The Research Of3D Reconstruction For Non-rigid Object In Trajectory Space

It has been a long history on the research of the relationship between2D imageprojection and3D potential scenes in optical and photography area. NRSFM (non-rigidstructure from motion) also develops fast and become very popular. NRSFM refers to thetask of recovering the time varying3D coordinates of points on a deforming object from their2D locations in an image sequence. Based on the factorization method, shape basisrepresentation method successfully recovers the3D structure of non-rigid object. But a typeof shape basis can not fit all non-rigid objects because of its specificity.The duality of spatial and temporal representation makes NRSFM research extend totrajectory space, in which non-rigid structure can be represented as a set of trajectory basiscombination. Trajectory basis can be predefined, but this is not simply equivalent that thebasis is totally known. There are too many kinds of trajectory basis and too many motionforms of objects. So it is difficult to determine which kind of trajectory basis to use. Thebasis size and combination form have much influence on the reconstruction algorithm.Existing approaches can not automatically select trajectory basis. In addition, optimizationmethod can directly influence accuracy and efficiency of the reconstruction algorithm. Sosearching the optimal solution of equations is also a difficult problem of NRSFM intrajectory space.Aiming at above problems, the main works of this paper are as follows:(1) The influence of different selection of trajectory basis on NRSFM in trajectory spaceis analyzed. Although trajectory basis can be predefined, it still needs to be selected becausetrajectory basis is not totally known. There are many kinds of trajectory basis. This paperanalyzes the influence on reconstruction by using different kinds of basis to determine theoptimal general trajectory basis. After basis kind is determined, basis size and combinationform also belongs to basis predefining. The scale of basis number is very large and there are many kinds of component combination form. All these factors can not be determinedarbitrarily. So at first，this paper analyzes the influence on reconstruction by trajectory basisnumber and combination form.(2) A method of automatic trajectory basis selection is proposed. With the optimaltrajectory basis, the research in this paper shows that basis size and combination form havegreat influence on NRSFM algorithm. So it is necessary to select appropriate set of trajectorybasis by a selection method. In fact, if the basis size is too small, the trajectory is poorlyrepresented by the basis, but too large basis size makes the system more ill-conditioned andthe reconstruction error becomes unbounded. So the basis size has much influence onreconstruction accuracy and efficiency. On the other hand, the combination of trajectorybasis on different frequency can also influence the reconstruction algorithm. The selectionmethod in this paper can automatically select trajectory basis size and combination ondifferent frequency by analyzing the spectrum of projection error. Most energy of trajectoryinformation is focused on the selected basis. The trajectory basis selection method can notonly guarantee the accuracy of the reconstruction algorithm, but also can improve theefficiency.(3) A reconstruction method with trajectory basis based on feature-sign search algorithmis researched. Most existing reconstruction approaches are based on nonlinear least squaremethods such as LM algorithm. These methods are all under orthogonal constraints tominimize the target function. But nonlinear optimization methods need to compute amountsof unknown parameters. As a result, reconstruction error accumulates and reconstructionaccuracy decreases. The reconstruction method proposed in this paper uses the feature-signsearch strategy to minimize the new target function. The feature-sign search algorithmautomatically maintains an active set of potentially nonzero coefficients and theircorresponding signs. It also can systematically search for the optimal active set andcoefficient signs. The whole algorithm converges to the optimal solution.