Research On Factorization In Structure From Motion

Reconstructing a 3D model of a scene from multiple uncalibrated 2D images is a one of difficult problems in computer vision. In structure from motion(SFM) area, the factorization methods is academically interesting, because not only it have an inherent advantage of being able to handle any number of images simultaneously without special treatment for reference image, but also it can be represented for bilinear formulation in motion and shape parameter. The bilinear formulation is powerful and efficient technique including Singlar Value Decompostion (SVD). In this paper the factorization methods are classified in terms of camera models, feature models and shape models. This classification method is new perspective for pointing new contents and directions of research.To order to construct the completed valid measure matrix, In this paper we provide a new based on gradient statistic feature detect and match method that can deal with image sequence that have large change (viewpoint, Illumination and scale). The new method not only describes the local region structure but also statistics orientation histogram of outer twelve 5x5 sample region. The constructed descriptor has more robust distinguish ability so that supports the following match step. In the match step, by filting the tentative feature pairs in orientation and amplitude of histogram, some outliers will be eliminated. Through comparing with traditional Harris Correlation coefficient’s match algorithm as well as theoretical analysis, the proposed algorithm in this paper has the higher stability as well as the anti-jamming.As occlusions exist in a long image sequence of a rigid scene, there are some missing entries in the measure matrix. A novel online multi-frame correspondence estimation algorithm is proposed in this work. The trajectory matrix and displacement matrix, which is weighted by image gradient statistics, reside in a low-dimensional linear subspace. Firstly, a complete sub-matrix selected from the displacement matrix is constrained by the rank of the low-dimensional linear subspaces and is reorganized into the corresponding trajectory matrix; the trajectory matrix is constrained by the corresponding rank and is decomposed into a base matrix and a coefficient matrix. Secondly, to solve the aperture problem, the displacement components are estimated from the base matrix and coefficient matrix. Then the estimated displacement components are backfilled into multi-frame displacement matrix by using the base matrix and coefficient matrix. Thirdly, as following frames acquired, the new data is integrated into the multi-frame correspondence estimation by using the increment SVD. Lastly, after processed all of the frames, the still missing entries, which can not be estimated during the above steps, are processed using the nonlinear optimization algorithm. We mathematically proved the feasibility of the algorithm. Compared with Irani’s correspondence estimation algorithm, our experimental results show that the proposed algorithm is more effective in error and run-time under different ratio of valid entries and error levels.There are some outliers in the measure matrix because of the feature correspondence algorithm’s limitation. The scaled measure matrix lies in 4-dimension subspace in factorization method for projective reconstruction. To correct the outlier and recover the missing data in mesure matrix, we propose a robust projective reconstruction algorithm based on subspace in this paper. The new projective reconstruction algorithm presented in this paper estimate projective shape, projective depths iteratively. The two estimation sub-problems are formulated within a subspace framework and minimize a single consistent objective function with regard to different variables iteratively, hence ensuring the convergence of the iterative solution. The projective shape be obtained by using the method of augmented Lagrange multipliers (ALM) that be constrained by the ideal rank of the measure matrix can be exactly solved via convex optimization that minimizes a combination of the nuclear norm and the L1-norm. Experimental results are provided to illustrate the performance of the proposed algorithm presented in this paper.When all data in measure matrix are valid, the classical SVD can be used in factorization method of SFM. The missing datum and outliers are often presented at measure matrix because of the feature correspondence algorithm’s limitation; their affects can be elimated by our scheme, which consist of three steps. In first step, a new based on gradient statistic feature detect and match method is provided for constructing valid datum as much as possible in measure matrix. By comparing with traditional Harris-Correlation matching algorithm as well as theoretical analysis, this algorithm proposed in this step has the higher stability as well as the anti-jamming. In second step, based rank constraint Multi-Frame correspondence estimation algorithm is provided for recovering the missing datum. We mathematically proved the feasibility of the algorithm. Compared with Irani’s correspondence estimation algorithm, our experimental results show that the proposed algorithm is faster and more effective in error-control under different valid entry ratios and error levels. In third step, a new robust subspace algorithm for projective reconstruction from multiple images can elimate the affects of missing datum and outliers to obtain the valid projective reconstruction results. Experimental results are provided to illustrate the effectiveness and reliability of the proposed algorithm in this step.