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结合二次曲线的鲁棒相机定位研究
王浩人
Subtype博士
Thesis Advisor吴毅红
2019-05-28
Degree Grantor中国科学院自动化研究所
Place of Conferral中国科学院自动化研究所智能化大厦
Degree Name工学博士
Degree Discipline模式识别与智能系统
Keyword二次曲线 相机定位 拟合 混合标志物 定位点优选
Abstract

二次曲线大量存在于生产生活环境中,与相机内外参数标定问题关系较为紧密。确定相机外参数或者位姿的过程,称为相机定位。相机定位的目标是确定相机相对于一个已知参考坐标系的六自由度位姿,是计算机视觉应用中的基础问题。在虚拟现实、增强现实、 机器人定位导航和无人驾驶等领域有着广泛的应用。然而,目前基于图像的相机定位在实际的应用场景中鲁棒性不够,尤其在弱纹理场景中更是如此。因此,本论文研究如何结合二次曲线进行相机的鲁棒定位。

论文的主要内容和贡献如下:

1. 针对一般二次曲线的拟合问题,推导出了一个新颖且解析的点到二次曲线的几何距离,并基于此距离提出了新的目标函数用于优化拟合二次曲线。从图像中拟合二次曲线是许多应用的初始步骤。一般的共识是基于几何距离的方法要比基于代数距离的方法更精确。然而,目前并没有一种点到一般二次曲线的几何距离能同时满足易于计算和高精度的要求。Sampson几何距离仅仅是一阶近似,拟合精度受限。而其他的几何距离计算太复杂,以至于在实际应用中很少使用。本文给出了一个新的二次曲线和点之间的几何距离。由于此距离是沿着点关于二次曲线的极线的法线方向计算,所以它对射影变换非常鲁棒。并且,此距离具有高精度的同时也是以解析形式表示的,非常易于实现。另外,此距离可以很轻易地推广到高维二次曲面的拟合。基于此距离设计了二次曲线拟合的目标函数。实验表明,此目标函数在优化时具有所有基于几何距离拟合方法的优点,同时避免了他们的缺点,既高效又鲁棒。

2. 针对基于平面标志物的相机定位,提出了一类结合简单几何图形边缘信息和自然图像的混合标志物,并以方形和圆形为例分别设计了两款实例,给出相应的相机定位方法。基于平面标志物的相机定位方法主要分为两种,即基于基准标志物的方法和基于自然图像标志物的方法。视觉应用中的基准标志物一般有方形或圆形边框,内部是二进制编码或简单的文字或图片,便于检测和定位。基准标志物在弱纹理应用中能增加定位成功率,但对场景有强侵入性。而基于自然图像标志物的方法相比之下有更丰富的纹理信息,对场景侵入性较弱,但计算量大,不利于推广应用。针对这些问题,提出了一类结合简单几何图形边缘信息和自然图像的混合标志物。首先设计了结合方形外边框和自然图像的方形混合标志物,并给出了相应的定位方法。实验表明方形混合标志物克服了基准标志物和自然图像标志物进行定位时各自的缺点,结合了它们的优势。进一步,由于方形边框对于遮挡等情况不够鲁棒,又设计了一种采用圆形边缘信息的混合标志物。它由黑色圆环和内部的不同颜色的自然图像组成。实验表明圆形混合标志物使用二次曲线边缘信息,可在一定程度上对抗快速运动、光照变化等复杂场景。总而言之,这两种标志物都通过结合自然图像特征,使得相机定位平滑连续,避免了抖动的出现。

3. 针对大规模场景下的数据量大、计算量大、场景复杂和相机定位误差漂移严重的问题,提出了基于几何信息的定位点优选方法,降低计算量,并将优选后的点集与二次曲线进行结合,有效地抑制了误差漂移。本方法综合考虑匹配特征数量以及有利于定位的空间点的几何特性,又约束了空间点的分布均匀性,进而用整数规划求解定位点优选问题,从而得到更有利于相机定位的更稀疏的优选点集。优选点后,计算功耗低,内存占用小,在各平台的实时定位成为可能。由于点匹配容易出现错误,误差漂移大,进一步结合场景中的二次曲线信息抑制误差,在一定程度上能提高定位的精度和鲁棒性。本方法可以适用于地图构建好之后的定位,也可以作为SLAM的重定位方法。

Other Abstract

Conics which abound in the common environments have the closest relationship with camera calibrations for intrinsic and extrinsic parameters. The process of computing the extrinsic parameters or camera poses is known as camera localization. The goal of camera localization is to calculate the $6$D pose relative to a known coordinate system, which is a fundamental problem in computer vision applications such as VR (Virtual Reality), AR (Augmented Reality), robot navigation and autonomous driving. However, the accuracies of the existing methods in real applications are still not robust enough. In this thesis, we study how to efficiently combine conics to obtain more robust camera localization results.

The main contents and contributions of this thesis are as follows:


1. For the general conic fitting problem, a novel and analytical geometric distance from a point to a conic is derived and a new cost function based on the distance is proposed. Fitting conics from images is a preliminary step for its plentiful applications. It is a common sense that geometric distance based fitting methods are better than algebraic distance based ones. However, for a long time, there has not been a geometric distance between a point and a general conic that allows easy computation and achieves high accuracy simultaneously. Though Sampson distance is widely accepted, it is only a first-order approximation. For other geometric distances, the computations are too complex to be popular in practice. To this end, we derive a new geometric distance between a point and a general conic, called Polar-N-Direction distance. The distance can be adapted to a projective transformation because it is computed along the normal direction of the polar line of the point, making conic fitting more robust. Moreover, Polar-N-Direction distance is accurate and simultaneously still analytical in an explicit representation, which is quite easy to be implemented. Then, based on the distance, a new cost function is constructed. The conic fitting optimization by minimizing this cost function has all the merits of the geometric distance-based methods and simultaneously avoids their limitations. Experiments show that the conic fitting method is greatly efficient and robust.

2. For the marker-based camera localization, a new class of hybrid markers is designed and the corresponding localization method is proposed. Planar markers for camera localization fall into two classes: fiducial markers and natural image markers. Fiducial markers usually have square or circular borders with simple and easily detected characters, graphics or encoded patterns inside. Fiducial markers are easy to be detected and localized. Though fiducial markers can increase the success rate of camera localization, their strong invasion to scenes should not be neglected. By contrast, natural markers have rich textures and make low invasive to scenes. But its computation of feature extractions and matching are quite heavy. This is not good for natural markers to be popularized and applied. To this end, we design a kind of hybrid marker which combines edge information of simple geometric shape with natural scenes. We first design a kind of hybrid markers by a square black border with natural scenes. Experiments show that this square hybrid marker takes the advantages of fiducial markers and natural image markers and simultaneously overcomes their shortcomings. Since the square border is not robust to occlusion, we further propose a circular hybrid marker using edges of conics. It is composed of black circular rings and different natural images with distinct colors. The proposed circle hybrid markers are robust to occlusions, fast motion, and illumination changes. Besides, features from natural images make the camera localization methods smooth and anti-jitter.

3. For the problems of error drift and heavy calculation of camera localization in large-scale environments, we propose an optimum-point selection method and then combine conics for camera localization to reduce errors and increase robustness. We formulate a novel objective function by taking both the number of matched features and the geometric property of the spatial points that provide high localization quality into consideration. Based on this formulation, a mixed integer programming scheme is utilized to solve the point cloud optimum selection problem, which selects points that are more beneficial to localization. The obtained selected points not only reduce the time of consumption but also make the memory footprint small. Based on the selection, conics are further used to restrain errors, which improves the accuracy and robustness of the localization result.

Pages122
Language中文
Document Type学位论文
Identifierhttp://ir.ia.ac.cn/handle/173211/23956
Collection毕业生_博士学位论文
Recommended Citation
GB/T 7714
王浩人. 结合二次曲线的鲁棒相机定位研究[D]. 中国科学院自动化研究所智能化大厦. 中国科学院自动化研究所,2019.
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