Camera calibration system using planar concentric circles and method thereof

US 7,155,030 B2
Filed: 03/08/2005
Issued: 12/26/2006
Est. Priority Date: 04/02/2001
Status: Expired due to Fees

First Claim

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1. A method of calibrating a camera using projection invariable characteristic of a concentric circle in order to calibrate the camera through a calculation of camera'"'"'s intrinsic parameters, the method comprises steps of:

a) taking a plurality of images of a calibration pattern consisting of two or more concentric circles located at a same plane and having different radiuses at different angles to obtain projected images resulted from the projection of the concentric circles;

b) calculating central points of the projected images using a given algorithm; and

c) calculating an optimum principal point (u₀, v₀) and focal length (ƒ

) of the camera using a nonlinear minimizing method based on a given principal point and focal length, which are the camera'"'"'s intrinsic parameters, and the central point of the projected images calculated in the step b),wherein the concentric circle includes two circles and the step b) includes the steps of;

d) calculating the central points (O) of the two projected images obtained from the step a) to obtain a straight line passing through the central points;

e) calculating crossing points of the straight line and the two projected images; and

f) calculating the central point of the projected images using a cross ratio depending on the central point (O) of the projected images, a given point (M_∞) infinitely separated from the central point (O) on the straight line passing through the central points (O), and the crossing points of the straight line and the projected images.

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Abstract

The invention relates to a camera calibration system and method thereof which is capable of easily performing camera calibration using a concentric circle pattern. According to the invention, a method of calibrating a camera calibrates the intrinsic parameters of the camera required to measure geometric information of an object using projection invariable characteristics of concentric circles. The method includes the steps of taking images of the calibration pattern consisting of two or more concentric circles located in the same plane and having different radius at different angles to obtain projected images calculating the central point of the projected images using a given algorithm, and calculating the principal point and focal point of camera using a nonlinear minimization algorithm based on the central point thus obtained.

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6 Claims

1. A method of calibrating a camera using projection invariable characteristic of a concentric circle in order to calibrate the camera through a calculation of camera'"'"'s intrinsic parameters, the method comprises steps of:
- a) taking a plurality of images of a calibration pattern consisting of two or more concentric circles located at a same plane and having different radiuses at different angles to obtain projected images resulted from the projection of the concentric circles;
  
  b) calculating central points of the projected images using a given algorithm; and
  
  c) calculating an optimum principal point (u₀, v₀) and focal length (ƒ
  
  ) of the camera using a nonlinear minimizing method based on a given principal point and focal length, which are the camera'"'"'s intrinsic parameters, and the central point of the projected images calculated in the step b),wherein the concentric circle includes two circles and the step b) includes the steps of;
  
  d) calculating the central points (O) of the two projected images obtained from the step a) to obtain a straight line passing through the central points;
  
  e) calculating crossing points of the straight line and the two projected images; and
  
  f) calculating the central point of the projected images using a cross ratio depending on the central point (O) of the projected images, a given point (M_∞) infinitely separated from the central point (O) on the straight line passing through the central points (O), and the crossing points of the straight line and the projected images.
- View Dependent Claims (2, 3, 4)
- - 2. The method of claim 1, wherein the step d) calculates the straight line passing through the centers of the projected images by Equation 1:
    - (B′
      
      E′
      
      −
      
      A′
      
      F′
      
      )X′
      
      +(A′
      
      D′
      
      −
      
      B′
      
      C′
      
      )Y′
      
      +(D′
      
      E′
      
      +F′
      
      C′
      
      )=0(where A′
      
      , B′
      
      , C′
      
      , D′
      
      , E′ and
      
      F′
      
      are constants with respect to the radius of the circle and, X′
      
      ,Y′
      
      are the coordinates of the center of the projected image.).
  - 3. The method of claim 2, wherein the step f) calculates the central point of the projected image by Equation 2:
    - $\begin{matrix} Cr (A, O, B, M_{\infty}) = \frac{\overline{{BAM}_{\infty} O}}{\overline{{BOM}_{\infty} A}} = 2 Cr (A^{'}, O, B^{'}, M_{\infty}) = \frac{\overline{B^{'} A^{'} M_{\infty} O}}{\overline{B^{'} {OM}_{\infty} A^{'}}} = 2 \end{matrix}$ (where A,B are the coordinates of crossing points of an projected image generated by projection of smaller circle and the straight line, A′
      
      ,B′
      
      are the coordinates of crossing points of an projected image generated by projection of an external circle surrounding the smaller circle and the straight line, and M_∞is a given point separated infinitely on the straight line.).
  - 4. The method of claim 2, wherein said step c) includes the steps of:
    - g) assuming that normal vectors ({overscore (n)}) of the plane and distance (d) to the plane from a central coordinate of the camera of each of the central point calculated in the step b) based on a given principal point (u₀, V₀) and focal length (ƒ
      
      ) of the camera;
      
      h) calculating F(u₀, v₀, ƒ
      
      ) by applying the normal vectors and distance which were assumed from the step g) to a cost function defined as below Equation 3; and
      
      i) setting up a new principal point and focal length of the camera and repeating the steps g) and h) until F(u₀,v₀,ƒ
      
      ) is minimized;
      
      $\begin{matrix} F (u_{0}, v_{0}, f) = {α ({\overline{n}}_{1} - {\overline{n}}_{2})}^{2} + {β ({\overline{n}}_{3} - {\overline{n}}_{4})}^{2} + {γ (d_{1} - d_{2})}^{2} + {λ (d_{3} - d_{4})}^{2} + ρ_{1} \sum \langle R_{C_{1}} (n_{1}, d_{1}) - R_{1} \rangle + ρ_{2} \sum \langle R_{C_{2}} (n_{2}, d_{2}) - R_{2} \rangle + ρ_{3} \sum \langle R_{C_{3}} (n_{3}, d_{3}) - R_{3} \rangle + ρ_{4} \sum \langle R_{C_{4}} (n_{4}, d_{4}) - R_{4} \rangle \end{matrix}$ (where R_iis radius of the circle i, and R_ci(n_i,d_i) is radius estimation function between points of the projected image Ci and center of the projected image. α
      
      , β
      
      , γ
      
      , λ
      
      , ρ
      
      ₁,ρ
      
      ₂, ρ
      
      ₃, and ρ
      
      ₄are the weighting factors representing the confidence of each constraint.).

5. A system for calibrating intrinsic parameters of a camera using projection invariable characteristic of a concentric circle in order to calibrate the camera through a calculation of camera'"'"'s intrinsic parameters, comprising:
- a camera that an arbitrary principal point and an arbitrary focal length are preset;
  
  a calibration pattern located on a same plane and consisting of two or more concentric circles having different radiuses, said pattern being taken by the camera in order to calibrate the camera'"'"'s intrinsic parameter; and
  
  a controller for calculating a straight line connecting the central points of the projected images obtained by projecting the calibration pattern to the camera at a given angle, and finding crossing points of the straight line and the projected images to obtain the central point coordinate of the projected images using a cross ratio (Cr), and calculating an optimum principal point (u₀, v₀) and focal length (ƒ
  
  ) of the camera using a nonlinear minimizing method based on the obtained principal point and focal length, which are the camera'"'"'s intrinsic parameters,wherein, the controller assuming that normal vectors ({overscore (n)}) of the plane and distance (d) from a central coordinate of the camera of each of the calculated central point based on a principal point (u₀, v₀) and focal length (ƒ
  
  ) of the camera, calculating F(u₀, v₀,ƒ
  
  ) by applying the assumed normal vectors and focal length to a cost function defined as below Equation 3, and setting up an optimum principal point and focal length of the camera when F(u₀, v₀,ƒ
  
  ) is minimized;
  
  $\begin{matrix} F (u_{0}, v_{0}, f) = {α ({\overline{n}}_{1} - {\overline{n}}_{2})}^{2} + {β ({\overline{n}}_{3} - {\overline{n}}_{4})}^{2} + {γ (d_{1} - d_{2})}^{2} + {λ (d_{3} - d_{4})}^{2} + ρ_{1} \sum \langle R_{C_{1}} (n_{1}, d_{1}) - R_{1} \rangle + ρ_{2} \sum \langle R_{C_{2}} (n_{2}, d_{2}) - R_{2} \rangle + ρ_{3} \sum \langle R_{C_{3}} (n_{3}, d_{3}) - R_{3} \rangle + ρ_{4} \sum \langle R_{C_{4}} (n_{4}, d_{4}) - R_{4} \rangle \end{matrix}$ (where R_iis radius of the circle i, and R_ci(n_i, d_i) is radius estimation function between points of the projected image Ci and center of the projected image. α
  
  , β
  
  , γ
  
  , λ
  
  , ρ
  
  ₁, ρ
  
  ₂, ρ
  
  ₃, and ρ
  
  ₄are the weighting factors representing the confidence of each constraint.).
- View Dependent Claims (6)
- - 6. The system of claim 5, wherein said camera is a CCD camera.

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Current Assignee
Korea Advanced Institute of Science and Technology
Original Assignee
Korea Advanced Institute of Science and Technology
Inventors
Kim, Jun-Sik, Kweon, In-So
Primary Examiner(s)
CHAWAN, SHEELA C

Application Number

US11/074,562
Publication Number

US 20050207640A1
Time in Patent Office

658 Days
Field of Search

382/106, 382/154, 382/275, 382/294, 382/296, 348/39, 348/38, 348/37, 348/36, 348/92, 348/42, 348/187, 348/335, 348/188, 348/340, 348/360, 356/515, 356/127, 356/603, 356/606, 359/662, 359/664
US Class Current

382/100
CPC Class Codes

G06T 7/80 Analysis of captured images...

H04N 17/002 for television cameras

Camera calibration system using planar concentric circles and method thereof

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Camera calibration system using planar concentric circles and method thereof

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