基于偏好统计数据表征的鲁棒几何模型拟合方法

A Preference-Statistic-Based Data Representation for Robust Geometric Model Fitting

鲁棒几何模型拟合是计算机视觉的一个基础性研究问题,广泛应用于各类计算机视觉任务,如单应性矩阵或基础矩阵估计、图像匹配、医学图像分析等.它的主要任务是:在包含噪声点和离群点的数据集中估计模型实例的参数和个数.针对该任务,本文提出一种基于新型数据表征(称之为偏好统计数据表征)的模型拟合方法.该新型数据表征算法将残差值进行排序然后映射到不同的区间以构建残差直方图数据表征,来描述数据分布的特征.该算法充分利用传统模型拟合方法中偏好分析和一致性统计分析的优点,更加有效地对数据分布特征进行描述,从而有效地提高数据表征的准确性和鲁棒性.为了进一步有效地利用该数据表征中的统计信息(内点和离群点显示出显著的信息熵值差异),本文利用直方图中不同区间段所映射的残差值的出现频次,以分析直方图的特性.并且采用一种简单的自适应熵阈值算法,来区分内点与离群点以进行离群点检测.最后,为了能够更好地处理分布在交叉模型实例附近的数据点,本文引入一种基于相似矩阵学习的图聚类技术,提出一个有效的模型实例估计算法.该算法先是用聚类技术以实现数据的分割,进而估计模型实例的参数.同时,该模型实例估计算法结合拉普拉斯矩阵特征值的分析以及最小子集数目的约束,使其能够自适应地估计模型实例的个数.在合成数据集和真实数据集上的实验结果表明,本文提出的偏好统计数据表征算法能够有效提高模型拟合方法的准确性和鲁棒性.同时,与当前一些流行的模型拟合方法相比,本文基于偏好统计数据表征的鲁棒几何模型拟合方法取得了更好的拟合精度,并且在速度方面要比大部分拟合方法更加高效.

Robust geometric model fitting is a fundamental research problem in computer vision.It has been widely used in a variety of applications such as homography/fundamental matrix estimation,motion segmentation,image matching and medical image analysis.Given that data usually contain noise and outliers caused by sensing or preprocessing errors,the main task of robust geometric model fitting is to estimate the number and the parameters of model instances in data.Although a number of robust geometric model fitting methods have been proposed during the past few decades,it is still a challenging task since a scene typically contains multiple geometric structures,especially,when the observed data are largely contaminated with noise and outliers.Traditional robust model fitting methods can be roughly classified into consensus statistic based methods and preference analysis based methods.The consensus statistic based methods aim to search the maximum consensus sets that yield the underlying model instances in data,and then segment the data points into inliers and outliers by a certain threshold.Preference analysis based methods describe the relationship of data points based on the preference information which is usually used to define a similarity measurement,and then the data points are grouped into inliers and outliers based on a similarity-based clustering algorithm.However,the preference analysis potentially keeps redundant information(small differences in the residuals are probably unimportant),whilst the consensus statistic throws away too much potentially useful information.These methods might lead to poor fitting results.In this paper,we aim to use a compromise statistic that keeps sufficient and compact information for model fitting and segmentation purposes.We present an effective robust geometric fitting method based on a novel data representation(called preference-statistic-based data representation)algorithm to deal with multiple-structure data contaminated with noise and outliers.Specifically,the proposed data representation algorithm analyzes the residuals(of each data point with respect to model hypotheses)in a histogram for the data representation,taking advantage of both preference analysis and consensus statistic.Thus,the accuracy and robustness for the proposed data representation are boosted.To utilize the statistical information embedded in the proposed data representation,a simple entropy threshold algorithm is used for the adaptive outlier detection,based on using the frequency count of bins of histogram.In addition,we present an effective model selection algorithm(which is able to effectively deal with data points near the intersection of model instances),based on similarity matrix learning for graph clustering.Specifically,we analyze the eigenvalues of the Laplacian matrix and use a constraint of the number of a minimal subset to automatically estimate the number of model instances.We evaluate the performance of the proposed method on both synthetic datasets and real image pairs.We firstly compare the proposed data representation algorithm(preference-statistic-based data representation)with the consensus statistic based data representation algorithm and the preference analysis based data representation algorithm,in the framework of T-Linkage method.Experimental results demonstrate that the proposed data representation algorithm is effective and helpful to achieve better fitting results for different fitting tasks.Then,we compare the proposed fitting method with several state-of-the-art fitting methods to show the promising fitting results of the proposed method.