Image lens distortion correcting method

• US 6,791,616 B2
• Filed: 07/13/2001
• Issued: 09/14/2004
• Est. Priority Date: 09/05/2000
• Status: Expired due to Fees

• Current Assignee: Riken
• Original Assignee: Riken
• Inventors: Yamamura, Tsuyoshi, Ohnishi, Noboru, Tamaki, Toru
• Primary Examiner(s): Christensen, Andrew
• Assistant Examiner(s): TRAN, NHAN T
• Application Number:
  US09/903,619
• Publication Number:
  US 20020057345A1
• Time in Patent Office: 1,159 Days
• Field of Search: 348/335, 348/340, 348/175, 348/187-189, 348/192, 348/207.99, 396/91, 382/275, 358/406, 356/124, 356/394
• US Class Current: 348/335
• CPC Class Codes: G06T 5/80 Geometric correction
• CPC Class Codes: H04N 23/81 for suppressing or minimising disturbance in the image signal generation

Abstract

An image lens distortion correcting method having step (A) for printing an arbitrary image I₁ in a computer; step (B) for photographing the printed image I₁ with a camera having a lens distortion and obtaining a photographed image I₂ in the computer; step (C) for obtaining a parameter θ such that the image I₁ is artificially distorted with the parameter θ and an obtained distorted image I₁^ud equals with the photographed image ₂; and step (D) for using the obtained parameter θ to correct the image photographed by the camera. Thereby, (1) no correspondence point needs to be given, (2) no special tool or object is used, and (3) all points on the image are used, so that an internal parameter can automatically be obtained with high precision, and image lens distortion can be corrected with high precision.

Claims

1. An image lens distortion correcting method comprising:

an image printing step (A) for printing a prepared calibration pattern image I₁ in a computer;

an image pickup step (B) for photographing the printed image I₁ with a camera having a lens distortion and obtaining a photographed image I₂ in the computer;

a parameter estimating step (C) for obtaining a parameter θ

such that the image I₁ is artificially distorted with the parameter θ and

so as to obtain a distorted image I₁^ud equal with the photographed image I₂; and

an image correcting step (D) for using the parameter θ

to correct the photographed image I₂.

2. The image lens distortion correcting method according to claim 1 wherein said parameter θ

comprises a position correction parameter θ

^u for correcting a position, and a distortion correction parameter θ

^d for correcting the distortion.

3. The image lens distortion correcting method according to claim 2, wherein said position correction parameter θ

^u is a first parameter for conversion to an image I₁^u with the corrected position from the image I₁, the first conversion parameter is calculate in a least-squares method such that a difference r=I₁(p)−

I₁^u(p+u) between a luminance value I_i(p) of a point p in the image I₁ and a luminance value I₁^u(p+u) of a point p+u in the image I₁^u corresponding to the point p is minimized entirely on the image I₁, and the first parameter thus calculated is used as the position correction parameter θ

^u.

4. The image lens distortion correcting method according to claim 3, wherein said distortion correction parameter θ

^d is a second parameter for conversion to the image I₁^u from the distorted image I₁^ud, the second conversion parameter is calculated in the least-squares method such that a difference r=I₂(p)−

I₁^u(f(p)) between a luminance value I₂(p) of the point p in the image I₂ and a luminance value I₁^u(f(p)) of a point f(p) in the image I₁^u corresponding to the point p is minimized entirely on the image I₂, and the second parameter thus calculated is used as the distortion correction parameter θ

^d.

5. The image lens distortion correcting method according to claim 4, wherein said parameter estimating step (C) comprises a step of alternately repeatedly using said position correction parameter θ

_u and said distortion correction parameter θ

^d to calculate the parameter θ

.

6. The image lens distortion correcting method according to claim 1, wherein said parameter θ

is a parameter for conversion to the image I₁^ud from the image I₁, the conversion parameter is calculated in a least-squares method by using an implicit function theorem such that a difference r=I₁(p)−

I₂(d(p+u(p)) between a luminance value I₁(p) of a point p in the image I₁ and a luminance value I₂(d(p+u(p)) of a point d(p+u(p)) in the image I₂ corresponding to the point p is minimized entirely on the image I₁, and the conversion parameter thus calculated is used as the parameter θ

.

7. The image lens distortion correcting method according to claim 4, wherein said image correcting step (D) comprises a step of using the calculated distortion correction parameter θ

^d to correct the photographed image I₂.

8. An image lens distortion correcting method comprising the steps of:

(a) printing a prepared calibration pattern image I₁ in a computer;

(b) photographing the printed image I₁ with a camera having a lens distortion to obtain a distorted photographed image I₂ in the computer;

(c) calculating a parameter θ

such that the image I₁ is artificially distorted with the parameter θ

so as to obtain a distorted image I₁^ud equal with the photographed image I₂; and

(d) using the calculated parameter θ

to correct the photographed image I₂.

9. An image lens distortion correcting method according to claim 8, wherein said parameter θ

comprises a position correction parameter θ

^u for correcting a position, and a distortion correction parameter θ

_d for correcting distortion.

10. An image lens distortion correcting method according to claim 9, wherein said position correction parameter θ

^u is a first parameter for conversion to an image I₁^u with the corrected position from the image I₁, the first conversion parameter is calculated in a least-squares method such that a difference r=I₁(p)−

I₁^u(p+u) between a luminance value I₁(p) of a point p in the image I₁ and a luminance value I₁^u(p+u) of a point p+u in the image I₁^u, corresponding to the point p, is minimized entirely on the image I₁, and the first conversion parameter thus calculated is used as the position correction parameter θ

^u.

11. An image lens distortion correcting method according to claim 10, wherein said distortion correction parameter θ

^d is a second parameter for conversion to the image I₁^u from the distorted image I₁^ud, the second conversion parameter is calculated in the least-squares method such that a difference r=I₂(p)−

I₁^u(f(p)) between a luminance value I₂(p) of the point p in the image I₂ and a luminance value I₁^u(f(p)) of a point f(p) in the image I₁^u, corresponding to the point p, is minimized entirely on the image I₂, and the second conversion parameter thus calculated is used as the distortion correction parameter θ

^d.

12. An image lens distortion correcting method according to claim 11, wherein calculation of the parameter θ

comprises alternately repeatedly using said position correction parameter θ

^u and said distortion correction parameter θ

^d to calculate the parameter θ

.

13. An image lens distortion correcting method according to claim 8, wherein said parameter θ

is a parameter for conversion to the image I₁^ud from the image I₁ that is calculated in a least-squares method by using an implicit function theorem such that a difference r=I₁(p)−

₂(d(p+u(p)) between a luminance value I₁(p) of a point p in the image I₁ and a luminance value I₂(d(p+u(p)) of a point d(p+u(p)) in the image I₂, corresponding to the point p, is minimized entirely on the image I₁, and the parameter for conversion to the image I₁^ud from the image I₁ thus calculated is used as the parameter θ

.

14. The image lens distortion correcting method according to claim 11, wherein the calculated distortion correction parameter θ

^d is used to correct the photographed image I₂.

15. The image lens distortion correcting method according to claim 9, wherein said distortion correction parameter θ

^d is a five parameter distortion comprising k₁, k₂, c_x, c_y, and s_x, where k₁ and k₂ are distortion parameters, c_x and c_y represent an image center coordinate, and s_x is a ratio of pixel width to pixel height.

16. The image lens distortion correcting method according to claim 15, wherein said position correction parameter θ

^u is an eight parameter displacement comprising θ

₁^u, θ

₂^u, θ

₃^u, θ

₄^u, θ

₅^u, θ

₆^u, θ

₇^u, and θ

₈^u.