Method and apparatus for orientating a camera

• US 5,475,584 A
• Filed: 02/10/1995
• Issued: 12/12/1995
• Est. Priority Date: 06/24/1992
• Status: Expired due to Term

• Current Assignee: Siemens Corp. (Siemens AG)
• Original Assignee: Ali R. Bani-Hashemi
• Inventors: Bani-Hashemi, Ali R.
• Primary Examiner(s): Trammell, James P.
• Application Number:
  US08/386,603
• Time in Patent Office: 305 Days
• Field of Search: 364/167.01, 364/516, 364/525, 364/550, 364/559, 358/101, 358/107, 358/209, 358/103, 358/903, 356/138, 356/152, 356/153, 356/363, 356/376, 250/561, 382/28, 382/42, 382/27, 382/65
• US Class Current: 700/62
• CPC Class Codes: G06T 7/70 Determining position or orientation of objects or cameras camera calibration G06T7/80
• CPC Class Codes: G06T 7/80 Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration
• CPC Class Codes: G06T 7/85 Stereo camera calibration

Abstract

A method for recovering orientation of a camera or other apparatus with respect to a coordinate system, where the orientation corresponds to a set of first, second, and third orientation vectors, comprises projecting onto an image plane respective first, second, and third images of first, second, and third gratings respectively formed on first, second, and third mutually orthogonal supporting planes and having respective first, second, and third wavelength vectors. The supporting planes are aligned with respective ones of the first, second, and third orientation vectors such that the wavelength vectors are in predetermined relationship with the orientation vectors. The first, second, and third images are associated with respective first, second, and third image wavelength vectors. Thereafter, the image wavelength vectors are measured; the wavelength vectors are derived therefrom; and the orientation vectors are thereby derived.

Claims

1. A method for recovering an orientation vector of an object, comprising the steps of:

projecting onto an image plane an image of a grating formed on a supporting plane and having a wavelength vector, said supporting plane being in a predetermined alignment relationship with said orientation vector such that said wavelength vector is in predetermined relationship with said orientation vector;

measuring said image wavelength vector;

deriving therefrom said wavelength vector; and

thereby deriving said orientation vector.

2. A method for recovering orientation of an object in accordance with claim 1, wherein said grating has a constant spatial frequency.

3. A method for recovering orientation of an object in accordance with claim 1, wherein said grating represents a spatial waveform of sine-wave function.

4. A method for recovering orientation of an object in accordance with claim 1, wherein said grating represents a spatial square-wave function, approximating a spatial sine-wave function.

5. A method for recovering orientation of apparatus with respect to a coordinate system, said orientation corresponding to a set of first, second, and third orientation vectors, comprising the steps of:

projecting onto an image plane respective first, second, and third images of first, second, and third gratings respectively formed on first, second, and third mutually orthogonal supporting planes and having respective first, second, and third wavelength vectors, said supporting planes being aligned with respective ones of said first, second, and third orientation vectors such that said wavelength vectors are in predetermined relationship with said orientation vectors, said first, second, and third images being associated with respective first, second, and third image wavelength vectors;

measuring said image wavelength vectors;

deriving therefrom said wavelength vectors; and

thereby deriving said orientation vectors.

6. A method for recovering orientation of apparatus in accordance with claim 5, wherein said gratings have identical spatial frequencies such that said first, second, and third wavelength vectors are of identical lengths.

7. A method for recovering orientation of apparatus in accordance with claim 6, wherein the step of deriving said wavelength vectors comprises solving in accordance with constraints wherein said image wavelength vectors are orthographic projections of said wavelength vectors, and wherein said wavelength vectors are of identical lengths and are mutually orthogonal.

8. A method for recovering orientation of apparatus in accordance with claim 7, wherein said solving in accordance with constraints comprises forming a cost-function having a minimum satisfying said constraints.

9. A method for recovering orientation of a camera with respect to a coordinate system, said orientation corresponding to a set of first, second, and third orientation vectors, comprising the steps of:

projecting onto an image plane respective first, second, and third images of first, second, and third gratings respectively formed on first, second, and third mutually orthogonal supporting planes and having respective first, second, and third wavelength vectors, said supporting planes being aligned with respective ones of said first, second, and third orientation vectors such that said wavelength vectors are in predetermined relationship with said orientation vectors, said first, second, and third images being associated with respective first, second, and third image wavelength vectors;

measuring said image wavelength vectors;

deriving therefrom said wavelength vectors; and

thereby deriving said orientation vectors.

10. A method for recovering orientation of apparatus in accordance with claim 9, wherein said gratings have identical spatial frequencies such that said first, second, and third wavelength vectors are of identical lengths.

11. A method for recovering orientation of apparatus in accordance with claim 10, wherein said gratings represent a spatial waveform approximating a sine-wave function.

12. A method for recovering orientation of apparatus in accordance with claim 10, wherein said gratings represent a spatial waveform approximating a square-wave function.

13. A method for recovering orientation of apparatus in accordance with claim 12, wherein the step of deriving said wavelength vectors comprises solving in accordance with constraints wherein said image wavelength vectors are orthographic projections of said wavelength vectors, and wherein said wavelength vectors are of identical lengths and are mutually orthogonal.

14. A method for recovering orientation of apparatus in accordance with claim 13, wherein said solving in accordance with constraints comprises forming a cost-function having a minimum satisfying said constraints.

15. A method for recovering orientation of apparatus in accordance with claim 14, wherein said cost-function is formed by taking the squared sum of functions f₁ through f₁₂, as follows, wherein t'"'"'s represent respective ones of said wavelength vectors and suffixes x, y, and z represent mutually orthogonal coordinate axes:

##EQU7## and solving for a minimization of said cost function.

16. Apparatus for recovering orientation of a camera with respect to a coordinate system, said orientation corresponding to a set of first, second, and third orientation vectors, comprising:

means for projecting onto an image plane respective first, second, and third images of first, second, and third gratings respectively formed on first, second, and third mutually orthogonal supporting planes and having respective first, second, and third wavelength vectors, said supporting planes being aligned with respective ones of said first, second, and third orientation vectors such that said wavelength vectors are in predetermined relationship with said orientation vectors, said first, second, and third images being associated with respective first, second, and third image wavelength vectors;

means for measuring said image wavelength vectors; and

means for deriving therefrom said wavelength vectors so as to thereby derive said orientation vectors.

17. Apparatus for recovering orientation of a camera in accordance with claim 16, wherein said gratings have identical spatial frequencies such that said first, second, and third wavelength vectors are of identical lengths.

18. Apparatus for recovering orientation of a camera in accordance with claim 17, wherein said means for deriving said wavelength vectors comprises means for solving in accordance with constraints wherein said image wavelength vectors are orthographic projections of said wavelength vectors, and wherein said wavelength vectors are of identical lengths and are mutually orthogonal.

19. Apparatus for recovering orientation of a camera in accordance with claim 18, wherein said means for solving in accordance with constraints comprises means for forming a cost-function having a minimum satisfying said constraints.

20. Apparatus for orientating a camera in a desired orientation with respect to a coordinate system, said desired orientation corresponding to a set of first, second, and third orientation vectors, comprising:

means for projecting onto an image plane respective first, second, and third images of first, second, and third gratings respectively formed on first, second, and third mutually orthogonal supporting planes and having respective first, second, and third wavelength vectors, said supporting planes being aligned with respective ones of said first, second, and third orientation vectors such that said wavelength vectors are in predetermined relationship with said orientation vectors, said first, second, and third images being associated with respective first, second, and third image wavelength vectors;

means for measuring said image wavelength vectors;

means for deriving therefrom said wavelength vectors so as to thereby derive said orientation vectors; and

means for utilizing said orientation vectors derived by said means for deriving for orienting said camera in accordance therewith.