points is c iAnd c j, obtain the image l of line at infinity by these two points ∞=c i* c j
(4) make space point rotate formed space circle and be projected as quafric curve C i, its corresponding center o then i=C il ∞, promptly be the projection of certain point on the turning axle;
(5) after obtaining the central point of quafric curve, rebuild said central point and promptly obtain the spatial point on the turning axle;
Get wherein two width of cloth images and promptly can rebuild certain point on the turning axle, suppose that certain unknown point is X on the turning axle w, its projection calculates through said method and is o i, the projection matrix that wherein two width of cloth images are corresponding is P 1And P 2, then obtain by linear camera model:
o i＝P 1X w
o i＝P 2X w
Get a spatial point on the turning axle by top solution of equation;
(6) according to the point on the turning axle, match obtains the rotating stereovision turning axle.
In the present embodiment; Under the constant situation of the intrinsic parameter of video camera; When rotating with rotation platform, the rotary motion trace of any point on the rotation platform on the object (removing the point on the turning axle) is a space circle, and such space circle will become a quafric curve through projection.Confirm that based on the turning axle of conic fitting the method concrete steps are following:
(1) obtains the tracking of certain point.The tracking of point can realize automatically, but for for the purpose of accurately, we by hand method obtain the tracking of certain point.Also possibly have some error owing to manually confirm certain point on the image, can be auxiliary with program, promptly searching for angle point in the scope around the determined point of mouse, the some tracking meeting that obtains like this is more accurate.
(2) match quafric curve.After some discrete points on the projected image that has obtained the formed space circle of certain some rotation, obtain corresponding quafric curve according to these discrete point matches, the equation of quafric curve is:
ax 2+by 2+cx+dy+e＝0
Being written as matrix form is:
x 2 y 2 x y 1 a b c d e = 0
As n discrete point, then matrix of coefficients is n * 5 matrixes, can go out quafric curve with least square fitting.
(3) ask the image of line at infinity.The most directly and simply asking the method for line at infinity image for the image of having demarcated is that image by focoid calculates.Focoid are on line at infinity, and the space focoid are [1,0, ± i, 0] T, after the projection matrix projection, can form two points is c iAnd c j, obtain the image l of line at infinity by these two points ∞=c i* c j
The another kind of method of asking the line at infinity image is to find the solution through each limit.Under the single shaft rotation; Every other image with respect to the limit of some imaging planes all on same straight line; And this straight line is exactly the hachure that disappears of this Plane of rotation, so another kind of method then is to be the image of line at infinity through every other image with respect to the hachure that disappears that the limit of some imaging planes simulates this Plane of rotation.As shown in Figure 1, the center of all video cameras on same imaging plane, o i, o jAnd o kProjection on first width of cloth image is limit e I1, e J1And e K1, all on same straight line L, L promptly is the image l of line at infinity to these limits ∞
(4) center of calculating quafric curve, the i.e. image of certain point on the turning axle.Make space point rotate formed space circle and be projected as quafric curve C i, its corresponding center o then i=C il ∞, promptly be the projection of certain point on the turning axle.
(5) point on the turning axle of reconstruction space.After obtaining the central point of some quafric curves, rebuild these central points and promptly obtain the spatial point on the turning axle.The image of turning axle is a not moving-wire in all images, so the coordinate of the image of certain point in any image all is identical on the turning axle that we ask, gets wherein two width of cloth images and promptly can rebuild certain point on the turning axle.Suppose that certain unknown point is X on the turning axle w, its projection calculates through said method and is o i, the projection matrix that wherein two width of cloth images are corresponding is P 1And P 2, then have linear camera model to obtain:
o i＝P 1X w
o i＝P 2X w
Can solve a spatial point on the turning axle by top equation.
(6) match space turning axle.As long as the point on enough turning axles is arranged, the space turning axle promptly can be tried to achieve in match.

Claims (2)

1. based on definite method of the rotating stereovision turning axle of conic fitting, it is characterized in that:
Definite method of said rotating stereovision turning axle may further comprise the steps:
(1) obtains the tracking of putting on the image;
(2) after some discrete points on the projected image that has obtained the formed space circle of certain some rotation, obtain corresponding quafric curve according to said discrete point match, the equation of quafric curve is:
ax 2+by 2+cx+dy+e＝0
Wherein a, b, c, d and e are the coefficients of quafric curve, are written as matrix form to be:
x 2 y 2 x y 1 a b c d e = 0
As n discrete point, then matrix of coefficients is n * 5 matrixes, goes out quafric curve with least square fitting;
(3) ask the image of line at infinity: focoid are on line at infinity, and the space focoid are [1,0, ± i, 0] T, after the projection matrix projection, can form two points is c iAnd c j, obtain the image l of line at infinity by these two points ∞=c i* c j
(4) make space point rotate formed space circle and be projected as quafric curve C i, its corresponding center o then i=C il ∞, promptly be the projection of certain point on the turning axle;
(5) after obtaining the central point of quafric curve, rebuild said central point and promptly obtain the spatial point on the turning axle;
Get wherein two width of cloth images and promptly can rebuild certain point on the turning axle, suppose that certain unknown point is X on the turning axle w, its projection calculates through said method and is o i, the projection matrix that wherein two width of cloth images are corresponding is P 1And P 2, then obtain by linear camera model:
o i＝P 1X w
o i＝P 2X w
Get a spatial point on the turning axle by top solution of equation;
(6) according to the point on the turning axle, match obtains the rotating stereovision turning axle.
2. definite method of the rotating stereovision turning axle based on conic fitting as claimed in claim 1; It is characterized in that: in the said step (3), be the image of line at infinity with respect to the hachure that disappears that the limit of some imaging planes simulates this Plane of rotation through every other image.
CN2012100785794A 2012-03-22 2012-03-22 Determination method of rotary stereo visual rotation axis based on quadratic curve fitting Pending CN102663742A (en)

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Publication number Priority date Publication date Assignee Title
WO2015096509A1 (en) * 2013-12-26 2015-07-02 华中科技大学 Robust estimation method for rotation axis and barycentre of space object based on binocular light stream
CN106570864A (en) * 2016-10-26 2017-04-19 中国科学院自动化研究所 Quadratic curve fitting method based on geometric error optimization in image

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2015096509A1 (en) * 2013-12-26 2015-07-02 华中科技大学 Robust estimation method for rotation axis and barycentre of space object based on binocular light stream
CN106570864A (en) * 2016-10-26 2017-04-19 中国科学院自动化研究所 Quadratic curve fitting method based on geometric error optimization in image
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Application publication date: 20120912