Displacement detection method, displacement detection device, displacement detection program, phase singularity matching method and phase singularity matching program

1. A displacement detection method to be implemented in a computer, comprising:

a Fourier transform procedure causing the computer to subject an intensity signal of an acquired image to a Fourier transform to obtain a Fourier transformed signal;

a procedure causing the computer to carry out a filtering process which destroys an Hermitian symmetry of the Fourier transformed signal to obtain a filtered Fourier transformed signal;

a procedure causing the computer to obtain a complex analytic signal by carrying out an inverse Fourier transform on the filtered Fourier transformed signal;

a phase singularity acquiring procedure causing the computer to acquire a phase singularity where values of both a real part and an imaginary part of the complex analytic signal become zero;

a phase singularity specifying procedure causing the computer to acquire predetermined feature parameters from a phase structure of the phase singularity and to specify the phase singularity based on the feature parameters; and

a displacement detecting procedure causing the computer to detect a displacement by detecting a position of the phase singularity after the displacement based on the feature parameters acquired by the phase singularity specifying procedure.

2. The displacement detection method as claimed in claim 1 , wherein the feature parameters acquired by the phase singularity specifying procedure include an angle at which a line segment making a real part zero and a line segment making an imaginary part zero intersect when values of the real part and the imaginary part of the complex analytic signal in a vicinity of the phase singularity are interpolated with a plane.

3. The displacement detection method as claimed in claim 1 , wherein the feature parameters acquired by the phase singularity specifying procedure include an eccentricity of a shape of an intensity distribution of the complex analytic signal in a vicinity of the phase singularity.

4. The displacement detection method as claimed in claim 1 , wherein the feature parameters acquired by the phase singularity specifying procedure include a vector product of a gradient of the real part of the complex analytic signal in a vicinity of the phase singularity and a gradient of the imaginary part of the complex analytic signal.

5. The displacement detection method as claimed in claim 1 , wherein the feature parameters acquired by the phase singularity specifying procedure include an angle at which a line segment making a real part zero and a line segment making an imaginary part zero intersect when values of the real part and the imaginary part of the complex analytic signal in a vicinity of the phase singularity are interpolated with a plane, an eccentricity of a shape of an intensity distribution of the complex analytic signal in the vicinity of the phase singularity, and a voracity which is a vector product of a gradient of the real part of the complex analytic signal in a vicinity of the phase singularity and a gradient of the imaginary part of the complex analytic signal.

6. The displacement detection method as claimed in claim 1 , wherein the displacement detecting procedure further comprises:

a position detecting procedure causing the computer to specify positions of the phase singularities before and after the displacement and specified by the phase singularity specifying procedure based on the feature parameters; and

a displacement measuring procedure causing the computer to measure displacements of the phase singularities based on the positions of the phase singularities before and after the displacement and detected by the position detecting procedure.

7. The displacement detection method as claimed in claim 6 , wherein the displacement measuring procedure further comprises:

a rotation center acquiring procedure causing the computer to acquire, as a center of rotation, a point where a sum of distances among a plurality of normal bisectors of line segments connecting the positions of a plurality of sets of phase singularities before and after the displacement and detected by the position detecting procedure becomes a minimum; and

a rotation angle acquiring procedure causing the computer to acquire, as a rotation angle, an angle of sides sandwiching a center of rotation of a triangle which is defined by the positions of the phase singularities before and after the displacement and detected by the position detecting procedure and the center of rotation acquired by the rotation center acquiring procedure.

8. The displacement detection method as claimed in claim 1 , wherein the filtering process includes carrying out a process using a Laguerre-Gaussian beam filter characteristic having a spiral phase characteristic with the phase singularity at the center with respect to the Fourier transformed signal and having a donut-shaped amplitude characteristic.

9. A displacement detection device comprising:

a Fourier transform means for subjecting an intensity signal of an acquired image to a Fourier transform to obtain a Fourier transformed signal;

a means for carrying out a filtering process which destroys an Hermitian symmetry of the Fourier transformed signal to obtain a filtered Fourier transformed signal;

a means for obtaining a complex analytic signal by carrying out an inverse Fourier transform on the filtered Fourier transformed signal;

a phase singularity acquiring means for acquiring a phase singularity where values of both a real part and an imaginary part of the complex analytic signal become zero;

a phase singularity specifying means for acquiring predetermined feature parameters from a phase structure of the phase singularity and for specifying the phase singularity based on the feature parameters; and

a displacement detecting means for detecting a displacement by detecting a position of the phase singularity after the displacement based on the feature parameters acquired by the phase singularity specifying means.

10. The displacement detection device as claimed in claim 9 , wherein the feature parameters acquired by the phase singularity specifying means include an angle at which a line segment making a real part zero and a line segment making an imaginary part zero intersect when values of the real part and the imaginary part of the complex analytic signal in a vicinity of the phase singularity are interpolated with a plane.

11. The displacement detection device as claimed in claim 9 , wherein the feature parameters acquired by the phase singularity specifying means include an eccentricity of a shape of an intensity distribution of the complex analytic signal in a vicinity of the phase singularity.

12. The displacement detection device as claimed in claim 9 , wherein the feature parameters acquired by the phase singularity specifying means include a vector product of a gradient of the real part of the complex analytic signal in a vicinity of the phase singularity and a gradient of the imaginary part of the complex analytic signal.

13. The displacement detection device as claimed in claim 9 , wherein the feature parameters acquired by the phase singularity specifying means include an angle at which a line segment making a real part zero and a line segment making an imaginary part zero intersect when values of the real part and the imaginary part of the complex analytic signal in a vicinity of the phase singularity are interpolated with a plane, an eccentricity of a shape of an intensity distribution of the complex analytic signal in the vicinity of the phase singularity, and a vorticity which is a vector product of a gradient of the real part of the complex analytic signal in the vicinity of the phase singularity and a gradient of the imaginary part of the complex analytic signal.

14. The displacement detection device as claimed in claim 9 , wherein the displacement measuring means comprises:

a position detecting means for specifying positions of the phase singularities before and after the displacement and specified by the phase singularity specifying means based on the feature parameters;

a displacement measuring means for measuring displacements of the phase singularities based on the positions of the phase singularities before and after the displacement and detected by the position detecting means;

a rotation center acquiring means for acquiring, as a center of rotation, a point where a sum of distances among a plurality of normal bisectors of line segments connecting the positions of a plurality of sets of phase singularities before and after the displacement and detected by the position detecting means becomes a minimum; and

a rotation angle acquiring means for acquiring, as a rotation angle, an angle of sides sandwiching a center of rotation of a triangle which is defined by the positions of the phase singularities before and after the displacement and detected by the position detecting means and the center of rotation acquired by the rotation center acquiring means.

15. The displacement detection device as claimed in claim 9 , wherein the filtering means carries out a process using a Laguerre-Gaussian beam filter characteristic having a spiral phase characteristic with the phase singularity at the center with respect to the Fourier transformed signal and having a donut-shaped amplitude characteristic.

16. A non-transitory computer-readable storage medium which stores a displacement detection program which, when executed by a computer, causes the computer to perform a process comprising:

a Fourier transform procedure causing the computer to subject an intensity signal of an acquired image to a Fourier transform to obtain a Fourier transformed signal;

a procedure causing the computer to carry out a filtering process which destroys an Hermitian symmetry of the Fourier transformed signal to obtain a filtered Fourier transformed signal;

a procedure causing the computer to obtain a complex analytic signal by carrying out an inverse Fourier transform on the filtered Fourier transformed, signal;

a phase singularity acquiring procedure causing the computer to acquire a phase singularity where values of both a real part and an imaginary part of the complex analytic signal become zero;

a phase singularity specifying procedure causing the computer to acquire predetermined feature parameters from a phase structure of the phase singularity and to specify the phase singularity based on the feature parameters; and

a displacement detecting procedure causing the computer to detect a displacement by detecting a position of the phase singularity after the displacement based on the feature parameters acquired by the phase singularity specifying procedure.

17. The non-transitory computer-readable storage medium as claimed in claim 16 , wherein the filtering process includes carrying out a process using a Laguerre-Gaussian beam filter characteristic having a spiral phase characteristic with the phase singularity at the center with respect to the Fourier transformed signal and having a donut-shaped amplitude characteristic.

18. A feature point matching method to be implemented in a computer, comprising:

a Fourier transform procedure causing the computer to subject an intensity signal of an acquired image to a Fourier transform to obtain a Fourier transformed signal;

a procedure causing the computer to carry out a filtering process which destroys an Hermitian symmetry of the Fourier transformed signal to obtain a filtered Fourier transformed signal;

a procedure causing the computer to obtain a complex analytic signal by carrying out an inverse Fourier transform on the filtered Fourier transformed signal;

a phase singularity acquiring procedure causing the computer to acquire a phase singularity where values of both a real part and an imaginary part of the complex analytic signal become zero;

a phase singularity specifying procedure causing the computer to acquire predetermined feature parameters from a phase structure of the phase singularity and to specify the phase singularity based on the feature parameters; and

a procedure causing the computer to detect a position of the phase singularity after a displacement based on the feature parameters acquired by the phase singularity specifying procedure,

wherein a phase singularity after the displacement and corresponding to a phase singularity before the displacement is searched based on a difference between feature parameters of the phase singularity before the displacement and feature parameters of the phase singularity after the displacement, and the phase singularity after the displacement and corresponding to the phase singularity before the displacement is subjected to a matching, from a similarity of geometrical structural relationships of the phase singularities.

19. The feature point matching method as claimed in claim 18 , wherein the phase singularities include, as the feature parameters, position information, an eccentricity of a shape of an intensity distribution of the complex analytic signal in a vicinity of the phase singularity, a vorticity which is a vector product of a gradient of the real part of the complex analytic signal in the vicinity of the phase singularity and a gradient of the imaginary part of the complex analytic signal, and an angle at which a line segment making the real part of the complex analytic signal in the vicinity of the phase singularity zero and a line segment making the imaginary part of the complex analytic signal zero intersect.

20. A non-transitory computer-readable storage medium which stores a phase singularity matching program which, when executed by a computer, causes the computer to perform a process comprising:

a Fourier transform procedure causing the computer to subject an intensity signal of an acquired image to a Fourier transform to obtain a Fourier transformed signal;

a procedure causing the computer to carry out a filtering process which destroys an Hermitian symmetry of the Fourier transformed signal to obtain a filtered Fourier transformed signal;

a procedure causing the computer to obtain a complex analytic signal by carrying out an inverse Fourier transform on the filtered Fourier transformed signal;

a phase singularity acquiring procedure causing the computer to acquire a phase singularity where values of both a real part and an imaginary part of the complex analytic signal become zero;

a phase singularity specifying procedure causing the computer to acquire predetermined feature parameters from a phase structure of the phase singularity and to specify the phase singularity based on the feature parameters; and

a procedure causing the computer to detect a position of the phase singularity after a displacement based on the feature parameters acquired by the phase singularity specifying procedure,

wherein a phase singularity after the displacement and corresponding to a phase singularity before the displacement is searched based on a difference between feature parameters of the phase singularity before the displacement and feature parameters of the phase singularity after the displacement, and the phase singularity after the displacement and corresponding to the phase singularity before the displacement is subjected to a matching, from a similarity of geometrical structural relationships of the phase singularities, and

the phase singularities include, as the feature parameters, position information, an eccentricity of a shape of an intensity distribution of the complex analytic signal in a vicinity of the phase singularity, a voracity which is a vector product of a gradient of the real part of the complex analytic signal in the vicinity of the phase singularity and a gradient of the imaginary part of the complex analytic signal, and an angle at which a line segment making the real part of the complex analytic signal in the vicinity of the phase singularity zero and a line segment making the imaginary part of the complex analytic signal zero intersect.