Method and apparatus for smoothing a motion trajectory in a video

An apparatus for smoothing a motion trajectory in a video, comprising:

• a first acquisition module, configured for obtaining a video frame sequence of an input video, and obtaining an original rotation matrix Rold of each video frame;
• a second acquisition module, configured for obtaining an original rotation matrix sequence xold=[R1old, R2old, . . . , Rnold]T of the video frame sequence that varies with time, according to the original rotation matrix of each video frame Rold;
• a determination module, wherein assuming a smooth rotation matrix sequence obtained after smoothing the original rotation matrix xold is xnew=[R1new, R2new, . . . , Rnnew]T then a geodesic distance between a smooth rotation matrix Rnnew and a corresponding original rotation matrix Rnold is dg2=(Rnold, Rnnew), and a geodesic distance between two adjacent smooth rotation matrices is dg2=(Rnnew, Rn+1new);
• the determination module is configured for determining an objective function according to Riemann manifold architecture:
• min
• {
• R
• n
• new
• }
• ⁢
• ∑
• n
• =
• 1
• N
• ⁢
• 1
• 2
• ⁢
• d
• g
• 2
• ⁡
• (
• R
• n
• old
• ,
• R
• n
• new
• )
• +
• α
• ⁢
• ∑
• n
• =
• 1
• N
• -
• 1
• ⁢
• 1
• 2
• ⁢
• d
• g
• 2
• ⁡
• (
• R
• n
• new
• ,
• R
• n
• +
• 1
• new
• )
• a third acquisition module, configured for iteratively solving for the smooth rotation matrix Rnnew that minimizes the objective function according to Riemannian manifold constrained smoothing algorithm, and further obtaining the smooth rotation matrix sequence xnew;
• and
• a processing module, configured for performing image stabilization on the video frame sequence based on the smooth rotation matrix sequence xnew.

A non-transitory computer readable storage medium, storing at least one instruction, which when executed on one or more processors is configured to perform a method for smoothing a motion trajectory in a video, the method comprising the following operations:

• obtaining a video frame sequence of an input video, and obtaining an original rotation matrix Rold of each video frame;
• obtaining an original rotation matrix sequence xold=[R1old, R2old, . . . , Rnold]T of the video frame sequence that varies with time, according to the original rotation matrix of each video frame Rold;
• assuming a smooth rotation matrix sequence obtained after smoothing the original rotation matrix xold is xnew=[R1new, R2new, . . . , Rnnew]T, then a geodesic distance between a smooth rotation matrix Rnnew and a corresponding original rotation matrix Rnold is dg2(Rnold, Rnnew), and a geodesic distance between two adjacent smooth, rotation matrices is dg2(Rnnew, Rn+1new);
• determining an objective function based on Riemann manifold architecture:
• min
• {
• R
• n
• new
• }
• ⁢
• ∑
• n
• =
• 1
• N
• ⁢
• 1
• 2
• ⁢
• d
• g
• 2
• ⁡
• (
• R
• n
• old
• ,
• R
• n
• new
• )
• +
• α
• ⁢
• ∑
• n
• =
• 1
• N
• -
• 1
• ⁢
• 1
• 2
• ⁢
• d
• g
• 2
• ⁡
• (
• R
• n
• new
• ,
• R
• n
• +
• 1
• new
• )
• iteratively solving for the smooth rotation matrix Rnnew that minimizes the objective function according to Riemannian manifold constrained smoothing algorithm, and further obtaining the smooth rotation matrix sequence xnew;
• and
• performing image stabilization on the video frame sequence based on the smooth rotation matrix sequence xnew.