The Research On Non-Rigid Structure From Motion Based On Trajectory Piecewise Representation Algorithm

Non-Rigid Structure from Motion (NRSFM) is an active research theme in the field ofComputer Vision. The purpose is to recover the non-rigid object’s3D structure and the camera’sparameters from2D video sequences. This technique can be widely applied on fields likemachine vision, medical imaging, military reconnaissance, athletic training, film and televisionproduction and et al.Solution to this problem is first proposed in shape space. The core of the algorithm is, todecompose the projection matrix by factorization first, then describe the non-rigid motion bylinear combination of some pre-defined shape basis, and finally get the result by iteration. Recentyears, some researchers propose a factorization method based on pre-defined trajectory basisaccording to the duality of trajectory space and shape space. This method overcome weaknessessuch as the difficulty of basis chosen and the instability appeared in shape space methods.Compared to shape basis method, the calculation amount decreases when using trajectory basismethod. However, the recovery meets with quite large error at where the abrupt change occurs innon-rigid motion. The reason for the phenomenon is the absence of high order information intrajectory basis representation. To solve this problem, this thesis focuses on following researchwork from the perspective of trajectory representation.(1) Describe the motion trajectory of characteristic points on non-rigid object according tothe relative independence between points in trajectory space. The description is made on theanalysis of non-rigid motion and also the piecewise representation method. It first gets the abrupttime information and the corresponding coordinates of trajectory by change point detection. Andsecondly recover the whole trajectory by interpolation. Then the research turns to the problemthat for a single characteristic point, there are different abrupt point sets for different dimensioncoordinates. An integration method is proposed. Thus a description model for non-rigid motion isbuilt which is different from shape basis method and trajectory basis method. (2) In the research of piecewise linear representation for the description of NRSFM, asliding window Mann-Kendall (SWMK) method for change point detection and segmentation isproposed from the perspective of time series, based on Mann-Kendall trend test. The thesis alsoconclude some research on parameter setting for the algorithm. Different kinds of time series arechosen to do the recovery comparison. It is shown that under the same compressing ratio, theSWMK performs better than some existing methods on recovery error or calculation speed.(3) On the basis of trajectory piecewise representation and description model of non-rigidmotion, a non-rigid structure recovery method based on trajectory piecewise representationmethod (TPR) is proposed. The TPR method combines factorization, orthogonality constraint,projection error constraint and continuity constraint. Several3D recovery tests are done by usingthis algorithm. The result shows that for the motion trajectory which has abrupt change, the newmethod remarkably improve the reconstruction effect at the segments where changes happen,compared to the pre-defined trajectory basis method. The new method also decreases the overallrecovery error. Compared to some other normal methods in shape space or trajectory space, theTPR method performs better or at least similar to their results.