Study On Error Distribution Of Geometric Model In 3D Reconstruction

In the field of computer vision,3D reconstruction is a method to recover the 3D geometric structure of the object from the images captured by the camera.According to whether the reconstructed object deforms with time,it can be divided into rigid reconstruction and non-rigid reconstruction.Most of the existing researches focus on rigid reconstruction,and the typical method is structure-from-motion(SFM).In recent years,researchers have paid more attention to non-rigid objects because they are more common in the real world.Projective geometry is the primary theoretical basis for 3D reconstruction of rigid and non-rigid objects,and a large number of geometric models,such as projective transformation,homography matrix and fundamental matrix,are used in each step of reconstruction.How to estimate these geometric models accurately has always been a hot topic among researchers.Existing theories pay little attention to the error distribution of'the geometric model,or simply assume that it obeys isotropic Gaussian distribution.However,in practice,affected by environmental changes,measurement hardware accuracy and other factors,the model error distribution rarely meets this assumption,which greatly affects the estimation accuracy of the model.In order to deal with this situation,the Gaussian hypothesis is generalized.In this paper,the estimation problem of the geometric model is studied when the error obeys the elliptic distribution and the distribution information is unknown.In addition,this paper starts with a simple homography matrix model and applies it to the complex non-rigid structure-from-motion(NR SFM)problem.It should be pointed out that the method proposed in this paper can be applied not only to the homography matrix model,but also to the estimation of other geometric models such as the fundamental matrix.The main work of this paper is as follows:(1)In this paper,we apply the Elliptical distribution in statistics to the estimation of the homography matrix,and generalize the traditional error Gaussian distribution assumption.Then we proposed the adaptive scale elliptical residual kernel consensus(ASERKC)algorithm and the normalized elliptical weight levenberg-marquard(EW L-M)algorithm to filter the outlier points and optimize the homography matrix.Both simulation experiment and real image experiment show that the model estimated by the proposed algorithm has higher accuracy and stronger robustness.In addition,the integrity of the reconstructed model can be significantly improved by applying the proposed algorithm in the incremental SFM.(2)Under the condition that the error covariance matrix of the characteristic points is unknown,this paper assumes that the error of the geometric model obeys the Elliptical distribution.Then inspired by finite Gaussian Mixture model can approximate the nonlinear probability density function arbitrarily,a homographic matrix estimation method based on Gaussian Mixture Approximation(Gaussian Mixture Approximation,GMA)algorithm was proposed.The validity of the proposed algorithm is checked by experiments.(3)In this paper,a non-rigid structure-from-motion algorithm based on Gaussian mixture approximation is proposed.Without any prior information about the error distribution,the Gaussian mixture model was used to fit the actual error distribution in NR SFM.And the expectation maximization algorithm was used to calculate the camera poses and shapes matrix using only the prior information of low-rank constraints.In some global data sets,the error of the proposed algorithm is lower than the most state-of-art algorithms,and the accuracy of the proposed algorithm in other data sets is also in the forefront of the most state-of-art algorithm.