Method and system for detecting matrix-based motion including frequency transform and filtering
A method and system for detecting motion are provided. The method includes: generating a time domain matrix including vectors corresponding to variation of pixel values as elements of the time domain matrix, of a video image including a plurality of frames; generating a motion matrix from which a low frequency area of the video image is removed by multiplying the time domain matrix by a low rank matrix; and generating a result image including a plurality of frames in which vectors, which are elements of the motion matrix, are included as variation of motion pixel values.
1. A method of detecting motion, the method comprising:
generating a time domain matrix comprising vectors corresponding to variation of pixel values as elements of the time domain matrix, of a video image comprising a plurality of frames;
generating a motion matrix from which a low frequency area of the video image is removed by multiplying the time domain matrix by a low rank matrix; and
generating a result image comprising a plurality of frames in which vectors, which are elements of the motion matrix, are included as variation of motion pixel values.
2. The method of claim 1 , wherein after transforming the time domain matrix into a frequency domain, the low rank matrix filters the low frequency area, and restores a time domain image from the frequency domain matrix, and
wherein the low rank matrix is a matrix that is calculated in advance before the video image is obtained from a camera.
3. The method of claim 1 , wherein the low rank matrix has centro-symmetry.
4. The method of claim 1 , wherein the elements of the low rank matrix comprise only fixed points.
5. A motion detection system comprising:
a camera; and
an image preprocessor which transforms input image data, provided from the camera, from an analog signal into a digital signal;
the motion detection system configured to:
generate a time domain matrix comprising vectors corresponding to variation in pixel values as elements of the time domain matrix, of a video image, provided from the camera, comprising a plurality of frames;
generate a motion matrix from which a low frequency area of the video image is removed, by multiplying the time domain matrix by a low rank matrix;
generate a result image comprising a plurality of frames in which vectors, which are elements of the motion matrix, are included as variation of motion pixel values.
6. The motion detection system of claim 5 , wherein after transforming the time domain matrix into a frequency domain, the low rank matrix filters the low frequency area, and restores a time domain image from the frequency domain matrix, and
wherein the low rank matrix is a matrix that is calculated in advance before the video image is obtained from a camera.
7. The motion detection system of claim 5 , wherein the low rank matrix has centro-symmetry.
8. The motion detection system of claim 5 , wherein the elements of the low rank matrix comprise only fixed points.
9. A method of detecting motion, the method comprising:
generating a frequency domain transforming matrix which transforms a time domain matrix into a frequency domain matrix;
generating a filtering matrix which filters a low frequency component of a video image;
generating a time domain transform matrix which transforms the frequency domain matrix into a time domain matrix; and
generating a low rank matrix by multiplying the frequency domain transform matrix, the filtering matrix, and the time domain transform matrix; and
multiplying the low rank matrix by a time domain matrix comprising vectors regarding variation of pixel values of an input video image as elements of the time domain matrix.
10. The method of claim 9 , wherein a rank of the frequency domain transform matrix corresponds to a number of frames of the input video image from which the variation of the pixel values are extracted.
11. The method of claim 9 , wherein the low rank matrix L is expressed as L=D N T ·E M,N ·D N by using the frequency domain transform matrix D N , the filtering matrix E M,N , and the time domain transform matrix D N T ,
where N denotes a number of frames of the input video image from which the variation of the pixel values are extracted, and M denotes a bandwidth of the filtering matrix.
12. The method of claim 9 , wherein a rank of the low rank matrix is a value obtained by subtracting a rank of the filtering matrix from a rank of the frequency domain transform matrix.
13. The method of claim 9 , wherein the low rank matrix L has centro-symmetry.
14. The method of claim 9 , wherein the elements of the low rank matrix comprise only fixed points.
15. The method of claim 9 , wherein the frequency domain transform matrix uses a discrete cosine transform method.
16. The method of claim 9 , wherein the filtering matrix E M,N is expressed as
E
M
,
N
=
diag
(
0
,
⋯
,
0
︸
,
1
,
⋯
,
1
M
N
-
M
︸
N
)
(
where
M
<
N
)
,
where M is a bandwidth of the filtering matrix, and N is a number of frames of the input video image from which the variation of the pixel values are extracted.
17. A motion detection system, comprising:
a camera; and
an image preprocessor which transforms input image data, provided from the camera, from an analog signal into a digital signal;
the motion detection system configured to:
generate a frequency domain transform matrix transforming a time domain matrix into a frequency domain matrix;
generate a filtering matrix filtering a low frequency component of a video image;
generate a time domain transform matrix transforming the frequency domain matrix into a time domain matrix;
generate a low rank matrix by multiplying the frequency domain transform matrix, the filtering matrix, and the time domain transform matrix; and
multiply the low rank matrix by a time domain matrix comprising vectors with respect to variation of pixel values of an input video image as elements of the time domain matrix.
18. The motion detection system of claim 17 , wherein a rank of the frequency domain transform matrix corresponds to a number of frames of the input video image from which variation of the pixel values are extracted.
19. The motion detection system of claim 17 , wherein the low rank matrix L is expressed as L=D N T ·E M,N ·D N by using the frequency domain transform matrix D N , the filtering matrix E M,N , and the time domain transform matrix D N T ,
where N denotes a number of frames of the input video image from which the variation of the pixel values are extracted, and M denotes a bandwidth of the filtering matrix.
20. The motion detection system of claim 17 , wherein a rank of the low rank matrix is a value obtained by subtracting a rank of the filtering matrix from a rank of the frequency domain transform matrix.
21. The motion detection system of claim 17 , wherein the low rank matrix L has centro-symmetry.
22. The motion detection system of claim 17 , wherein the elements of the low rank matrix comprise only fixed points.
23. The motion detection system of claim 17 , wherein the frequency domain transform matrix uses a discrete cosine transform method.
24. The motion detection system of claim 17 , wherein the filtering matrix E M,N is expressed as
E
M
,
N
=
diag
(
0
,
⋯
,
0
︸
,
1
,
⋯
,
1
M
N
-
M
︸
N
)
(
where
M
<
N
)
,
where M is a bandwidth of the filtering matrix, and N is a number of frames of the input video image from which the variation of the pixel values are extracted.