Cepstral method and system for detecting/classifying objects from air-based or space-based images

• US 6,333,986 B1
• Filed: 05/08/1998
• Issued: 12/25/2001
• Est. Priority Date: 05/08/1998
• Status: Expired due to Term

• Current Assignee: Lockheed Martin Corporation (Martin Marietta Corporation)
• Original Assignee: Lockheed Martin Corporation (Martin Marietta Corporation)
• Inventors: Petty, Joe V.
• Primary Examiner(s): Patel, Jayanti K.
• Application Number:
  US09/075,100
• Time in Patent Office: 1,327 Days
• Field of Search: 382/100, 382/103, 382/109, 382/250, 382/260, 382/275, 382/276, 382/278-279, 382/280, 342/22-27, 342/192-193, 342/196, 342/53, 250/330
• US Class Current: 382/103
• CPC Class Codes: G01S 13/867 Combination of radar systems with cameras
• CPC Class Codes: G01S 13/9027 Pattern recognition for feature extraction
• CPC Class Codes: G01S 7/411 Identification of targets based on measurements of radar reflectivity G01S7/415 takes precedence
• CPC Class Codes: G06V 10/431 Frequency domain transformation; Autocorrelation

Abstract

A system and method for detecting and/or classifying an obscured discrete cultural object and/or an obscured replicated object using image data from an optical, infrared or synthetic aperture radar imaging system is disclosed. Generally, the method and system of the present invention are directed to performing a cepstral analysis on the image data to attentuate the corruption signal in the image data and/or to enhance the discrete cultural object signal and/or the replicated object signature, and displaying an output of the cepstral analysis in the pixel and/or the spatial quefrency domain to detect and/or classify the discrete cultural object and/or the replicated object.

Claims

1. A method for detecting at least a first cultural object using at least first image data from one of a first optical, a first infrared and a first synthetic aperture radar image, wherein the first image data includes signals corresponding to noise and to at least a first cultural object convolved with corruption, said method comprising the steps of:

processing the first image data from a pixel domain into the spatial quefrency domain to produce from said corruption and at least the first cultural object signals separable cepstral coefficients corresponding to at least the first cultural object and corruption signals in the spatial quefrency domain;

processing in the spatial quefrency domain at least a first cepstral coefficient corresponding to the corruption signal to attenuate at least a portion of the corruption signal, wherein at least a first cepstral coefficient corresponding to at least a portion of at least the first cultural object signal remains; and

processing at least the first cepstral coefficient corresponding to at least the portion of the first cultural object signal in the spatial quefrency domain to obtain at least the portion of at least the first cultural object signal corresponding to at least the first cultural object in the pixel domain, wherein at least a portion of the first cultural object is displayable.

2. A method, as claimed in claim 1, further comprising the step of:

displaying at least the portion of the first cultural object corresponding to the portion of the first cultural object signal in the pixel domain.

3. A method, as claimed in claim 1, wherein said processing said first image data step comprises the steps of:

applying a two-dimensional Fourier transform to the first image data in the pixel domain to at least transform the first image data into at least a first discrete term, wherein the first discrete term comprises a product of a spatial frequency of at least the first cultural object signal and a spatial frequency of the corruption signal in the spatial frequency domain;

applying in the spatial frequency domain a complex logarithm to at least the first discrete term, wherein the output of the complex logarithm comprises a discrete sum, said discrete sum comprising a sum of the complex logarithm of the spatial frequency of at least the first cultural object signal and the complex logarithm of the spatial frequency of the corruption signal; and

applying an inverse two-dimensional Fourier transform to the discrete sum to transform the discrete sum into at least the first cepstral coefficients corresponding to at least the first cultural object signal and the corruption signal in the spatial quefrency domain.

4. A method, as claimed in claim 1, wherein said processing in the spatial quefrency domain at least the first cepstral coefficient corresponding to the corruption signal step comprises the step of:

modifying at least the first cepstral coefficient corresponding to at least the corruption signal to attenuate at least the portion of the corruption signal.

5. A method, as claimed in claim 1, wherein said processing at least the first cepstral coefficient corresponding to at least the first cultural object signal step comprises the steps of:

applying a two-dimensional Fourier transform to transform at least the first cepstral coefficient corresponding to at least the portion of the first cultural object signal in the spatial quefrency domain to a complex logarithm of a spatial frequency of at least the portion of the first cultural object signal;

applying an inverse complex logarithm to the complex logarithm of the spatial frequency of at least the portion of the first cultural object signal, wherein the output of the inverse complex logarithm comprises a spatial frequency of the portion of at least the first cultural object signal in the spatial frequency domain; and

applying a two-dimensional inverse Fourier transform to transform at least the spatial frequency of at least the portion of at least the first cultural object signal into at least the portion of at least the first cultural object signal in the pixel domain.

6. A method for detecting at least a first replicated object using at least first image data from one of a first optical, a first infrared and a first synthetic aperture radar image, the first replicated object comprising a plurality of objects arranged in a first array, wherein the first image data includes signals corresponding to corruption and at least a first replicated signature corresponding to at least the first replicated object, said method comprising the steps of:

processing the first image data from a pixel domain into a spatial quefrency domain to produce separable cepstral coefficients corresponding to at least a first amplification factor, the first replicated object signature and corruption signal in the spatial quefrency domain;

processing in the spatial quefrency domain at least a first cepstral coefficient corresponding to the corruption signal to attenuate at least a portion of the corruption signal, wherein at least a first cepstral coefficient corresponding to at least a portion of the first replicated object signature remains; and

processing at least the first cepstral coefficients corresponding to at least the portion of the first replicated object signature and the first amplification factor to obtain an enhanced first replicated object signature corresponding to at least the portion of the first replicated object signature in the pixel domain, wherein at least a portion of the first replicated object is displayable in the pixel domain.

7. A method as claimed in claim 6, wherein said processing said first image data step comprises the steps of:

applying a two-dimensional Fourier transform to the first image data in the pixel domain to transform the first image data into at least a first replicated term, wherein the first replicated term comprises a product of the first amplification factor and a spatial frequency of each of the first replicated object signature and the corruption signal;

applying in a spatial frequency domain a complex logarithm to at least the first replicated term, wherein the output of the complex logarithm comprises a replicated sum, said replicated sum comprising a sum of the complex logarithm of the first amplification factor, the complex logarithm of the spatial frequency of the first replicated object signature and the complex logarithm of the spatial frequency of the corruption signal; and

applying an inverse two-dimensional Fourier transform to the replicated sum to transform the replicated sum into at least the first cepstral coefficients corresponding to the first replicated object signature, the first amplification factor and the corruption signal in the spatial quefrency domain.

8. A method, as claimed in claim 7, further comprising, after said applying the inverse two-dimensional Fourier transform step, the step of:

mapping at least the first cepstral coefficients corresponding to the first replicated object signature and the first amplification factor in the spatial quefrency domain to produce at least a first displayable representation of at least the first cepstral coefficients corresponding to the first replicated object signature and the first amplification factor in the spatial quefrency domain, wherein the first replicated object is detectable.

9. A method, as claimed in claim 6, wherein said step of processing in the spatial quefrency domain at least the first cepstral coefficient corresponding to the corruption signal comprises the step of:

modifying at least the first cepstral coefficient corresponding to the corruption signal to attenuate at least the portion of the corruption signal.

10. A method, as claimed in claim 6, further comprising the step of:

modifying at least the first cepstral coefficients corresponding to the portion of the first replicated object signature and the first amplification factor to accentuate at least the portion of the first replicated object signature.

11. A method, as claimed in claim 6, wherein said step of processing at least the first cepstral coefficients corresponding to at least the portion of the first replicated object signature and the first amplification factor comprises the steps of:

applying a two-dimensional Fourier transform to transform at least the first cepstral coefficients corresponding to at least the portion of the first replicated object signature and the first amplification factor in the spatial quefrency domain to a complex logarithm of a spatial frequency of at least the portion of at least the first replicated object signature and a complex logarithm of the first amplification factor;

applying an inverse complex logarithm to the complex logarithm of the spatial frequency of at least the portion of the first replicated object signature and the first amplification factor, wherein the output of the inverse logarithm comprises a spatial frequency of at least the portion of the first replicated object signature and the first amplification factor in the spatial frequency domain; and

applying a two-dimensional inverse Fourier transform to transform at least the spatial frequency of at least the portion of the first replicated object signature and first amplification factor into at least the portion of the enhanced first replicated object signature in the pixel domain.

12. A method, as claimed in claim 6, further comprising the step of:

displaying at least the portion of the enhanced first replicated object in the pixel domain.

13. A method for detecting at least a first cultural object using at least first image data from one of a first optical, a first infrared and a first synthetic aperture radar image, wherein the first image data includes signals corresponding to at least the first cultural object convolved with corruption, said method comprising the steps of:

applying a two-dimensional Fourier transform to the first image data in a pixel domain to at least transform the first image data into at least a first discrete term, wherein the first discrete term comprises a product of a spatial frequency of at least the first cultural object signal and a spatial frequency of the corruption signal in the spatial frequency domain;

applying in the spatial frequency domain a complex logarithm to at least the first discrete term, wherein the output of the complex logarithm comprises a discrete sum, said discrete sum comprising a sum of the complex logarithm of the spatial frequency of at least the first cultural object signal and the complex logarithm of the spatial frequency of the corruption signal;

applying an inverse two-dimensional Fourier transform to the discrete sum to transform the discrete sum into cepstral coefficients corresponding to at least the first cultural object signal and the corruption signal in a spatial quefrency domain; and

processing in the spatial quefrency domain at least a first cepstral coefficient corresponding to the corruption signal to attenuate at least a portion of the corruption signal, wherein at least a first cepstral coefficient corresponding to at least a portion of the first cultural object remains.

14. A method, as claimed in claim 13, further comprising the steps of:

processing at least the first cepstral coefficient corresponding to at least the portion of the first cultural object signal to obtain at least the portion of the first cultural object signal corresponding to at least a portion of the first cultural object signature in the pixel domain, wherein at least the portion of the first cultural object is displayable.

15. A method, as claimed in claim 14, wherein said step of processing in the spatial quefrency domain at least the first cepstral coefficient corresponding to at least the portion of the corruption signal comprises the step of:

modifying at least the first cepstral coefficient corresponding to at least the corruption signal to attenuate at least the portion of the corruption signal.

16. A method, as claimed in claim 14, wherein said step of processing at least the first cepstral coefficient corresponding to at least the portion of the first cultural object signal comprises the steps of:

applying a two-dimensional Fourier transform to transform at least the first cepstral coefficient corresponding to at least the portion of the first cultural object signal in the spatial quefrency domain to a complex logarithm of the spatial frequency of at least the portion of at least the first cultural object signal;

applying an inverse complex logarithm to the complex logarithm of the spatial frequency of at least the portion of the first cultural object signal, wherein the output of the inverse logarithm comprises a spatial frequency of at least the portion of at least the first cultural object signal in the spatial frequency domain; and

applying a two-dimensional inverse Fourier transform to transform at least the spatial frequency of the portion of at least the first cultural object signal into at least the portion of at least the first cultural object signal in the pixel domain.

17. A method, as claimed in claim 16, further comprising the step of:

displaying at least one of a representation of the first cultural object in the spatial quefrency domain and the portion of the first cultural object in the pixel domain.

18. A method for detecting at least a first replicated object using first image data from one of a first optical, a first infrared and a first synthetic aperture radar image, the first replicated object comprising a plurality of objects arranged in a first pattern, wherein the first image data includes signals corresponding to corruption and at least a first replicated object signature corresponding to at least the first replicated object, said method comprising the steps of:

applying a two-dimensional Fourier transform to the first image data in a pixel domain to transform the first image data into at least a first replicated term, wherein the first replicated term comprises a product of a first amplification factor and a spatial frequency of each of the first replicated object signature and the corruption signal in a spatial frequency domain;

applying in the spatial frequency domain a complex logarithm to at least the first replicated term, wherein the output of the complex logarithm comprises a replicated sum, said replicated sum comprising a sum of the complex logarithm of the first amplification factor, the complex logarithm of the spatial frequency of the first replicated object signature and the complex logarithm of the spatial frequency of the corruption signal; and

applying an inverse two-dimensional Fourier transform to the replicated sum to transform the replicated sum into the cepstral coefficients corresponding to the first replicated object signature, the first amplification factor and the corruption signal in a spatial quefrency domain, wherein at least the first replicated object is detectable.

19. A method, as claimed in claim 18, further comprising the step of:

mapping at least first cepstral coefficients corresponding to the first replicated object signature and the first amplification factor in the spatial quefrency domain to produce at least a first displayable representation of at least one of the first cepstral coefficients corresponding to the first replicated object signature and the first amplification factor in the spatial quefrency domain.

20. A method, as claimed in claim 19, further comprising the step of:

displaying at least the first displayable representation of at least one of the first cepstral coefficients corresponding to the first replicated object signature and first amplification factor to detect at least the first replicated object.

21. A method, as claimed in claim 18, further comprising the steps of:

processing in the spatial quefrency domain at least a first cepstral coefficient corresponding to the corruption signal to attenuate at least a portion of the corruption signal, wherein at least the first cepstral coefficients corresponding to at least a portion of the first replicated object signature and the first amplification factor remain; and

processing at least the first cepstral coefficients corresponding to at least the portion of the first replicated object signature and the first amplification factor to obtain an enhanced first replicated object signature corresponding to at least a portion of the first replicated object signature in the pixel domain, wherein at least a portion of the enhanced first replicated object is displayable.

22. A method, as claimed in claim 21, wherein said step of processing at least the first cepstral coefficients corresponding to at least the portion of the first replicated object signature and the first amplification factor comprises the step of:

modifying at least the first cepstral coefficient corresponding to at least the portion of the first replicated object signature to accentuate at least the portion of the first replicated object signature.

23. A method, as claimed in claim 21, wherein said step of processing at least the first cepstral coefficients corresponding to at least the portion of the first replicated object signature and the first amplification factor comprises the steps of:

applying a two-dimensional Fourier transform to transform at least the first cepstral coefficients corresponding to at least the portion of the first replicated object signature and the first amplification factor in the spatial quefrency domain to a complex logarithm of the spatial frequency of at least the portion of at least the first replicated object signature and the first amplification factor;

applying an inverse complex logarithm to the complex logarithm of the spatial frequency of at least the portion of the first replicated object signature and the first amplification factor, wherein the output of the inverse logarithm comprises a spatial frequency of at least the portion of at least the first replicated object signature and the first amplification factor in the spatial frequency domain; and

applying a two-dimensional inverse Fourier transform to transform at least the spatial frequency of at least the portion of at least the first replicated object signature and the first amplification factor into at least the portion of at least the enhanced first replicated object signature in the pixel domain.

24. A method, as claimed in claim 23, further comprising the step of:

displaying at least the portion of the first replicated object corresponding to at least the portion of at least the enhanced first replicated object signature in the pixel domain.

25. A method for detecting at least one of a first cultural object and a first replicated object using at least first image data from one of a first optical, a first infrared and a first synthetic aperture radar image, the first replicated object comprising replicated objects, wherein the first image data in a pixel domain includes signals corresponding to noise and corruption and at least one of a first cultural object signal corresponding to the first cultural object and a first replicated object signature corresponding to at least the first replicated object, said method comprising the steps of:

performing a cepstral analysis on at least the first image data to at least one of attenuate a portion of the corruption signal and enhance at least one of the first cultural object signal and the first replicated object signature; and

detecting at least one of the first cultural object and the first replicated object in at least one of a spatial quefrency domain and the pixel domain.

26. A method, as claimed in claim 25, wherein said detecting step comprises the step of:

displaying in at least one of the spatial quefrency domain and the pixel domain a first representation corresponding to the first replicated object to detect the first replicated object.

27. A method, as claimed in claim 25, wherein said detecting step comprises the step of:

displaying in at least one of the spatial quefrency domain and the pixel domain a first representation corresponding to the first cultural object to detect the first cultural object.

28. A method, as claimed in claim 25, wherein said performing step comprises the step of:

mapping a representation of at least one of the first cultural object signal and the first replicated object signature in the spatial quefrency domain.

29. A system for detecting at least one of a first cultural object and a first replicated object using at least first image data from one of a first optical, a first infrared and a first synthetic aperture radar image, the first replicated object comprising a plurality of objects arranged in a pattern, wherein the first image data in a pixel domain includes signals corresponding to noise and corruption and at least one of a first cultural object signal corresponding to the first cultural object and a first replicated object signature corresponding to at least the first replicated object, said system comprising:

means for performing a cepstral analysis on at least said first image data to at least one of attenuate a portion of the corruption signal and enhance at least the first replicated object signature; and

means for displaying an output of said means for performing in at least one of the pixel domain and a spatial quefrency domain to detect at least one of the first cultural object and the first replicated object.

30. A system, as claimed in claim 29, wherein said means for performing the cepstral analysis comprises:

means for processing said first image data from the pixel domain into the spatial quefrency domain to obtain from said first image data separable cepstral coefficients corresponding to at least one of the first cultural object and corruption signals in the spatial quefrency domain and at least the first replicated object signature, a first amplification factor and the corruption signal in the spatial quefrency domain.

31. A system, as claimed in claim 30, wherein said means for performing further comprises:

means for mapping displayable representations of at least a first of said cepstral coefficients corresponding to at least one of the first cultural object and the first replicated object signature to detect at least one of the first cultural object and the first replicated object.

32. A system, as claimed in claim 30, wherein said means for processing said first image data comprises:

means for taking a two-dimensional Fourier transform of said first image data in the pixel domain to at least transform said first image data into at least one of a first discrete term and a first replicated term, said first discrete term including a product of spatial frequencies of at least the first cultural object signal and the corruption signal in a spatial frequency domain, said first replicated term including a product of a first amplification factor and the spatial frequencies of at least the first replicated object signature and corruption signal;

means for taking a complex logarithm in the spatial frequency domain of at least one of said first discrete term and said first replicated term to obtain at least one of a first discrete sum and a first replicated sum, respectively, said first discrete sum including a sum of the complex logarithms of the spatial frequencies of at least the first cultural object and corruption signals, said first replicated sum including a sum of the complex logarithms of the first amplification factor and the spatial frequencies of at least the first replicated object signature and the corruption signal; and

means for taking an inverse two-dimensional Fourier transform of at least one of said first discrete sum and said first replicated sum to at least transform said at least one of said first discrete sum and said first replicated sum into said cepstral coefficients corresponding to at least one of said first cultural object signal and the corruption signal, and said first replicated object signature, the first amplification factor and the corruption signal in the spatial quefrency domain.

33. A system, as claimed in claim 30, wherein said means for performing further comprises:

means for mapping, in the spatial quefrency domain, at least a first of said cepstral coefficients corresponding to at least one of the first cultural object and the first replicated object signature to detect at least one of the first cultural object and the first replicated object signature.

34. A system, as claimed in claim 30, wherein said means for performing further comprises:

means for modifying at least a first of said cepstral coefficients corresponding to the corruption signal to substantially reject at least a portion of the corruption signal and to substantially retain at least a portion of at least one of said the first cultural object signal and the first replicated object signature and the first amplification factor.

35. A system, as claimed in claim 30, wherein said means for performing further comprises:

means for modifying at least a first of said cepstral coefficients corresponding to at least one of at least a portion of the first cultural object and the first replicated object signature to enhance at least one of the first cultural object signal and the first replicated object signature.

36. A system, as claimed in claim 30, wherein said means for performing further comprises:

means for processing at least a first of said cepstral coefficients corresponding to at least one of at least a portion of the first cultural object signal and at least a portion of the first replicated object signature and first amplification factor to obtain at least a portion of at least one of the first cultural object signal and an enhanced first replicated object signature in the pixel domain.

37. A system, as claimed in claim 30, wherein said means for performing further comprises:

means for taking a two-dimensional Fourier transform to transform said first of said cepstral coefficients corresponding to at least one of at least a portion of the first cultural object signal and at least a portion of the first replicated object signature and first amplification factor in the spatial quefrency domain to a complex logarithm of the spatial frequencies of at least one of at least the portion of the first cultural object signal and at least the portion the first replicated object signature and the first amplification factor;

means for taking, in the spatial frequency domain, an inverse complex logarithm to the complex logarithm of the spatial frequencies of at least one of at least the portion of the first cultural object signal and at least the portion of the first replicated object signature and the first amplification factor, wherein the output of the inverse logarithm comprises the spatial frequency of at least one of at least the portion of the first cultural object signal and at least the portion of the first replicated object signature and the first amplification factor; and

means for taking a two-dimensional inverse Fourier transform to transform the spatial frequency of at least one of at least the portion of the first cultural object signal and at least the portion of the first replicated object signature and the first amplification factor into one of at least the portion the first cultural object signal and at least a portion of an enhanced first replicated object signature in the pixel domain.