Imaging system calibration using structured light

Abstract

The present disclosure relates to systems and methods for calibrating an imaging system comprising an image-forming optical system between an image display device and an image capture device. The method comprises determining a mapping function that associates a plurality of image display pixels of the image display device with a corresponding plurality of image capture pixels of the image capture device; determining an ideal image capture pixel for one or more of the plurality of image display pixels; and determining a correction function by reducing an error measure between the ideal image capture pixel and the corresponding image capture pixel of the one or more of the plurality of image display pixels, the correction function associating the one or more image capture pixels with one or more corrected image capture pixels. The method may be used to calibrate a camera of a drone, phone camera, a display, a projector, etc.

Description

This disclosure relates to systems and methods for calibrating imaging systems, including imaging optics located between an image display device and an image acquisition device. The method includes: determining a mapping function that associates a plurality of image display pixels of the image display device with a corresponding plurality of image acquisition pixels of the image acquisition device; determining an ideal image acquisition pixel for one or more image display pixels; and determining a correction function by reducing an error metric between the ideal image acquisition pixel and the corresponding image acquisition pixels of the one or more image display pixels, the correction function associating the one or more image acquisition pixels with one or more corrected image acquisition pixels. This method can be used to calibrate cameras on drones, mobile phone cameras, displays, projectors, etc. Abstract

Claims

CLAIMS 1. A calibration method for an imaging system comprising an image-forming optical system between an image display device and an image capture device, the method comprising: - determining a mapping function that associates a plurality of image display pixels (B, C) of the image display device with a corresponding plurality of image capture pixels (@, A) of the image capture device; - using a predetermined camera model to approximate the image-forming optical system, determining an ideal image capture pixel (@^, A^) for one or more of the plurality of image display pixels (B, C); and - determining a correction function by reducing an error measure between the ideal image capture pixel (@^, A^) and the corresponding image capture pixel (@, A) of the one or more of the plurality of image display pixels (B, C), the correction function associating the one or more image capture pixels (@, A) with one or more corrected image capture pixels (@j, Aj).

2. The image calibration method of claim 1, wherein determining a mapping function that associates a plurality of image display pixels (B, C) of the image display device with a corresponding plurality of image capture pixels (@, A) of the image capture device comprises: 1 displaying a set of encoded images on the display device, the set of encoded images comprising pixel information that allows identification of image display pixels (B, C) when the encoded images are captured by the image capture device; 1 acquiring each displayed image using the image capture device; and1 for each image capture pixel (@, A), identifying the corresponding image display pixel (B, C) using pixel information in the acquired images.

3. The image calibration method of claim 1 or claim 2, wherein determining a mapping function that associates a plurality of image display pixels (B, C) with a corresponding plurality of image capture pixels (@, A) further comprises generating the set of encoded images.

4. The image calibration method of any one of claims 1 to 3, wherein determining an ideal image capture pixelone or more of the plurality of image display pixels (B, C) further comprises: 1 determining ideal image display space coordinates [L, M, N]kq,rof the plurality of image display pixels (B, C); and 1 determining ideal image capture space coordinates [L, M, N]jo,pof the plurality of image capture pixels (@, A), wherein the ideal image display and the ideal image capture space coordinates indicate 3D positional information of the ideal image display and the ideal image capture pixels, respectively.

5. The image calibration method of claim 4, wherein the ideal image display space coordinates[L, M, N]kq,rare determined using initialized image display space coordinates [L, M, N]kq,rgiven by ^[L, M, N]kq,r^i= [Oz_k+ (C 1 Cf); O{_k+ (B 1 Bf); 0] with: Oz_kbeing an image display pixel column width size, O{_kbeing an image display pixel row height size, Bfbeing a display origin pixel row, Cfbeing a display origin pixel column,B being an image display pixel row index, and C being an image display pixel column index; and wherein the ideal image capture space coordinates [L, M, N]jo,pare determined using initialized image capture space coordinates [L , M , N ]jgiven by [L , M , N ]j i\ o,p^ o,p^ = + 1 + 1 with: pixel column width size,O{_jbeing an image capture pixel row height size, @fbeing a camera origin pixel row, Afbeing a camera origin pixel column, @ being an image capture pixel row index, and A being an image capture pixel column index.

6. The image calibration method of any one of claims 1 to 5, wherein the predetermined camera model is a pinhole model and wherein determining an ideal image capture pixel one or more of the plurality of image display pixels (B, C) comprises: - for each image display pixel (B, C), determining a line equation of a line that traverses a focal point of the image-forming optical system and the image display pixel (B, C); and - determining an intersection between the line and an imaging plane of the image forming optical system, the intersection being the ideal image capture pixel (@^, A^).

7. The image calibration method of any one of claims 1 to 5, wherein the predetermined camera model is a fisheye model and wherein determining an ideal image capture pixel (@^, A^) for one or more of the plurality of image display pixels (B, C) comprises:- for each image display pixel (B, C), determining a line equation of a line that traverses a focal point of the image-forming optical system and the image display pixel (B, C); and - determining an intersection between the line and an imaging sphere, the intersection being the ideal image capture .

8. The image calibration method of any one of claims 1 to 7, wherein the correction function is limited to rotations and / or translations of the image display pixels (B, C) and / or the image capture pixels (@, A) and wherein reducing the error measure is performed by varying angles of the rotations and / or distances of the translations.

9. The image calibration method of any one of claims 1 to 8, wherein the method is used for calibrating one or more image capture device channels and / or image display channels by applying the steps of the method to the one or more color channels.

10. The image calibration method of any one of claims 1 to 8, wherein the method is used for calibrating one or more image capture device channels, and wherein once the method is applied to a first channel, the method further comprises, for each subsequent channel of the one or more channels: - determining a subsequent channel mapping function that associates a plurality of image display pixels (B, C)xjof the subsequent channel with a corresponding plurality of image capture pixels (@, A)xjof the subsequent channel, so that eachimage display pixel (B, C) is associated with a first image capture pixel (@, A)sfrom the first channel and a second image capture pixel(@, A)xjfrom the subsequent channel, and- determining a subsequent channel correction function that is the sum between the correction function determined for the first channel and a displacement vector, the displacement vector being a vector that extends from the second image capture pixel to the first image capture pixel.

11. The image calibration method of claim 10, further comprising: - applying the correction function to one or more image capturesofthe first channel to obtain corrected image capture pixels(@j, Aj)sfor the first channel; and / or - applying the subsequent channel correction function to one or more image capture pixels(@, A)xjof the second channel to obtain corrected image capture pixels(@j, Aj)xjfor the second channel.

12. The image calibration method of any one of claims 1 to 8, wherein the method is used for calibrating one or more image display device channels, and wherein once the method is applied to a first channel, the method further comprises, for each subsequent channel of the one or more channels: - determining a subsequent channel mapping function that associates a plurality of image display pixels(@, A)of the subsequent channel with a corresponding plurality of image capture pixels (B, C) of the subsequent channel, so that each image capture pixel is associated with a first image display pixel from the first channel and a second image display pixel from the subsequent channel, and - determining a subsequent channel correction function that is the sum between the correction function determined for the first channel and a displacementvector, the displacement vector being a vector that extends from the second image display pixel to the first image display pixel.

13. The image calibration method of claim 12, further comprising: - applying the correction function to one or more image display pixels (B, C)sof the first channel to obtain corrected image display pixels (Bj, Cj)sfor the first channel; and / or - applying the subsequent channel correction function to one or more image display pixels(B, C)xjof the second channel to obtain corrected image display pixels(Bj, Cj)xjfor the second channel.

14. The image calibration method of any one of claims 1 to 8, wherein the method is used for calibrating a multi-parameter image capture device, the method comprising: having corrected pixels determined for a plurality of camera multi-parameter configurations, and a multi-parameter configuration associated with a new image capture device configuration: 1 interpolating the corrected pixels determined for the plurality of image capture device multi-parameter configurations to obtain corrected pixels associated with the new image capture device configuration.

15. The image calibration method of claim 14, wherein the image capture device multi- parameter configurations comprise: focal positions, magnification, polarization states, spectral band, and / or device geometry.

16. The image calibration method of any one of claims 1 to 8, wherein when the method is used for calibrating a focusing image capture device, and wherein once the method is applied to a first focal position >v_jof the focusing image capture device, the method further comprises, for each subsequent focal position >x_j: - determining a subsequent mapping function that associates a plurality of image display pixels (B, C)xof the subsequent focal position with a corresponding plurality of image capture pixels (@, A)xof the subsequent focal position >x_j, so that each image display pixel (B, C) is associated with a first image capture pixel (@, A)vfrom the first focal position and a second image capture pixel (@, A)xfrom the subsequent focal position; and - determining a subsequent correction function that is the sum between the correction function determined for the first focal position and a displacement vector, the displacement vector being a vector that extends from the second image capture pixel to the first image capture pixel.

17. The image calibration method of claim 16, wherein the method is used for calibrating one or more channels of a focusing image capture device, and wherein once the method is applied to a first channel of each focal position >vof the focusing image capture device, the method further comprises, for each subsequent channel of each focal position: - determining a subsequent channel mapping function that associates a plurality of image display pixels (B, C)xjof the subsequent channel with a corresponding plurality of image capture pixels (@, A)xjof the subsequent channel, so that each image display pixel (B, C) is associated with a first image capture pixel (@, A)sfrom the first channel and a second image capture pixel (@, A)xjfrom the subsequent channel, and- determining a subsequent channel correction function that is the sum between the subsequent channel correction function determined for the first channel and a displacement vector, the displacement vector being a vector that extends from the second image capture pixel to the first image capture pixel.

18. The image calibration method of any one of claims 1 to 8, wherein when the method is used for calibrating a focusing image display device, and wherein once the method is applied to a first focal position of the focusing image display device, the methodfurther comprises, for each subsequent focal position >x_k: - determining a subsequent mapping function that associates a plurality of image display pixels (B, C)xof the subsequent focal position with a corresponding plurality of image capture pixels (@, A)xof the subsequent focal position >x_k, so that each image capture pixel (@, A) is associated with a first image display pixel (B, C)vfrom the first focal position >v_kand a second image display pixel (B, C)xfrom the subsequent focal position >x_k; and - determining a subsequent correction function that is the sum between the correction function determined for the first focal position and a displacement vector, the displacement vector being a vector that extends from the second image display pixel to the first image display pixel.

19. The image calibration method of claim 17, wherein the method is used for calibrating one or more channels of a focusing image display device, and wherein once the method is applied to a first channel of each focal position of the focusing image display device, the method further comprises, for each subsequent channel of each focal position:- determining a subsequent channel mapping function that associates a plurality of image display pixels (B, C)xjof the subsequent channel with a corresponding plurality of image capture pixels(@, A)xjof the subsequent channel, so that each image capture pixel (@, A) is associated with a first image display pixel(B, C)sfrom the first channel and a second image display pixel(B, C)I; from the subsequent channel, and - determining a subsequent channel correction function that is the sum between the subsequent channel correction function determined for the first channel and a displacement vector, the displacement vector being a vector that extends from the second image display pixel to the first image display pixel.

20. The image calibration method of any one of claims 1 to 8, wherein when the method is used for calibrating a zooming image capture device, the method comprises performing the method of claim 1 for each desired zoom position.

21. The image calibration method of any one of claims 1 to 8, wherein when the method is used for calibrating one or more channels of a zooming image capture device, and wherein once the method is performed for first channel of each desired zoom position, the method further comprises, for each subsequent channel of each desired zoom position: - determining a subsequent channel mapping function that associates a plurality of image display pixels (B, C)xjof the subsequent channel with a corresponding plurality of image capture pixels (@, A)xjof the subsequent channel, so that eachimage display pixel (B, C) is associated with a first image capture pixel (@, A)sfrom the first channel and a second image capture pixel (@, A)xjfrom the subsequent channel, and- determining a subsequent channel correction function for the subsequent channel, the subsequent channel correction function being a sum between the correction function determined for the first channel and a displacement vector, the displacement vector being a vector that extends from the second image capture pixel to the first image capture pixel.

22. The image calibration method of any one of claims 1 to 21, wherein the plurality of pixels represents a subset of all pixels of an image, and wherein corrected pixels of remaining image pixels are obtained by interpolating adjacent corrected pixels.

23. The image calibration method of any one of claims 1 to 22, wherein the method is performed to calibrate the imaging system comprising the image-forming optical system between the image display device and the image capture device, the method comprising: - performing the method of claim 1 to calibrate the image capture device; and / or - performing the method of claim 1 to calibrate the image display device.

24. The image calibration method of any one of claims 1 to 23, further comprising applying the image calibration method to an image or a feed of images acquired using the image capture device.

25. The image calibration method of any one of claims 1 to 24, further comprising applying the image calibration method to an image or a feed of images to be displayed using the image display device.

26. The image calibration method of any one of claims 1 to 25, wherein the image-forming optical system forms part of the image capture device.

27. The image calibration method of claim 26, wherein the image capture device is a camera.

28. The image calibration method of claim 27, wherein the image capture device is a camera forming part of a drone.

29. The image calibration method of claim 27, wherein the image capture device is a camera forming part of a targeting system of an unmanned combat aerial vehicle (UCAV).

30. The image calibration method of claim 26, wherein the image capture device is any one of a doorbell camera, a mobile phone camera, a tablet camera, a telescope, a microscope, an endoscope, and a vehicle camera.

31. The image calibration method of any one of claims 1 to 30, wherein the image-forming optical system forms part of the image display device.

32. The image calibration method of claim 31, wherein the image display device is a projector.

33. The image calibration method of claim 32, wherein the image display device is one of a Virtual Reality (VR) headset display, and an Augmented Reality (AR) glass display.

34. An image calibration system for calibrating an imaging system comprising an image- forming optical system between an image display device and an image capture device, wherein the image calibration system comprises: one or more computer processors;one or more computer readable storage media for storing computer-implemented instructions, wherein the one or more computer processors are configured to execute the computer-implemented instructions to cause the computer system to perform a method comprising: - determining a mapping function that associates a plurality of image display pixels (B, C) of the image display device with a corresponding plurality of image capture pixels (@, A) of the image capture device; - using a predetermined camera model to approximate the image-forming optical system, determining an ideal image capture pixel (@^, A^) for one or more of the plurality of image display pixels (B, C); and - determining a correction function by reducing an error measure between the ideal image capture pixel (@^, A^) and the corresponding image capture pixel (@, A) of the one or more of the plurality of image display pixels (B, C), the correction function associating the one or more image capture pixels (@, A) with one or more corrected image capture pixels (@j, Aj).

35. The image calibration system of claim 34, wherein determining a mapping function that associates a plurality of image display pixels (B, C) of the image display device with a corresponding plurality of image capture pixels (@, A) of the image capture device comprises: 1 displaying a set of encoded images on the display device, the set of encoded images comprising pixel information that allows identification of image display pixels (B, C) when the encoded images are captured by the image capture device; 1 acquiring each displayed image using the image capture device; and1 for each image capture pixel (@, A), identifying the corresponding image display pixel (B, C) using pixel information in the acquired images.

36. The image calibration system of claim 34 or claim 35, wherein determining a mapping function that associates a plurality of image display pixels (B, C) with a corresponding plurality of image capture pixels (@, A) further comprises generating the set of encoded images.

37. The image calibration system of any one of claims 34 to 36, wherein determining an ideal image capture pixelone or more of the plurality of image display pixels (B, C) further comprises: 1 determining ideal image display space coordinates [L, M, N]kq,rof the plurality of image display pixels (B, C); and 1 determining ideal image capture space coordinates [L, M, N]jo,pof the plurality of image capture pixels (@, A), wherein the ideal image display and the ideal image capture space coordinates indicate 3D positional information of the ideal image display and the ideal image capture pixels, respectively.

38. The image calibration system of claim 37, wherein the ideal image display space coordinates [L, M, N]kq,rare determined using initialized image display space coordinates [L, M, N]kq,rgiven by ^[L, M, N]kq,r^i= [Oz_k+(C 1 Cf); O{_k+(B 1 Bf); 0] with: Oz_kbeing an image display pixel column width size, O{_kbeing an image display pixel row height size, Bfbeing a display origin pixel row,Cfbeing a display origin pixel column, B being an image display pixel row index, and C being an image display pixel column index; and wherein the ideal image capture space coordinates [L, M, N]jo,pare determined using initialized image capture space coordinates [L , M , N ]jgiven by^[L , M , N ]j^i\ o,p o,p= with:Oz_jbeing an image capture pixel column width size, O{_jbeing an image capture pixel row height size, @fbeing a camera origin pixel row, Afbeing a camera origin pixel column, @ being an image capture pixel row index, and A being an image capture pixel column index.

39. The image calibration system of any one of claims 34 to 38, wherein the predetermined camera model is a pinhole model and wherein determining an ideal image capture pixel (@^, A^) for one or more of the plurality of image display pixels (B, C) comprises: - for each image display pixel (B, C), determining a line equation of a line that traverses a focal point of the image-forming optical system and the image display pixel (B, C); and - determining an intersection between the line and an imaging plane of the image forming optical system, the intersection being the ideal image capture pixel (@^, A^).

40. The image calibration system of any one of claims 34 to 38, wherein the predetermined camera model is a fisheye model and wherein determining an ideal image capture pixel (@^, A^) for one or more of the plurality of image display pixels (B, C) comprises: - for each image display pixel (B, C), determining a line equation of a line that traverses a focal point of the image-forming optical system and the image display pixel (B, C); and - determining an intersection between the line and an imaging sphere, the intersection being the ideal image capture .

41. The image calibration system of any one of claims 34 to 40, wherein the correction function is limited to rotations and / or translations of the image display pixels (B, C) and / or the image capture pixels (@, A) and wherein reducing the error measure is performed by varying angles of the rotations and / or distances of the translations.

42. The image calibration system of one of claims 34 to 41, wherein the method is used for calibrating one or more image capture device channels and / or image display channels by applying the steps of the method to the one or more color channels.

43. The image calibration system of any one of claims 34 to 41, wherein the method is used for calibrating one or more image capture device channels, and wherein once the method is applied to a first channel, the method further comprises, for each subsequent channel of the one or more channels: - determining a subsequent channel mapping function that associates a plurality of image display pixels(B, C)xjof the subsequent channel with a corresponding plurality of image capture pixels(@, A)xjof the subsequent channel, so that eachimage display pixel (B, C) is associated with a first image capture pixel(@, A)sfrom the first channel and a second image capture pixel(@, A)xjfrom the subsequent channel, and - determining a subsequent channel correction function that is the sum between the correction function determined for the first channel and a displacement vector, the displacement vector being a vector that extends from the second image capture pixel to the first image capture pixel.

44. The image calibration system of claim 43, wherein the method further comprises: - applying the correction function to one or more image capturesof the first channel to obtain corrected image capture pixels(@j, Aj)sfor the first channel; and / or - applying the subsequent channel correction function to one or more image capture pixels (@, A)xjof the second channel to obtain corrected image capture pixels (@j, Aj)xjfor the second channel.

45. The image calibration system of claims 34 to 41, wherein the method is used for calibrating one or more image display device channels, and wherein once the method is applied to a first channel, the method further comprises, for each subsequent channel of the one or more channels: - determining a subsequent channel mapping function that associates a plurality of image display pixels (@, A) of the subsequent channel with a corresponding plurality of image capture pixels (B, C) of the subsequent channel, so that eachimage capture pixel is associated with a first image display pixel from the first channel and a second image display pixel from the subsequent channel, and - determining a subsequent channel correction function that is the sum between the correction function determined for the first channel and a displacement vector, the displacement vector being a vector that extends from the second image display pixel to the first image display pixel.

46. The image calibration system of claim 45, wherein the method further comprises: - applying the correction function to one or more image display pixels(B, C)sof the first channel to obtain corrected image display pixels(Bj, Cj)sfor the first channel; and / or - applying the subsequent channel correction function to one or more image display pixels (B, C)xjof the second channel to obtain corrected image display pixels (Bj, Cj)xjfor the second channel.

47. The image calibration system of any one of claims 34 to 41, wherein the method is used for calibrating a multi-parameter image capture device, the method comprising: having corrected pixels determined for a plurality of camera multi-parameter configurations, and a multi-parameter configuration associated with a new image capture device configuration: 1 interpolating the corrected pixels determined for the plurality of image capture device multi-parameter configurations to obtain corrected pixels associated with the new image capture device configuration.

48. The image calibration system of claim 47, wherein the image capture device multi- parameter configurations comprise: focal positions, magnification, polarization states, spectral bands, and / or device geometry.

49. The image calibration system of any one of claims 34 to 41, wherein when the method is used for calibrating a focusing image capture device, and wherein once the method is applied to a first focal position >v_jof the focusing image capture device, the method further comprises, for each subsequent focal position >x_j: - determining a subsequent mapping function that associates a plurality of image display pixels(B, C)xof the subsequent focal position with a corresponding plurality of image capture pixels(@, A)xof the subsequent focal position >x_j, so that each image display pixel (B, C) is associated with a first image capture pixelthe first focal position and a second image capture pixel(@, A)xfrom the subsequent focal position; and - determining a subsequent correction function that is the sum between the correction function determined for the first focal position and a displacement vector, the displacement vector being a vector that extends from the second image capture pixel to the first image capture pixel.

50. The image calibration system of claim 49, wherein the method is used for calibrating one or more channels of a focusing image capture device, and wherein once the method is applied to a first channel of each focal position of the focusing image capture device, the method further comprises, for each subsequent channel of each focal position: - determining a subsequent channel mapping function that associates a plurality of image display pixels(B, C)xjof the subsequent channel with a correspondingplurality of image capture pixels(@, A)xjof the subsequent channel, so that each image display pixel (B, C) is associated with a first image capture pixel (@, A)sfrom the first channel and a second image capture pixel (@, A)xjfrom the subsequent channel, and - determining a subsequent channel correction function that is the sum between the subsequent channel correction function determined for the first channel and a displacement vector, the displacement vector being a vector that extends from the second image capture pixel to the first image capture pixel.

51. The image calibration system of any one of claims 34 to 41, wherein when the method is used for calibrating a focusing image display device, and wherein once the method is applied to a first focal positionof the focusing image display device, the method further comprises, for each subsequent focal position >x_k: - determining a subsequent mapping function that associates a plurality of image display pixels (B, C)xof the subsequent focal position with a corresponding plurality of image capture pixels (@, A)xof the subsequent focal position, so that each image capture pixel (@, A) is associated with a first image display pixel (B, C)vfrom the first focal position and a second image display pixel (B, C)xfrom the subsequent focal position; and - determining a subsequent correction function that is the sum between the correction function determined for the first focal position and a displacement vector, the displacement vector being a vector that extends from the second image display pixel to the first image display pixel.

52. The image calibration system of claim 51, wherein the method is used for calibrating one or more channels of a focusing image display device, and wherein once the method is applied to a first channel of each focal position of the focusing image display device, the method further comprises, for each subsequent channel of each focal position: - determining a subsequent channel mapping function that associates a plurality of image display pixels (B, C)xjof the subsequent channel with a corresponding plurality of image capture pixels (@, A)xjof the subsequent channel, so that each image capture pixel (@, A) is associated with a first image display pixel (B, C)sfrom the first channel and a second image display pixel (B, C)I; from the subsequent channel, and - determining a subsequent channel correction function that is the sum between the subsequent channel correction function determined for the first channel and a displacement vector, the displacement vector being a vector that extends from the second image display pixel to the first image display pixel.

53. The image calibration system of any one of claims 34 to 41, wherein when the method is used for calibrating a zooming image capture device, the method comprises performing the method of claim 1 for each desired zoom position.

54. The image calibration system of any one of claims 43 to 41, wherein when the method is used for calibrating one or more channels of a zooming image capture device, and wherein once the method is performed for first channel of each desired zoom position, the method further comprises, for each subsequent channel of each desired zoom position: - determining a subsequent channel mapping function that associates a plurality of image display pixels (B, C)xjof the subsequent channel with a corresponding plurality of image capture pixels (@, A)xjof the subsequent channel, so that eachimage display pixel(B, C)is associated with a first image capture pixel(@, A)sfrom the first channel and a second image capture pixel(@, A)xjfrom thesubsequent channel, and - determining a subsequent channel correction function for the subsequent channel, the subsequent channel correction function being a sum between the correction function determined for the first channel and a displacement vector, the displacement vector being a vector that extends from the second image capture pixel to the first image capture pixel.

55. The image calibration system of any one of claims 34 to 54, wherein the plurality of pixels represent a subset of all pixels of an image, and wherein corrected pixels of remaining image pixels are obtained by interpolating adjacent corrected pixels.

56. The image calibration system of any one of claims 34 to 55, further comprising applying the image calibration method to an image or a feed of images acquired using the image capture device.

57. The image calibration system of any one of claims 34 to 56, further comprising applying the image calibration method to an image or a feed of images to be displayed using the image display device.

58. The image calibration system of any one of claims 34 to 57, wherein the image-forming optical system forms part of the image capture device.

59. The image calibration system of claim 58, wherein the image capture device is a camera.

60. The image calibration system of claim 59, wherein the image capture device is a camera forming part of a drone.

61. The image calibration system of claim 59, wherein the image capture device is a camera forming part of a targeting system of an unmanned combat aerial vehicle (UCAV).

62. The image calibration system of claim 58, wherein the image capture device is any one of a doorbell camera, a mobile phone camera, a tablet camera, a telescope, a microscope, an endoscope, and a vehicle camera.

63. The image calibration system of any one of claims 34 to 57, wherein the image-forming optical system forms part of the image display device.

64. The image calibration system of claim 63, wherein the image display device is a projector.

65. The image calibration system of claim 63, wherein the image display device is one of a Virtual Reality (VR) headset display, and an Augmented Reality (AR) glass display.

66. The image calibration system of any one of claims 34 to 65, wherein the ideal image ^^capture pixels (@ , A ) are used as the corrected image capture , .

67. A non-transitory computer program product comprising computer-implemented instructions to cause a computer system to execute the method of any one of claims 1 to 33.

68. The calibration method of any one of claims 1 to 33, wherein the ideal image capture pixels (@^, A^) are used as the corrected image capture pixels (@j, Aj).

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