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一个有关移动机器人定位的视觉传感器模型Matthias Fichtner Axel Gro_mannArti_cial Intelligence InstituteDepartment of Computer ScienceTechnische Universitat DresdenTechnical Report WV-03-03/CL-2003-02摘要我们提出一个在走廊和传感器模型凌乱的奥西环境下的概率估计。该模型是基于在相机中所获得的图像特性与本发明的特征的环境中的一个给定的三维几何模型的比较。所涉及的技术比最先进的摄影测量方法还简单。这使得模型用于概率机器人的定位方法中。此外，他非常适合传感器融合。传感器模型已经用于蒙特卡罗定位跟踪的移动机器人位置导航任务里。实证结果提出了这个应用程序。1 介绍准确的本地化问题是移动机器人技术的基础。为了成功的解决复杂的任务，自主机器人必须可以正确的可靠地估计其目前的状态。该定位方法的选择通常取决于传感器的种类和号码，有关操作环境的先验知识，和可用的计算资源。最近，应用导航技术已经越来越受欢迎。在室内机器人的技术中，我们可以区分的方法是古人的摄影测量和计算机视觉，该方法起源于人工智能机器人。以视觉为基础的导航技术的发展的一个重要的技术贡献是通过识别来自未知的观点在使用特征不变的特征单幅图像的3D对象的工作。后来，这种技术拓展到全球定位和同步地图建设。最后系统进行位置跟踪通过使用一个环境的几何模型和统计模型的机器人的不确定性运动姿势和吩咐。机器人的位置是由一个高斯分布表示，并通过卡尔曼滤波更新。寻找相应的摄像机图像和模型的特点进行了优化，由此突出姿势的不确定性为摄像机图像。在蒙特卡洛定位的基础上，凝结算法已经成功的应用于导游机器人。这种基于视觉的贝叶斯过滤技术利用一个基于采样的密度表示。在结论的对比中，他可以代表多峰概率分布。由于天花板的视觉地图，它能定位全球范围内使用标量的亮度测量机器人。结合了视觉距离特性和视觉地标在机器人中的应用程序提出了一个建立产线的方法。由于他们的方法依赖于专业的标志性建筑，它并不适用于一次环境。我们工作的目的是开发一种概率传感器模式的摄像机位置估计。给定一个3D几何环境地图，我们想近似测量当前相机图像在某个地方获得的机器人的工作环境。我们使用这个传感器模型与MCL跟踪在走廊移动机器人导航的位置。可能的话，它也可以用于定位在杂乱的办公环境和基于形状的物体的检测。一方面，我们结合摄影技术基于地图的特征摄影与韧带的灵活性和鲁棒性，如处理本地化歧义的能力。另一方面，特征匹配操作应该足够快，以允许传感器融合。除了视觉输入，我们想使用距离读数从声波和激光来提高定位精度。本文组织如下。在第二节中，我们讨论之前的工作。在第三节中，我们描述了视觉传感器模型的组件。在第四节中，我们目前的实验结果通过MCL位置跟踪。我们的结论在第五节。2 相关工作在经典的基于模型的构成方法测定中，我们可以区分两个相互关联的问题。对应的问题是涉及到求相应的模型和图像特征。这种映射发生之前，位置模型的模型特性生成使用给定的相机姿势。据说特性可以匹配如果他们相互靠近。而造成的问题由3D相机坐标对世界起源的模型考虑到相对应的功能结束。显然，有一个问题需要对方事先解决，这使得解决任何耦合问题非常困难。上面的经典问题的解决方案如下假设测试途径：（1） 给定一个摄像机位置估计，最佳匹配特征对群体提供初始猜测。（2） 对于每一个假说，估计的相对相机的姿势被给定计算误差的函数最小化。（3） 现在有一个更准确的姿势估计用于每个假说，其余模型特性投射到的图像与使用相机的姿势有关。匹配的质量评估使用合适的误差函数，在所有的假设收益率中排名。（4） 排名最高的假设被选中。注意，对应的问题解决步骤（1）和（3），构成问题（2）和（4）。该算法的性能将取决于所使用的特征的类型，例如边缘，线段，或色彩，以及图像和模型之间的相似性度量的选择，在这里被称为误差函数。线段是我们的选择，因为他们可以在改变光照条件下被相对可靠地检测到。作为世界模型，我们使用的操作环境是一个线框模型，在VRML中表示。设计一个合适的相似性度量是更加困难的。原则上，误差函数是基于取向差异相应行段在图像和模型中，他们的距离和长度的差异，为了减少重要性，考虑到目前多有的功能对。这个已经建立在以下三种常见的措施中。3D被定义为模型线端点之间距离的总和和相应的平面。这一措施很大程度上依赖于与相机相反投影的距离。e2D称为无限图像行，是预测模型线的垂直距离对应的端点与无限延伸线在平面上的图像。双测度，e2D2，简称为在有限模型的线条，是总和超过所有的图像线条端点对应在图像平面奈特雷扩展模型的行。图1：视觉传感器模型的处理步骤限制搜索空间的匹配步骤，提出了限制可能的对应数量，对于一个给定的姿势估计通过结合线特性引入感性结构。因为这些初始的对应是通过e2D1和e2D2评价很高的要求强加在初始姿态估计与图像处理作业，包括去除失真和噪声和特征提取的精度。假设在完整的长度下获得所有可见模型。已经证明了一些异常值会严重影响最初的通讯，在老的原始方法中由于频繁截断引起的线路坏下，阻塞和杂物。3 传感器模型我们的方法是出于这个问题是否解决通信问题的估计可以避免相机姿势。相反，我们建议进行的图像和模型的功能相对简单，直接匹配。我们想调查的准确性和鲁棒性是这种方式所能达到的水平。参与本方法的处理步骤示于图1.从相机中取出图像失真后，我们用算子提取边缘。这个操作符合在改变光照条件下提取。从边缘线段确定结束点的坐标被忽略。在这种表示中，截断或分割线将有类似的坐标在霍夫空间。同样，行3D地图投影到图像平面使用摄像机姿态估计，并考虑到可见性约束，被表示为坐标空间。我们已经在匹配步骤中设计了几种误差函数被用来作为相似性度量。他们在下面描述。中心匹配计数该RST相似性度量是基于线段在霍夫空间的距离。我们认为只能在一个长方形细胞内的霍夫空间模型周围为中心的功能，这些图像特征作为可能匹配，对这些匹配结果进行计数，并由此对产生的总和归一化。从模型特征来测量措施应该是不变的，就在3D地图或是经营环境的变化不是模仿的对象。通过归一化得到明显特点的人数的不变性。具体而言，集中匹配计数测量SCMC被定义为：其中未命名的使用距离参数的有效匹配。一般来说，这种相似性度量计算预期模型的比例至少由一个测量图像点组成。注意，这里端点坐标和长度都不考虑。网格长度匹配所述第二相似性度量是基于行组的总长度值的比较。图像中分割线条组合在一起使用一个统一的离散空间。这种方法类似于霍夫变换拟合的直线。执行相同的线路段的三维模型。让测量线的长度落入网格单元，同样根据模型，然后网格长度匹配测量是：对所有包含模型的所有特性的网格单元，这种方法测量的长度与预期的来衡量。再次，该映射是有方向性的，也就是说，该模型被用作参考，以获得噪声，杂波和动态对象的不确定性。近邻和豪斯多夫距离此外，我们尝试了两个通用的方法对两组几何实体的比较：近邻和豪斯多夫距离。详细信息请参阅【7】。都依赖于距离函数，我们基于离散坐标空间，即线路参数和可选的长度，线性和指数的方式。查看完整描述【5】。常见的错误功能为了比较，我们还实施了常用的误差函数e3D,e2D1和e2D2，在笛卡尔空间中定义，我们代表行黑森符号xsin-ycos=d。通用误差函数f，我们定义了相似度测量：其中M是一组测量线，E是一组预期的行。在e2D1的情况下，f是由两个模型之间的垂直距离线端点e1,e2，和无限扩展的图像行定义为：同样，双重相似性度量，通过使用误差函数e2D2，基于图像之间的垂直距离线端点和无限扩展行模式。回忆的误差函数e3D模型线端点的距离成正比，视图平面通过一个图像行和相机，我们可以使用f3D实例化方程定义为：获取概率理想情况下，我们希望返回单递减值的相似性度量方法用于预测模型的姿势估计和实际偏离特性的姿势估计。一般，我们的目标是在一个有效而简单的视觉传感器模型中，抽象的想法是特定的姿势和环境条件平均了大量的，独立的情况。对于公度，我们想表达模型机器人的相对坐标而不是绝对坐标。换句话说，我们假设测量m的概率，鉴于姿势lm的这张照片姿势估计W的世界模型，等于这测量三维姿势偏差的概率和世界模型。由视觉传感器模型返回的概率是通过简单的比例获得：4 实验结果我们已经在一系列实验中提出了评估传感器模型的相似措施。使用理想化条件下人为创建图像，然后我们将扭曲和噪声添加到测试图像中。随后，我们使用在走廊已经获得的机器人真实图像。最后，我们使用了传感器模型穿越走廊跟踪机器人的位置。在所有这些情况下，得到的三维可视化模型，他被用来评估解决方案。模拟使用人为创造的图像作为第一种评价，我们生成的合成图像特性通过从某个相机姿势中生成一个视图的模型。一般来说，我们从右分支到左边重复图1。通过引入带来，我们可以直接显示其影响相似度值。对可视化的目的，平移偏差x和y组成一个空间偏差t。初步实验显示只有微不足道的差异时，他们被认为是独立的。图2 :在人为创造的图像中CMC的性能对于每一个上面给出的相似性度量，至少1500万个随机相机姿势加上一个随机造成偏差的范围构成收益率模型。中央军委测量的结果如图2所示。使用GNUPLOT的平滑算子得到表面的3D图。我们注意到一个独特的峰值在零偏差处理单递减相似性值误差增加。请注意，这个简单的测量认为端点坐标和长度的行。然而，我们已经取得了良好的结果。而由此产生的GLM，CMC类似于一个标准曲线，峰值则更加与众不同。这符合我们的预期，因为在这里考虑到图像和模型线非常的重要。与中央的测量相比，在这种方法中会有偶然的错误匹配，由于不同的长度。紧邻的衡量是不使用的。虽然线性和指数加权方案尝试，即使考虑到线段的长度，没有获得独特的高峰，在进一步考虑中导致其被排除。基于豪斯多夫距离测量的表现不如前两个，CMC和GLM，但是它的方式是所需要的。但其温和的表现并不支付其最长的计算时间消耗在所有提出的措施中，并随后被忽视。到目前为止，我们已经表明我们的相似性措施可执行。接下来，我们将使用误差函数在这个框架中。在我们的设置函数e2D1表现很好。由此产生的曲线非常相似措施GLM中的曲线。这两种方法都表现出一种独特的峰值在正确的位置姿态中偏差为零。注意，线段的长度直接影响测量返回的相似度值，虽然两个线性属性有助于衡量e2D1。令人惊讶的是，其他两个误差函数e2D2和e3D表现不佳。更现实的条件在我们的传感器模型中为了排除扭曲和嘈杂的图像数据，我们描述进行另一组实验。为此，我们应用一下所有综合误差模型生成的图像特征匹配模型特性。每个原始行被复制的小概率（p值=0.2），并移入空间。任何线路长度超过30 像素被分成以概率p=0.3.此外，设有不存在于模型和噪声通过添加随机线条图像中的均匀分布进行了模拟。本方向是根据电流分布的角度产生相当的典型特征。从第一组实验中，这些模拟的结果没有显著地差异。相似度在零偏差的最大值降低，所有的形状和特征相似性措施仍在考虑保持不变。使用真实的走廊照片对现实世界的情况自上述模拟结果可能是有问题的，我们进行了另一组实验取代合成特性测量的实际相机图像。比较结果为各种参数设置，我们收集图片2在先驱机器人在走廊上离线和记录功能。对于走廊示例典型的观点，机器人姿态在三维空间中的两个不同的位置几乎被离散化。后将手动机器人在每个顶点归零，它执行一个完整的当场将逐步记录图像。这样可以确保最高的准确性造成坐标和图像想关联。这样，已经有超过3200张图片收集到64个不同的位置（x,y）。同样以上面的模拟，对姿势进行了系统选择从所涵盖的测量范围内。通过传感器模型指的姿态偏差l中的相同的离散值计算出的值，根据公式2中的假设进行平均。图3：GLM对从走廊真实图像中表现结果可视化的相似性度量空间（x,y）和旋转偏离正确的相机姿态CMC衡量展览一个独特的峰值约零点误差。当然，由于数量小得多的数据样本相对于模拟使用合成数据，曲线的形状更崎岖不平，但这是符合我们的期望。采用此设置中的GLM措施的结果示于图3。因为他揭示了一个更独特的峰值相比，CMC的曲线，他或多或少的演示了特征图谱之间的比较，考虑到了线路的长度。蒙特卡洛本地化使用了视觉传感器模型我们的目标是设计一个概率传感器相机安装在移动机器人的模型上，我们继续呈现的结果应用到移动机器人的本地化上。传感器的通用接口模型允许它用于贝叶斯本地化方法的校正步骤，例如，标准版的蒙特卡洛本地化算法。统计独立以来，传感器读书中呈现了一个基本假设线，我们希望的是使用相机来代替获得更高的准确度和鲁棒性除了常用的距离传感器还有声呐获激光。图4 ：本地化图像和预测模型在走廊实验中，移动机器人配备了固定安装的CCD相机必须按照预定的路线形状的双重循环。途中，他必须停在八个预定义的位置，或者打开视图在附近的一个角落里。每个图像捕获启动MCL的所谓校正步骤和所有样本的权重，根据该传感器模型重新计算，收益率密度最高的样品可能在重新采样正确的姿势坐标。在上述预测步骤中，将整个样本集根据机器人的运动模型和当前测距传感器的读数移入空间。我们的初步结果看起来很有希望。在位置跟踪实验中，机器人被赋予了其开始位置的估计值，大部分时间里，机器人的位置假设在最好的姿势。在这个实验中，我们已经使用了CMC措施，在图4中，一个典型的相机如图所示，而机器人如下所示请求路径。灰度级图像描绘了视觉输入的失真排除和预处理后的特征提取，也显示提取线特征。此外，世界模型是根据两个伸出姿势，该测距跟踪的构成和通过MCL计算出的估计值，他大约对应于正确的姿势，在他们之间，我们观察和旋转误差。画面还显示，旋转误差对巧合特性有很强的影响程度。对应于上述给出的结果，数据表现出旋转偏差比平移偏差表现出更高的梯度。这一发现可以解释出运动裸关节的功能空间，因此我们的相机传感器模型将在检测旋转中个出现分歧。像我们的先锋轴承旋转测程法远高于平移误差，这个属性使它特别适用于双轮驱动的机器人。5 结论和未来的工作我们已经提出了一个概率传感器模型摄像机位置估计。通用的设计使得它适合与距离传感器融合来感知来自其他的传感器。在理想和现实的条件下，我们展示了广泛的模拟和确定了合适的相似性度量。传感器模型的本地化任务的移动机器人的申请符合我们的预测偏差。在本文中我们强调了很多可以改进的空间。我们正在研究合适的技术来定量地评价定位算法的设计传感器模型的移动机器人的性能。这将使我们能够尝试杂乱的环境和动态对象。结合相机传感器模型使用的距离传感器融合信息呈现强劲的下一个步骤和导航。因为有用的功能数量显著变化作为机器人穿越室内环境，这个想法驾驭相机对准更丰富的视图（主动视觉）提供了一个很有前途的研究路径，以及强大的导航功能。参考文献1 F. Dellaert, W. Burgard, D. Fox, and S. Thrun. Using the condensation algorithm for robust, vision-based mobile robot localisation. In Proc. of the IEEE Conf. on Computer Vision and Pattern Recognition, 1999.2 D. DeMenthon, P. David, and H. Samet. SoftPOSIT: An algorithm for registration of 3D models to noisy perspective images combining Softassign and POSIT. Technical report, University of Maryland, MD, 2001.3 G. N. DeSouza and A. C. Kak. Vision for mobile robot navigation: A survey. IEEE Trans. on Pattern Analysis and Machine Intelligence, 24(2):237267, 2002.4 S. Enderle, M. Ritter, D. Fox, S. Sablatnog, G. Kraetzschmar, and G. Palm. Soccer-robot localisation using sporadic visual features. In Intelligent Autonomous Systems 6, pages 959966. IOS, 2000.5 M. Fichtner. A camera sensor model for sensor fusion. Masters thesis, Dept. of Computer Science, TU Dresden, Germany, 2002.6 S. A. Hutchinson, G. D. Hager, and P. I. Corke. A tutorial on visual servo control. IEEE Trans. on Robotics and Automation, 12(5):651 670, 1996.7 D. P. Huttenlocher, G. A. Klanderman, and W. J. Rucklidge. Comparing images using the Hausdor_ distance. IEEE Trans. on Pattern Analysis and Machine Intelligence, 15(9):850863, 1993.8 A. Kosaka and A. C. Kak. Fast vision-guided mobile robot navigation using model-based reasoning and prediction of uncertainties. Com- puter Vision, Graphics, and Image Processing Image Understanding, 56(3):271329, 1992.9 R. Kumar and A. R. Hanson. Robust methods for estimating pose and a sensitivity analysis. Computer Vision, Graphics, and Image Processing Image Understanding, 60(3):313342, 1994.10 D. G. Lowe. Three-dimensional object recognition from single twodimensional images. Arti_cial Intelligence, 31(3):355395, 1987.11 S. Se, D. G. Lowe, and J. Little. Vision-based mobile robot localization and mapping using scale-invariant features. In Proc. of the IEEE Int. Conf. on Robotics and Automation, pages 20512058, 2001.12 G. D. Sullivan, L. Du, and K. D. Baker. Quantitative analysis of the viewpoint consistency constraint in model-based vision. In Proc. of the 4th Int. IEEE Conf. on Computer Vision, pages 632639, 1993.- 12 -任务书题目多用途轮式自动行走小车论文时间20*年 2月 24日 至 20*年6 月14 日课题的主要内容及要求（含技术要求、图标要求等）内容：设计一轮式行走方式的自动行走小车，作为多用途的实验用载体平台，可在其上进一步安装多种作业机械，如收获机械手等其他机构，满足在田间和硬质土地路面行走的要求，在此机械产品基础上，加装电气控制机构，可达到自动行走进和遥控行走的功能。要求：1行走速度：1m/s 2负载能力：100kg 3行走方式：轮式 4防碰撞探测：机械方式 5工作平台提升方式：半闭环控制机械方式提升 6工作平台提升高度：500mm 7外形尺寸：宽600mm课题实施的方法、步骤及工作量要求1. 查阅有关资料，了解国家或行业对自动行走小车的要求等；2. 确定试验方案，拟定轮式自动行走小车的机械部分结构设计；3. 确定工程图样，完成零件图，装配图和总装图，完成图纸工作量累计3张A0图纸以上；4. 完成外文翻译汉子3000以上；5. 完成设计说明书1万字以上；指定参考文献1 廖权来等.电动汽车的关键技术及发展对策. 中国机械工程M ,19982 刘丽.世界电动汽车最新发展综述J.汽车电器.19933 时瑞祥.氢气发动机小型内燃机M.19944 王文清.世界汽车工业发展趋势J.汽车电器 19915 张准、汪凤泉编著,振动分析M.东南大学出版社 1991. 6 崔存.现代汽车新技术M.人民交通出版社7 廖大方、王志金译.未来汽车技术J.武汉汽车工业大学科技情报所8 刘岩、丁玉兰、林逸.汽车高速振动仿真与试验研究M.2000.179 鲁麦特车辆动力学模拟及其方法J北京理工大学出版社 200210 庞勇、贺益康.基于专用控制芯片的永磁无刷直流电机控制器J199911 侯志祥、李小颖.我国21世纪电动汽车发展的对策交道科技200212牵引用铅酸蓄电池产品品种和规格标准J GB 7403.2 1987毕业设计（论文）进度计划（以周为单位）第1周（20*年2月24日-20*年2月28日）：下达设计任务书，明确任务，熟悉课题，收集资料，上交外文翻译、参考文献和开题报告；第2周-第3周（20*年3月3日-20*年3月14日）：根据本课题的要求，制定总体方案，绘制草图；第4周-第5周（20*年3月17日-20*年3月28日）：完成设计方案，拟定自动行走小车的设计草图；第6周-第7周（20*年3月31日-20*年4月11日）：完成自动小车的设计总图及有关零件设计图；第8周（20*年4月14日-20*年4月18日）：提交第1-8周的指导记录表和已做的毕业设计内容，由指导老师初审后上交学院第9周-第13周（20*年4月21日-20*年5月23日）：在指导老师的指导下修改并完成设计，完成相关设计图纸，同时撰写毕业设计说明书，并提交指导老师初审；第14周-第16周（20*年5月26日-20*年6月14日）：修改毕业设计图纸及说明书，完成后参加毕业答辩；备注注：表格栏高不够可自行参加。此表由指导老师在毕业设计（论文）工作开始前填写，每位毕业生两份，一份发给学生，一份交院(系)留存。A Visual-Sensor Model for Mobile Robot LocalisationMatthias Fichtner Axel Gro_mannArti_cial Intelligence InstituteDepartment of Computer ScienceTechnische Universitat DresdenTechnical Report WV-03-03/CL-2003-02AbstractWe present a probabilistic sensor model for camera-pose estimation in hallways and cluttered o_ce environments. The model is based on the comparison of features obtained from a given 3D geometrical model of the environment with features presentin the camera image. The techniques involved are simpler than state-of-the-art photogrammetric approaches. This allows the model to be used in probabilistic robot localisation methods. Moreover, it is very well suited for sensor fusion. The sensor model has been used with Monte-Carlo localisation to track the position of a mobile robot in a hallway navigation task. Empirical results are presented for this application.1 IntroductionThe problem of accurate localisation is fundamental to mobile robotics. To solve complex tasks successfully, an autonomous mobile robot has to estimate its current pose correctly and reliably. The choice of the localization method generally depends on the kind and number of sensors, the prior knowledge about the operating environment, and the computing resources available. Recently, vision-based navigation techniques have become increasingly popular 3. Among the techniques for indoor robots, we can distinguish methods that were developed in the _eld of photogrammetry and computer vision, and methods that have their origin in AI robotics.An important technical contribution to the development of vision-based navigationtechniques was the work by 10 on the recognition of 3D-objects from unknown viewpoints in single images using scale-invariant features. Later, this technique was extended to global localisation and simultaneous map building 11.The FINALE system 8 performed position tracking by using a geometrical model of the environment and a statistical model of uncertainty in the robots pose given the commanded motion. The robots position is represented by a Gaussian distribution and updated by Kalman _ltering. The search for corresponding features in camera image and world model is optimized by projecting the pose uncertainty into the camera image.Monte Carlo localisation (MCL) based on the condensation algorithm has been applied successfully to tour-guide robots 1. This vision-based Bayesian _ltering technique uses a sampling-based density representation. In contrast to FINALE, it can represent multi-modal probability distributions. Given a visual map of the ceiling, it localises the robot globally using a scalar brightness measure. 4 presented a vision-based MCL approach that combines visual distance features and visual landmarks in a RoboCup application. As their approach depends on arti_cial landmarks, it is not applicable in o_ce environments.The aim of our work is to develop a probabilistic sensor model for camerapose estimation. Given a 3D geometrical map of the environment, we want to find an approximate measure of the probability that the current camera image has been obtained at a certain place in the robots operating environment. We use this sensor model with MCL to track the position of a mobile robot navigating in a hallway. Possibly, it can be used also for localization in cluttered o_ce environments and for shape-based object detection.On the one hand, we combine photogrammetric techniques for map-based feature projection with the exibility and robustness of MCL, such as the capability to deal with localisation ambiguities. On the other hand, the feature matching operation should be su_ciently fast to allow sensor fusion. In addition to the visual input, we want to use the distance readings obtained from sonars and laser to improve localisation accuracy.The paper is organised as follows. In Section 2, we discuss previous work. In Section 3, we describe the components of the visual sensor model. In Section 4, we present experimental results for position tracking using MCL. We conclude in Section 5.2 Related WorkIn classical approaches to model-based pose determination, we can distinguish two interrelated problems. The correspondence problem is concerned with _nding pairs of corresponding model and image features. Before this mapping takes place, the model features are generated from the world model using a given camera pose. Features are said to match if they are located close to each other. Whereas the pose problem consists of _nding the 3D camera coordinates with respect to the origin of the world model given the pairs of corresponding features 2. Apparently, the one problem requires the other to be solved beforehand, which renders any solution to the coupledproblem very di_cult 6.The classical solution to the problem above follows a hypothesise-and-test approach:(1) Given a camera pose estimate, groups of best matching feature pairs provide initial guesses (hypotheses).(2) For each hypothesis, an estimate of the relative camera pose is computed by minimising a given error function de_ned over the associated feature pairs.(3) Now as there is a more accurate pose estimate available for each hypothesis, the remaining model features are projected onto the image using the associated camera pose. The quality of the match is evaluated using a suitable error function, yielding a ranking among all hypotheses.(4) The highest-ranking hypothesis is selected.Note that the correspondence problem is addressed by steps (1) and (3), and the pose problem by (2) and (4).The performance of the algorithm will depend on the type of features used, e.g., edges, line segments, or colour, and the choice of the similarity measure between image and model, here referred to as error function. Line segments is the feature type of our choice as they can be detected comparatively reliably under changing illumination conditions. As world model, we use a wire-frame model of the operating environment, represented in VRML. The design of a suitable similarity measure is far more difficult.In principle, the error function is based on the di_erences in orientation between corresponding line segments in image and model, their distance and difference in length, in order of decreasing importance, in consideration of all feature pairs present. This has been established in the following three common measures 10. e3D is defined by the sum of distances between model line endpoints and the corresponding plane given by camera origin and image line. This measure strongly depends on the distance to the camera due to back-projection. e2D;1, referred to as in_nite image lines, is the sum over the perpendicular distances of projected model line endpoints tocorresponding, in_nitely extended lines in the image plane. The dual measure, e2D;2, referred to as in_nite model lines, is the sum over all distances of image line endpoints to corresponding, in_nitely extended model lines in the image plane.To restrict the search space in the matching step, 10 proposed to constrain the number of possible correspondences for a given pose estimate by combining line features into perceptual, quasi-invariant structures beforehand. Since these initial correspondences are evaluated by e2D;1 and e2D;2, high demands are imposed on the accuracy of the initial pose estimate and the image processing operations, including the removal of distortions and noise and the feature extraction. It is assumed to obtain all visible model lines at full length. 12, 9 demonstrated that a few outliers already can severely affect the initial correspondences in Lowes original approach due to frequent truncation of lines caused by bad contrast, occlusion, or clutter.3 Sensor ModelOur approach was motivated by the question whether a solution to the correspondence problem can be avoided in the estimation of the camera pose. Instead, we propose to perform a relatively simple, direct matching of image and model features. We want to investigate the level of accuracy and robustness one can achieve this way.The processing steps involved in our approach are depicted in Figure 1. After removing the distortion from the camera image, we use the Canny operator to extract edges. This operator is relatively tolerant to changing illumination conditions. From the edges, line segments are identi_ed. Each line is represented as a single point (_; _) in the 2D Hough space given by _ = x cos _ + y sin _. The coordinates of the end points are neglected. In this representation, truncated or split lines will have similar coordinates in the Hough space. Likewise, the lines in the 3D map are projected onto the image plane using an estimate of the camera pose and taking into account thevisibility constraints, and are represented as coordinates in the Hough space as well. We have designed several error functions to be used as similarity measure in the matching step. They are described in the following.Centred match count (CMC)The first similarity measure is based on the distance of line segments in the Hough space. We consider only those image features as possible matches that lie within a rectangular cell in the Hough space centred around the model feature. The matches are counted and the resulting sum is normalised. The mapping from the expectation (model features) to the measurement (image features) accounts for the fact that the measure should be invariant with respect to objects not modelled in the 3D map or unexpected changes in the operating environment. Invariance of the number of visible features is obtained by normalisation. Speci_cally, the centred match count measuresCMC is defined by:where the predicate p de_nes a valid match using the distance parameters (t_; t_) and the operator # counts the number of matches. Generally speaking, this similarity measure computes the proportion of expected model Hough points hei 2 He that are con_rmed by at least one measured image Hough point hmj 2 Hm falling within tolerance (t_; t_). Note that neither endpoint coordinates nor lengths are considered here.Grid length match (GLM)The second similarity measure is based on a comparison of the total length values of groupes of lines. Split lines in the image are grouped together using a uniform discretisation of the Hough space. This method is similar to the Hough transform for straight lines. The same is performed for line segments obtained from the 3D model. Let lmi;j be the sum of lengths of measured lines in the image falling into grid cell (i; j), likewise lei;j for expected lines according to the model, then the grid length match measure sGLM is de_ned as:For all grid cells containing model features, this measure computes the ratio of the total line length of measured and expected lines. Again, the mapping is directional, i.e., the model is used as reference, to obtain invariance of noise, clutter, and dynamic objects.Nearest neighbour and Hausdorf distanceIn addition, we experimented with two generic methods for the comparison of two sets of geometric entities: the nearest neighbour and the Hausdor_ distance. For details see 7. Both rely on the de_nition of a distance function, which we based on the coordinates in the Hough space, i.e., the line parameter _ and _, and optionally the length, in a linear and exponential manner. See 5 for a complete description.Common error functionsFor comparisons, we also implemented the commonly used error functions e3D, e2D;1, and e2D;2. As they are de_ned in the Cartesian space, we represent lines in the Hessian notation, x sin _ y cos _ = d. Using the generic error function f, we de_ned the similarity measure as:where M is the set of measured lines and E is the set of expected lines. In case of e2D;1, f is de_ned by the perpendicular distances between both model line endpoints, e1, e2, and the in_nitely extended image line m:Likewise, the dual similarity measure, using e2D;2, is based on the perpendiculardistances between the image line endpoints and the in_nitely extended model line.Recalling that the error function e3D is proportional to the distances of model line endpoints to the view plane through an image line and the camera origin, we can instantiate Equation 1 using f3D(m; e) de_ned as:where nm denotes the normal vector of the view plane given by the image endpoints mi = mx;my;wT in camera coordinates.Obtaining probabilitiesIdeally, we want the similarity measure to return monotonically decreasing values as the pose estimate used for projecting the model features departs from the actual camera pose. As we aim at a generally valid yet simple visual-sensor model, the idea is to abstract from speci_c poses and environmental conditions by averaging over a large number of di_erent, independent situations. For commensurability, we want to express the model in terms of relative robot coordinates instead of absolute world coordinates. In other words, we assumeto hold, i.e., the probability for the measurement m, given the pose lm this image has been taken at, the pose estimate le, and the world model w, is equal to the probability of this measurement given a three-dimensional pose deviation 4l and the world model w.The probability returned by the visual-sensor model is obtained by simple scaling:4 Experimental ResultsWe have evaluated the proposed sensor model and similarity measures in a series of experiments. Starting with arti_cially created images using idealized conditions, we have then added distortions and noise to the tested images. Subsequently, we have used real images from the robots camera obtained in a hallway. Finally, we have used the sensor model to track the position of the robot while it was travelling through the hallway. In all these cases, a three-dimensional visualisation of the model was obtained, which was then used to assess the solutions.Simulations using arti_cially created imagesAs a first kind of evaluation, we generated synthetic image features by generating a view at the model from a certain camera pose. Generally speaking, we duplicated the right-hand branch of Figure 1 onto the left-hand side. By introducing a pose deviation 4l, we can directly demonstrate its inuence on the similarity values. For visualisation purposes, the translational deviations 4x and 4y are combined into a single spatial deviation 4t. Initial experiments have shown only insigni_cant di_erences when they were considered independently.Fig. 2: Performance of CMC on arti_cially created images.For each similarity measure given above, at least 15 million random camera poses were coupled with a random pose deviation within the range of 4t 440cm and 4_ 90_ yielding a model pose.The results obtained for the CMC measure are depicted in Figure 2. The surface of the 3D plot was obtained using GNUPLOTs smoothing operator dgrid3d. We notice a unique, distinctive peak at zero deviation with monotonically decreasing similarity values as the error increases. Please note that this simple measure considers neither endpoint coordinates nor lengths of lines. Nevertheless, we obtain already a decent result.While the resulting curve for the GLM measure resembles that of CMC, the peak is considerably more distinctive. This conforms to our anticipation since taking the length of image and model lines into account is very signi_cant here. In contrast to the CMC measure, incidental false matches are penalised in this method, due to the differing lengths.The nearest neighbour measure turned out to be not of use. Although linear and exponential weighting schemes were tried, even taking the length of line segments into account, no distinctive peak was obtained, which caused its exclusion from further considerations.The measure based on the Hausdor_ distance performed not as good as the first two, CMC and GLM, though it behaved in the desired manner. But its moderate performance does not pay off the longest computation time consumed among all presented measures and is subsequently disregarded.So far, we have shown how our own similarity measures perform. Next, we demonstrate how the commonly used error functions behave in this framework.The function e2D;1 performed very well in our setting. The resulting curve closely resembles that of the GLM measure. Both methods exhibit a unique, distinctive peak at the correct location of zero pose deviation. Note that the length of line segments has a direct e_ect on the similarity value returned by measure GLM, while this attribute implicitly contributes to the measure e2D;1, though both linearly. Surprisingly, the other two error functions e2D;2 and e3D performed poorly.Toward more realistic conditionsIn order to learn the e_ect of distorted and noisy image data on our sensor model, we conducted another set of experiments described here. To this end, we applied the following error model to all synthetically generated image features before they are matched against model features. Each original line is duplicated with a small probability (p = 0:2) and shifted in space. Any line longer than 30 pixel is split with probability p=0:3. A small distortion is applied to the parameters (_; _; l) of each line according to a random, zeromean Gaussian. Furthermore, features not present in the model and noise are simulated by adding random lines uniformly distributed in the image. Hereof, the orientation is drawn according to the current distribution of angles to yield fairly typical features.The results obtained in these simulations do not di_er significantly from the first set of experiments. While the maximum similarity value at zero deviation decreased, the shape and characteristics of all similarity measures still under consideration remained the same.Using real images from the hallwaySince the results obtained in the simulations above might be questionable with respect to real-world conditions, we conducted another set of experiments replacing the synthetic feature measurements by real camera images.To compare the results for various parameter settings, we gathered images with a Pioneer 2 robot in the hallway o_-line and recorded the line features. For two di_erent locations in the hallway exemplifying typical views, the three-dimensional space of the robot poses (x; y; _) was virtually discretized. After placing the robot manually at each vertex (x; y; 0), it performed a full turn on the spot stepwise recording images. This ensures a maximum accuracy of pose coordinates associated with each image. That way, more than 3200 images have been collected from 64 di_erent (x; y) locations. Similarly to the simulations above, pairs of poses (le; lm) were systematically chosenFig. 3: Performance of GLM on real images from the hallway.from with the range covered by the measurements. The values computed by the sensor model referring to the same discretized value of pose deviation 4l were averaged according to the assumption in Equation 2.The resulting visualisation of the similarity measure over spatial (x and y combined) and rotational deviations from the correct camera pose for the CMC measure exhibits a unique peak at approximately zero deviation. Of course, due to a much smaller number of data samples compared to the simulations using synthetic data, the shape of the curve is much more bumpy, but this is in accordance with our expectation.The result of employing the GLM measure in this setting is shown in Figure 3. As it reveals a more distinctive peak compared to the curve for the CMC measure, it demonstrates the increased discrimination between more and less similar feature maps when taking the lengths of lines into account.Monte Carlo Localisation using the visual-sensor modelRecalling that our aim is to devise a probabilistic sensor model for a camera mounted on a mobile robot, we continue with presenting the results for an application to mobile robot localisation.The generic interface of the sensor model allows it to be used in the correction step of Bayesian localisation methods, for example, the standard version of the Monte Carlo localisation (MCL) algorithm. Since statistical independence among sensor readings renders one of the underlying assumptions of MCL, our hope is to gain improved accuracy and robustness using the camera instead of or in addition to commonly used distance sensors like sonars or laser.Fig. 4: Image and projected models during localisation.In the experiment, the mobile robot equipped with a _xed-mounted CCD camera had to follow a pre-programmed route in the shape of a double loop in the corridor. On its way, it had to stop at eight pre-de_ned positions, turn to a nearby corner or open view, take an image, turn back and proceed. Each image capture initiated the so-called correction step of MCL and the weights of all samples were recomputed according to the visual-sensor model, yielding the highest density of samples at the potentially correct pose coordinates in the following resampling step. In the prediction step, the whole sample set is shifted in space according to the robots motion model and thecurrent odometry sensor readings.Our preliminary results look very promising. During the position tracking experiments, i.e., the robot was given an estimate of its starting position, the best hypothesis for the robots pose was approximately at the correct pose most of the time. In this experiment, we have used the CMC measure. In Figure 4, a typical camera view is shown while the the robots follows the requested path. The grey-level image depicts the visual input for feature extraction after distortion removal and pre-processing. Also the extracted line features are displayed. Furthermore, the world model is projected according to two poses, the odometry-tracked pose and the estimate computed by MCL which approximately corresponds to the correct pose, between which we observe translational and rotational error.The picture also shows that rotational error has a strong inuence on the degree of coincidental feature pairs. This effect corresponds to the results presented above, where the figures exhibit a much higher gradient along the axis of rotational deviation than along that of translational deviation. The finding can be explained by the effect of motion on features in the Hou