基于自适应权值的点云三维物体重建算法研究

Point-Cloud 3D Object Reconstruction by Using Adaptive Weighting Function

基于三维扫描点云数据的三维物体重建是计算机图形学中非常重要的课题,在计算机动画、医学图像处理等多方面都有应用。其中基于最小二乘问题的Levenberg-Marquart算法和基于极大似然估计的M-Estimator算法都是不错的方案。但是当点的数量过多过少或者点云中有噪声时,这些方案产生的结果都会有较大的误差,影响重建的效果。为了解决这两个问题,结合Levenberg-Marquart算法和M-Estimator算法,提出了一种新的算法。该算法结合Levenberg-Marquart算法较快的收敛性和M-Estimator算法的抗噪性,能很好地解决点数量较多和噪声点影响结果的问题。通过在M-Estimator的权重函数上进行改进,提出自适应的权值函数,用灵活变动和自适应的值代替原来的固定值,使算法在噪声等级较高时也能表现良好。最后将算法应用在球体和圆柱上,并和最新的研究成果进行对比,数据说明算法无论是在点云数量较多还是在噪声等级较高的情况下都明显优于其他已知算法。

3D object reconstruction based on point clouds is an important field in computer graphics which have been used in computer animation, medical image processing and so on. Many good algorithms have been developed to solve this problem such as Levenberg-Marquart algorithm based on least squares and M-Estimator based on maximum likelihood estimation. But all of these algorithms are sensitive to noise and the data number of too lager or too little. And the result of these algorithms would have a larger error, which can influence the effect of reconstruction. In order to solve these problems, we propose a new algorithm which is based on Levenberg-Marquart algorithm and M-Estimator. Our algorithm takes advantage of high convergence of Levenberg-Marquart algorithm and noise proof of M-Estimator, so it can solve two problems mentioned above. And we improved the weighting function of M-Estimator which replaces the constant value with the flexible and adaptive value. This way makes our algorithm to behave very well in large number of points and high level of noise. We apply our algorithm on ball and cylinder and compare with the latest research results. From the experimental data we can see that our algorithm behaves much well than the others.