Method for recovering 3D scene structure and camera motion directly from image intensities
The present invention is directed to a method for recovering 3D scene structure and camera motion from image data obtained from a multi-image sequence, wherein a reference image of the sequence is taken by a camera at a reference perspective and one or more successive images of the sequence are taken at one or more successive different perspectives by translating and/or rotating the camera, the method comprising the steps of determining image data shifts for each successive image with respect to the reference image; constructing a shift data matrix that incorporates the image data shifts for each image, wherein a first vector corresponds to the 3D structure and a second vector corresponds to the size of the camera motion; dividing the successive images into windows; and determining the direction of camera motion and 3D structure from the first and second vector between the windows.
1. An image processing method for recovery of a scene structure from successive image data where motion of the scene structure is linear, the method comprising the steps of:
(a) computing rotational motion in the successive image data using rotational flow vectors derived from a set of intensity data collected from the successive image data where the rotational flow vectors are represented by
Ψ x ≡[∇I·r (1) ( p )], Ψ y ≡[∇I·r (2) ( p )], Ψ z ≡[∇I·r (3) ( p )],
where ∇I represents a gradient of the intensity data r (1) , r (2) , r (3) are three-point rotational flows with respect to a pixel position p;
(b) constructing a shift data representation for the intensity data that compensates for the rotational motion in the successive image data;
(c) decomposing the shift data representation into a motion vector and a structure vector;
(d) dividing the successive image data into smoothing windows; and
(e) computing a projection matrix which is block diagonal between different smoothing windows and which is used to recover the scene structure by solving for the structure vector.
2. The image processing method of claim 1 wherein the shift data representation is decomposed using singular value decomposition.
3. The image processing method of claim 2 wherein singular value decomposition is used to compute a rank-1 factorization of −Δ CH ≈M (1) S (1)T where M (1) is the motion vector and S (1) is the structure vector.
4. The image processing method of claim 1 wherein the method is iterated until it converges to a reconstruction of the scene structure.
5. The image processing method of claim 1 wherein the projection matrix is a N p by N p matrix which is defined to annihilate an expression
(H T S (1) )−Ψw
where N p is a number of pixels in an image, H is a matrix which annihilates the rotational flow vectors, S (1) is the structure vector, Ψ is a matrix formed from the rotational flow vectors, and w is a vector selected so as to allow the structure vector to be solved.
6. A device-readable medium comprising instructions for performing an image processing method for recovery of a scene structure from successive image data where motion of the scene structure is linear, the method comprising the steps of:
(a) computing rotational motion in the successive image data using rotational flow vectors derived from a set of intensity data collected from the successive image data, where the rotational flow vectors are represented by
Ψ x ≡[∇I·r (1) ( p )], Ψ y ≡[∇I·r (2) ( p )], Ψ z ≡[∇I·r (3) ( p )],
where ∇I represents a gradient of the intensity data, r (1) , r (2) , r (3) are three-point rotational flows with respect to a pixel position p;
(b) constructing a shift data representation for the intensity data that compensates for the rotational motion in the successive image data;
(c) decomposing the shift data representation into a motion vector and a structure vector;
(d) dividing the successive image data into smoothing windows; and
(e) computing a projection matrix which is block diagonal between different smoothing windows and which is used to recover the scene structure by solving for the structure vector.
7. The device-readable medium of claim 6 wherein the shift data representation is decomposed using singular value decomposition.
8. The device-readable medium of claim 7 wherein singular value decomposition is used to compute a rank-1 factorization of −Δ CH ~M (1) S (1)T where M (1) is the motion vector and S (1) is the structure vector.
9. The device-readable medium of claim 6 wherein the method is iterated until it converges to a reconstruction of the scene structure.
10. The device-readable medium of claim 6 wherein the projection matrix is a N p by N p matrix which is defined to annihilate an expression
(H T S (1) )−Ψw
where N p is a number of pixels in an image, H is a matrix which annihilates the rotational flow vectors, S (1) is the structure vector, Ψ is a matrix formed from the rotational flow vectors, and w is a vector selected so as to allow the structure vector to be solved.