Method and apparatus for passive autoranging using relaxation

• US 5,365,597 A
• Filed: 06/11/1993
• Issued: 11/15/1994
• Est. Priority Date: 06/11/1993
• Status: Expired due to Term

• Current Assignee: United Parcel Service Of America Incorporated (United Parcel Service Incorporated)
• Original Assignee: United Parcel Service Of America Incorporated (United Parcel Service Incorporated)
• Inventors: Holeva, Lee F.
• Primary Examiner(s): Mancuso, Joseph
• Assistant Examiner(s): Fox, David
• Application Number:
  US08/075,738
• Time in Patent Office: 522 Days
• Field of Search: 382/1, 382/8, 382/41, 382/43, 358/227, 354/400, 354/402, 250/201.2, 250/201.7
• US Class Current: 382/318
• CPC Class Codes: B07C 3/14 using light-responsive detecting means for information carriers G06K7/14
• CPC Class Codes: G06K 2207/1013 Multi-focal
• CPC Class Codes: G06K 7/1092 sensing by means of TV-scanning
• CPC Class Codes: G06V 10/10 Image acquisition document image scanning and transmission H04N1/00; control of digital cameras H04N23/60

Abstract

A method and apparatus for passive autoranging. Two cameras having different image parameters (e.g., focal gradients) generate two images of the same scene. A relaxation procedure is performed using the two images as inputs to generate a blur spread. The blur spread may then be used to calculate the range of at least one object in the scene. In one preferred embodiment, a temporal relaxation procedure is employed to focus a third camera. In another preferred embodiment, a spatial relaxation procedure is employed to determine the range of a plurality of objects.

Claims

1. A method for determining a differential blur spread corresponding to an object, comprising the steps of:

(a) providing a first image of said object, said first image being generated by a camera having a first camera parameter;

(b) providing a second image of said object, said second image being generated by a camera having a second camera parameter different from said first camera parameter; and

(c) performing a relaxation procedure in accordance with said first and second images to generate said differential blur spread.

2. The method of claim 1, further comprising the step of:

(d) determining a range of said object in accordance with said differential blur spread.

3. The method of claim 2, further comprising the step of:

(e) focussing a camera in accordance with said range.

4. The method of claim 3, wherein said object is a package on a conveyor system and said focussed camera is a high-resolution camera positioned overhead said conveyor system to generate images used to read a label on said package.

5. The method of claim 1, wherein said first camera parameter is a first focal gradient and said second camera parameter is a second focal gradient.

6. The method of claim 1, wherein:

step (a) comprises the step of generating said first image with a first camera having a first aperture size; and

step (b) comprises the step of generating said second image with a second camera having a second aperture size, said second aperture size being different from said first aperture size.

7. The method of claim 1, wherein:

step (a) comprises the step of generating said first image with a first camera having a first focal length; and

step (b) comprises the step of generating said second image with a second camera having a second focal length, said second focal length being different from said first focal length.

8. The method of claim 1, wherein:

step (a) comprises the step of generating said first image with a first camera having a first distance between a second principal plane and an image detector plane of said first camera; and

step (b) comprises the step of generating said second image with a second camera having a second distance between a second principal plane and an image detector plane of said second camera, said second distance being different from said first distance.

9. The method of claim 1, wherein step (c) comprises the step of performing a temporal relaxation procedure in accordance with said first and second images to generate said differential blur spread.

10. The method of claim 1, wherein step (c) comprises the steps of:

(1) generating a 2N point discrete Fourier transform of said first image;

(2) generating a 2N point discrete Fourier transform of said second image;

(3) generating a raw gain and said differential blur spread in accordance with said 2N point discrete Fourier transforms of said first and second images;

(4) generating a transform of a time-varying regularization vector in accordance with said raw gain and said differential blur spread;

(5) generating a transform of an impulse response in accordance with said time-varying regularization vector and said 2N point discrete Fourier transforms of said first and second images;

(6) updating said raw gain and said differential blur spread in accordance with said impulse response;

(7) generating a squared error in accordance with said impulse response, said updated raw gain, and said updated differential blur spread;

(8) testing said squared error for convergence; and

(9) repeating steps (c)(4) through (c)(7) in accordance with said testing of step (c)(8).

11. The method of claim 1, wherein step (c) comprises the step of performing a spatial relaxation procedure in accordance with said first and second images to generate said differential blur spread.

12. The method of claim 11, wherein:

step (c) comprises the step of performing said spatial relaxation procedure in accordance with a forward pass through said first and second images to generate a plurality of forward differential blur spreads and a plurality of forward cost function values; and

further comprising the steps of;

(d) determining a plurality of ranges corresponding to a plurality of objects in accordance with said plurality of forward differential blur spreads;

(e) performing said spatial relaxation procedure in accordance with a backward pass through said first and second images to generate a plurality of backward differential blur spreads and a plurality of backward cost function values;

(f) comparing said plurality of backward cost function values with said plurality of forward cost function values; and

(g) updating said plurality of ranges in accordance with said comparison of step (f).

13. The method of claim 1, wherein step (c) comprises the steps of:

(1) selecting a first first-image sample from said first image and a corresponding first second-image sample from said second image;

(2) generating a first differential blur spread in accordance with said first first-image and first second-image samples;

(3) selecting a second first-image sample from said first image and a corresponding second second-image sample from said second image; and

(4) generating a second differential blur spread in accordance with said second first-image and second second-image samples.

14. The method of claim 13, further comprising the steps of:

(d) determining a first range value corresponding to said first first-image and second-image samples in accordance with said first differential blur spread; and

(e) determining a second range value corresponding to said second first-image and second-image samples in accordance with said second differential blur spread.

15. The method of claim 14, wherein said first range value corresponds to the height of a first stack of nested packages and said second range value corresponds to the height of a second stack of nested packages.

16. The method of claim 1, wherein:

step (a) comprises the step of providing said first image with a first camera having a focal length, an aperture size, and a distance between a second principal plane and an image detector plane of said first camera, and

step (c) comprises the step of performing said relaxation procedure independent of said focal length, said aperture size, and said distance of said first camera.

63. The method of claim 1, wherein step (c) comprises the steps of:

(1) generating an initial differential blur spread in accordance with said first and second images; and

(2) performing a recursive relaxation procedure in accordance with said first and second images and said initial differential blur spread to generate an improved differential blur spread.

64. The method of claim 1, wherein step (c) comprises the steps of:

(1) generating a 2N point discrete Fourier transform of said first image;

(2) generating a 2N point discrete Fourier transform of said second image;

(3) generating an initial gain and an initial differential blur spread in accordance with said 2N point discrete Fourier transforms of said first and second images;

(4) generating the discrete Fourier transform of a time-varying regularization vector in accordance with said initial gain and said initial differential blur spread;

(5) generating the discrete Fourier transform of the differential impulse response between said camera of step (a) and said camera of step (b) in accordance with said discrete Fourier transformed time-varying regularization vector;

(6) updating said initial gain and said initial differential blur spread in accordance with said discrete Fourier transformed differential impulse response;

(7) generating a squared error in accordance with said discrete Fourier transformed differential impulse response, said updated gain, and said updated differential blur spread;

(8) testing for the convergence of said squared error; and

(9) repeating steps (c)(4) through (c)(7), in accordance with said testing of step (c)(8), using said updated gain and said updated differential blur spread.

65. The method of claim 64, wherein step (c)(4) employs a gaussian blur model.

66. The method of claim 64, wherein step (c)(4) employs a cylindrical sinc blur model.

67. The method of claim 1, where step (c) comprises the steps of:

(1) setting an initial differential blur spread equal to 1.0;

(2) performing a forward pass through said first and second images to generate a plurality of forward differential blur spreads and a plurality of forward cost function values using local recursive parameter adaption in the spatial domain;

(3) performing a backward pass through said first and second images, starting where the forward pass ended, to generate a plurality of backward differential blur spreads and a plurality of backward cost function values using local recursive parameter adaption in the spatial domain; and

(4) selecting a plurality of local differential blur spreads corresponding to a plurality of image pixel locations, whereby each local differential blur spread is selected from a corresponding local forward differential blur spread and a corresponding local backward differential blur spread in accordance with the minimum of a corresponding local forward cost function value and a corresponding local backward cost function value.

68. The method of claim 67, wherein step (c) further comprises the step of:

(5) generating a plurality of range values from said plurality of local differential blur spreads, wherein each range value corresponds to an image pixel location.

69. The method of claim 3, wherein step (e) comprises the step of time-delayed focussing the focussed camera, said focussed camera being located overhead a conveyor system downstream of said camera used to generate said first image and said camera used to generate said second image.

77. The method of claim 1, wherein step (a) further comprises the step of:

(1) generating a calibration mapping corresponding to a plurality of test differential blur spreads and a plurality of test range values.

78. The method of claim 77, wherein step (a)(1) comprises the steps of:

(A) providing a test object corresponding to a test range value;

(B) generating a test image corresponding to said test object;

(C) generating a test differential blur spread corresponding to said test image;

(D) repeating steps (a)(1)(A) through (a)(1)(C) for a plurality of test range values to generate a plurality of test differential blur spreads; and

(E) generating said calibration mapping by minimizing a cost function in accordance with said plurality of test range values and said plurality of test differential blur spreads.

79. The method of claim 3, wherein step (a) further comprises the step of:

(1) generating a calibration mapping corresponding to a plurality of test differential blur spreads and a plurality of test range values.

80. The method of claim 79, wherein step (a)(1) comprises the steps of:

(A) generating a first test image corresponding to a test object using said camera having said first camera parameter;

(B) generating a second test image corresponding to said test object using said camera having said second camera parameter;

(C) generating a test differential blur spread corresponding to said first and second test images;

(D) generating a third test image with a test focussing camera, said third test image corresponding to said test differential blur spread;

(E) determining a test focus distance corresponding to said test focussing camera during step (a)(1)(D);

(F) repeating steps (a)(1)(A) through (a)(1)(E) for a plurality of test differential blur spreads; and

(G) generating said calibration mapping by minimizing a cost function in accordance with said plurality of test differential blur spreads and said plurality of test focus distances.

17. An apparatus for determining a differential blur spread corresponding to object, comprising:

(a) a camera, having a first camera parameter, for providing a first image of said object;

(b) camera means, having a second camera parameter, for providing a second image of said object, said second camera parameter being different from said first camera parameter; and

(c) means for performing a relaxation procedure in accordance with said first and second images to generate said differential blur spread.

18. The apparatus of claim 17, further comprising:

(d) means for determining a range of said object in accordance with said differential blur spread.

19. The apparatus of claim 18, further comprising:

(e) means for focussing a camera in accordance with said range.

20. The apparatus of claim 19, wherein said object is a package on a conveyor system and said camera is a high-resolution camera positioned overhead said conveyor system to generate images used to read a label on said package.

21. The apparatus of claim 17, wherein said first camera parameter is a first focal gradient and said second camera parameter is a second focal gradient.

22. The apparatus of claim 17, wherein:

camera (a) comprises a first camera having a first aperture size; and

camera means (b) comprises a second camera having a second aperture size, said second aperture size being different from said first aperture size.

23. The apparatus of claim 17, wherein:

camera (a) comprises a first camera having a first focal length; and

camera means (b) comprises a second camera having a second focal length, said second focal length being different from said first focal length.

24. The apparatus of claim 17, wherein:

camera (a) comprises a first camera having a first distance between a second principal plane and an image detector plane of said first camera; and

camera means (b) comprises a second camera having a second distance between a second principal plane and an image detector plane of said second camera, said second distance being different from said first distance.

25. The apparatus of claim 17, wherein means (c) comprises means for performing a temporal relaxation procedure in accordance with said first and second images to generate said differential blur spread.

26. The apparatus of claim 17, wherein means (c) comprises:

(1) means for generating a 2N point discrete Fourier transform of said first image and for generating a 2N point discrete Fourier transform of said second image;

(2) means for generating a raw gain and said differential blur spread in accordance with said 2N point discrete Fourier transforms of said first and second images;

(3) means for generating a transform of a time-varying regularization vector in accordance with said raw gain and said differential blur spread;

(4) means for generating a transform of an impulse response in accordance with said time-varying regularization vector and said 2N point discrete Fourier transforms of said first and second images;

(5) means for updating said raw gain and said differential blur spread in accordance with said impulse response;

(6) means for generating a squared error in accordance with said impulse response, said updated raw gain, and said updated differential blur spread; and

(7) means for testing said squared error for convergence.

27. The apparatus of claim 17, wherein means (c) comprises means for performing a spatial relaxation procedure in accordance with said first and second images to generate said differential blur spread.

28. The apparatus of claim 27, wherein:

means (c) comprises means for performing said spatial relaxation procedure in accordance with a forward pass through said first and second images to generate a plurality of forward differential blur spreads and a plurality of forward cost function values; and

further comprising;

(d) means for determining a plurality of ranges corresponding to a plurality of objects in accordance with said plurality of forward differential blur spreads;

(e) means for performing said spatial relaxation procedure in accordance with a backward pass through said first and second images to generate a plurality of backward differential blur spreads and a plurality of backward cost function values;

(f) means for comparing said plurality of backward cost function values with said plurality of forward cost function values; and

(g) means for updating said plurality of ranges in accordance with said comparison of means (f).

29. The apparatus of claim 17, wherein means (c) comprises:

(1) means for;

(a) selecting a first first-image sample from said first image and a corresponding first second-image sample from said second image, and

(b) selecting a second first-image sample from said first image and a corresponding second second-image sample from said second image; and

(2) means for;

(a) generating a first differential blur spread in accordance with said first first-image and first second-image samples, and

(b) generating a second differential blur spread in accordance with said second first-image and second second-image samples,

30. The apparatus of claim 29, further comprising:

(d) means for;

(1) determining a first range value corresponding to said first first-image and second-image samples in accordance with said first differential blur spread; and

(2) determining a second range value corresponding to said second first-image and second-image samples in accordance with said second differential blur spread,

31. The apparatus of claim 30, wherein said first range value corresponds to the height of a first stack of nested packages and said second range value corresponds to the height of a second stack of nested packages.

32. The apparatus of claim 17, wherein:

camera (a) comprises a first camera having a focal length, an aperture size, and a distance between a second principal plane and an image detector plane of said first camera, and

means (c) comprises means for performing said relaxation procedure independent of said focal length, said aperture size, and said distance of said first camera.

70. The apparatus of claim 17, wherein means (c) comprises:

(1) means for generating an initial differential blur spread in accordance with said first and second images; and

(2) means for performing a recursive relaxation procedure in accordance with said first and second images and said initial differential blur spread to generate an improved differential blur spread.

71. The apparatus of claim 17, wherein means (c) comprises:

(1) means for generating a 2N point discrete Fourier transform of said first image;

(2) means for generating a 2N point discrete Fourier transform of said second image;

(3) means for generating an initial gain and an initial differential blur spread in accordance with said 2N point discrete Fourier transforms of said first and second images;

(4) means for generating the discrete Fourier transform of a time-varying regularization vector in accordance with said initial gain and said initial differential blur spread;

(5) means for generating the discrete Fourier transform of the differential impulse response between said camera (a) and said camera means (b) in accordance with said discrete Fourier transformed time-varying regularization vector;

(6) means for updating said initial gain and said initial differential blur spread in accordance with said discrete Fourier transformed differential impulse response;

(7) means for generating a squared error in accordance with said discrete Fourier transformed differential impulse response, said updated gain, and said updated differential blur spread;

(8) means for testing for the convergence of said squared error; and

(9) means for repeating the operations of means (c)(4) through (c)(7), in accordance with said testing of means (c)(8), using said updated gain and said updated differential blur spread.

72. The apparatus of claim 71, wherein means (c)(4) employs a gaussian blur model.

73. The apparatus of claim 71, wherein means (c)(4) employs a cylindrical sinc blur model.

74. The apparatus of claim 17, where means (c) comprises:

(1) means for setting an initial differential blur spread equal to 1.0;

(2) means for performing a forward pass through said first and second images to generate a plurality of forward differential blur spreads and a plurality of forward cost function values using local recursive parameter adaption in the spatial domain;

(3) means for performing a backward pass through said first and second images, starting where the forward pass ended, to generate a plurality of backward differential blur spreads and a plurality of backward cost function values using local recursive parameter adaption in the spatial domain; and

(4) means for selecting a plurality of local differential blur spreads corresponding to a plurality of image pixel locations, whereby each local differential blur spread is selected from a corresponding local forward differential blur spread and a corresponding local backward differential blur spread in accordance with the minimum of a corresponding local forward cost function value and a corresponding local backward cost function value.

75. The apparatus of claim 74, wherein means (c) further comprises:

(5) means for generating a plurality of range values from said plurality of local differential blur spreads, wherein each range value corresponds to an image pixel location.

76. The apparatus of claim 19, wherein means (e) comprises the means for time-delayed focussing the focussed camera, said focussed camera being located overhead a conveyor system downstream of said camera used to generate said first image and said camera used to generate said second image.

81. The apparatus of claim 17, wherein means (c) comprises means for generating a calibration mapping corresponding to a plurality of test differential blur spreads and a plurality of test range values.

82. The apparatus of claim 81, wherein means (c) comprises:

(1) test camera means for generating a plurality of test images corresponding to a plurality of test objects corresponding to said plurality of test range values;

(2) means for generating said plurality of test differential blur spreads corresponding to said plurality of test images; and

(3) means for generating said calibration mapping by minimizing a cost function in accordance with said plurality of test range values and said plurality of test differential blur spreads.

83. The apparatus of claim 19, further comprising:

(f) means for generating a calibration mapping corresponding to a plurality of test differential blur spreads and a plurality of test focus distances.

84. The apparatus of claim 83, wherein means (f) comprises:

(1) test camera means, having said first camera parameter, for generating a plurality of first test images corresponding to a test object;

(2) test camera means, having said second camera parameter, for generating a plurality of second test images corresponding to said test object;

(3) means for generating said plurality of test differential blur spreads corresponding to said pluralities of first and second test images;

(4) a test focussing camera for generating a plurality of third test images, said plurality of third test images corresponding to said plurality of test differential blur spreads;

(5) means for determining said plurality of test focus distances corresponding to said test focussing camera; and

(6) means for generating said calibration mapping by minimizing a cost function in accordance with said plurality of test differential blur spreads and said plurality of test focus distances.

33. A method for determining a differential blur spread corresponding to an object, comprising the steps of:

(a) providing a first image of said object with a first camera having a first focal length, a first aperture size, a first distance between a second principal plane and an image detector plane of said first camera, and a first camera parameter;

(b) generating a second image of said object, said second image being generated with a camera having a second camera parameter different from said first camera parameter; and

(c) generating said differential blur spread in accordance with said first and second images and independent of said first focal length, said first aperture size, and said first distance of said first camera.

34. The method of claim 33, further comprising the step of:

(d) determining a range of said object in accordance with said differential blur spread.

35. The method of claim 34, further comprising the step of:

(e) focussing a camera in accordance with said range.

36. The method of claim 35, wherein said object is a package on a conveyor system and said focussed camera is a high-resolution camera positioned overhead said conveyor system to generate images used to read a label on said package.

37. The method of claim 33, wherein said first camera parameter is a first focal gradient and said second camera parameter is a second focal gradient.

38. The method of claim 33, wherein step (b) comprises the step of generating said second image with a second camera having a second aperture size, said second aperture size being different from said first aperture size.

39. The method of claim 33, wherein step (b) comprises the step of generating said second image with a second camera having a second focal length, said second focal length being different from said first focal length.

40. The method of claim 33, wherein step (b) comprises the step of generating said second image with a second camera having a second distance between a second principal plane and an image detector plane of said second camera, said second distance being different from said first distance.

41. The method of claim 33, wherein step (c) comprises the step of performing a temporal relaxation procedure in accordance with said first and second images to generate said differential blur spread.

42. The method of claim 33, wherein step (c) comprises the steps of:

(1) generating a 2N point discrete Fourier transform of said first image;

(2) generating a 2N point discrete Fourier transform of said second image;

(3) generating a raw gain and said differential blur spread in accordance with said 2N point discrete Fourier transforms of said first and second images;

(4) generating a transform of a time-varying regularization vector in accordance with said raw gain and said differential blur spread;

(5) generating a transform of an impulse response in accordance with said time-varying regularization vector and said 2N point discrete Fourier transforms of said first and second images;

(6) updating said raw gain and said differential blur spread in accordance with said impulse response;

(7) generating a squared error in accordance with said impulse response, said updated raw gain, and said updated differential blur spread;

(8) testing said squared error for convergence; and

(9) repeating steps (c)(4) through (c)(7) in accordance with said testing of step (c)(8).

43. The method of claim 33, wherein step (c) comprises the step of performing a spatial relaxation procedure in accordance with said first and second images to generate said differential blur spread.

44. The method of claim 43, wherein:

step (c) comprises the step of performing said spatial relaxation procedure in accordance with a forward pass through said first and second images to generate a plurality of forward differential blur spreads and a plurality of forward cost function values; and

further comprising the steps of;

(d) determining a plurality of ranges corresponding to a plurality of objects in accordance with said plurality of forward differential blur spreads;

(e) performing said spatial relaxation procedure in accordance with a backward pass through said first and second images to generate a plurality of backward differential blur spreads and a plurality of backward cost function values;

(f) comparing said plurality of backward cost function values with said plurality of forward cost function values; and

(g) updating said plurality of ranges in accordance with said comparison of step (f).

45. The method of claim 33, wherein step (c) comprises the steps of:

(1) selecting a first first-image sample from said first image and a corresponding first second-image sample from said second image;

(2) generating a first differential blur spread in accordance with said first first-image and first second-image samples;

(3) selecting a second first-image sample from said first image and a corresponding second second-image sample from said second image; and

(4) generating a second differential blur spread in accordance with said second first-image and second second-image samples.

46. The method of claim 45, further comprising the steps of:

(d) determining a first range value corresponding to said first first-image and second-image samples in accordance with said first differential blur spread; and

(e) determining a second range value corresponding to said second first-image and second-image samples in accordance with said second differential blur spread.

47. The method of claim 46, wherein said first range value corresponds to the height of a first stack of nested packages and said second range value corresponds to the height of a second stack of nested packages.

48. An apparatus for determining a differential blur spread corresponding to an object, comprising:

(a) a first camera for providing a first image of said object, said first camera having a first focal length, a first aperture size, a first distance between a second principal plane and an image detector plane of said first camera, and a first camera parameter;

(b) means, having a second camera parameter, for generating a second image of said object, said second camera parameter being different from said first camera parameter; and

(c) means for generating said differential blur spread in accordance with said first and second images and independent of said first focal length, said first aperture size, and said first distance of said first camera.

49. The apparatus of claim 48, further comprising:

(d) means for determining a range of said object in accordance with said differential blur spread.

50. The apparatus of claim 49, further comprising:

(e) means for focussing a camera in accordance with said range.

51. The apparatus of claim 50, wherein said object is a package on a conveyor system and said camera is a high-resolution camera positioned overhead said conveyor system to generate images used to read a label on said package.

52. The apparatus of claim 48, wherein said first camera parameter is a first focal gradient and said second camera parameter is a second focal gradient.

53. The apparatus of claim 48, wherein means (b) comprises a second camera having a second aperture size, said second aperture size being different from said first aperture size.

54. The apparatus of claim 48, wherein means (b) comprises a second camera having a second focal length, said second focal length being different from said first focal length.

55. The apparatus of claim 48, wherein means (b) comprises a second camera having a second distance between a second principal plane and an image detector plane of said second camera, said second distance being different from said first distance.

56. The apparatus of claim 48, wherein means (c) comprises means for performing a temporal relaxation procedure in accordance with said first and second images to generate said differential blur spread.

57. The apparatus of claim 48, wherein means (c) comprises:

(1) means for generating a 2N point discrete Fourier transform of said first image and for generating a 2N point discrete Fourier transform of said second image;

(2) means for generating a raw gain and said differential blur spread in accordance with said 2N point discrete Fourier transforms of said first and second images;

(3) means for generating a transform of a time-varying regularization vector in accordance with said raw gain and said differential blur spread;

(4) means for generating a transform of an impulse response in accordance with said time-varying regularization vector and said 2N point discrete Fourier transforms of said first and second images;

(5) means for updating said raw gain and said differential blur spread in accordance with said impulse response;

(6) means for generating a squared error in accordance with said impulse response, said updated raw gain, and said updated differential blur spread; and

(7) means for testing said squared error for convergence.

58. The apparatus of claim 48, wherein means (c) comprises means for performing a spatial relaxation procedure in accordance with said first and second images to generate said differential blur spread.

59. The apparatus of claim 58, wherein:

means (c) comprises means for performing said spatial relaxation procedure in accordance with a forward pass through said first and second images to generate a plurality of forward differential blur spreads and a plurality of forward cost function values; and

further comprising;

(d) means for determining a plurality of ranges corresponding to a plurality of objects in accordance with said plurality of forward differential blur spreads;

(e) means for performing said spatial relaxation procedure in accordance with a backward pass through said first and second images to generate a plurality of backward differential blur spreads and a plurality of backward cost function values;

(f) means for comparing said plurality of backward cost function values with said plurality of forward cost function values; and

(g) mean for updating said plurality of ranges in accordance with said comparison of means (f).

60. The apparatus of claim 48, wherein means (c) comprises:

(1) means for;

(a) selecting a first first-image sample from said first image and a corresponding first second-image sample from said second image, and

(b) selecting a second first-image sample from said first image and a corresponding second second-image sample from said second image; and

(2) means for;

(a) generating a first differential blur spread in accordance with said first first-image and first second-image samples, and

(b) generating a second differential blur spread in accordance with said second first-image and second second-image samples.

61. The apparatus of claim 60, further comprising:

(d) means for;

(1) determining a first range value corresponding to said first first-image and second-image samples in accordance with said first differential blur spread; and

(2) determining a second range value corresponding to said second first-image and second-image samples in accordance with said second differential blur spread.

62. The apparatus of claim 61, wherein said first range value corresponds to the height of a first stack of nested packages and said second range value corresponds to the height of a second stack of nested packages.

85. An apparatus for determining a differential blur spread corresponding to object, comprising:

(a) camera means, having a first camera parameter, for providing a first image of said object;

(b) camera means, having a second camera parameter, or providing a second image of said object, said second camera parameter being different from said first camera parameter;

(c) means for performing a relaxation procedure in accordance with said first and second images to generate said differential blur spread;

(d) means for determining a range of said object in accordance with said differential blur spread; and

(e) means for focussing a camera in accordance with said range.

86. The apparatus of claim 85, wherein said object is a package on a conveyor system and said camera is a high-resolution camera positioned overhead said conveyor system to generate images used to read a label on said package.

87. The apparatus of claim 85, wherein means (e) comprises the means for time-delayed focussing the focussed camera, said focussed camera being located overhead a conveyor system downstream of said camera used to generate said first image and said camera used to generate said second image.

88. The apparatus of claim 85, further comprising:

(f) means for generating a calibration mapping corresponding to a plurality of test differential blur spreads and a plurality of test focus distances.

89. The apparatus of claim 88, wherein means (f) comprises:

(1) test camera means, having said first camera parameter, for generating a plurality of first test images corresponding to a test object;

(2) test camera means, having said second camera parameter, for generating a plurality of second test images corresponding to said test object;

(3) means for generating said plurality of test differential blur spreads corresponding to said pluralities of first and second test images;

(4) a test focussing camera for generating a plurality of third test images, said plurality of third test images corresponding to said plurality of test differential blur spreads;

(5) means for determining said plurality of test focus distances corresponding to said test focussing camera; and

(6) means for generating said calibration mapping by minimizing a cost function in accordance with said plurality of test differential blur spreads and said plurality of test focus distances.