Infinitesimal Plane-Based Pose Estimation
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Estimating the pose of a plane given a set of point correspondences is a core problem in computer vision with many applications including Augmented Reality (AR), camera calibration and 3D scene reconstruction and interpretation. Despite much progress over recent years there is still the need for a more efficient and more accurate solution, particularly in mobile applications where the run-time budget is critical. We present a new analytic solution to the problem which is far faster than current methods based on solving Pose from \(n\) Points (PnP) and is in most cases more accurate. Our approach involves a new way to exploit redundancy in the homography coefficients. This uses the fact that when the homography is noisy it will estimate the true transform between the model plane and the image better at some regions on the plane than at others. Our method is based on locating a point where the transform is best estimated, and using only the local transformation at that point to constrain pose. This involves solving pose with a local non-redundant 1st-order PDE. We call this framework Infinitesimal Plane-based Pose Estimation (IPPE), because one can think of it as solving pose using the transform about an infinitesimally small region on the surface. We show experimentally that IPPE leads to very accurate pose estimates. Because IPPE is analytic it is both extremely fast and allows us to fully characterise the method in terms of degeneracies, number of returned solutions, and the geometric relationship of these solutions. This characterisation is not possible with state-of-the-art PnP methods.
KeywordsPlane Pose SfM PnP Homography
This research has received funding from the EU FP7 ERC research Grant 307483 FLEXABLE. Code is available at http://www.tobycollins.net/research/IPPE.
- Ansar, A., & Daniilidis, K. (2003). Linear pose estimation from points or lines. Pattern Analysis and Machine Intelligence (PAMI), 25, 282–296.Google Scholar
- Barreto, J., Roquette, J., Sturm, P., & Fonseca, F. (2009). Automatic camera calibration applied to medical endoscopy. In: British machine vision conference (BMVC).Google Scholar
- Bouguet, J. Y. A camera calibration toolbox for matlab. http://www.vision.caltech.edu/bouguetj/calib_doc/. Accessed May 2013.
- Collins, T., Durou, J. D., Gurdjos, P., & Bartoli, A. (2010). Single-view perspective shape-from-texture with focal length estimation: A piecewise affine approach. In 3D data processing visualization and transmission (3DPVT10).Google Scholar
- Faugeras, O., Luong, Q. T., & Papadopoulou, T. (2001). The geometry of multiple images: The laws that govern the formation of images of a scene and some of their applications. Cambridge, MA: MIT Press.Google Scholar
- Geiger, A., Moosmann, F., Car, M., & Schuster, B. (2012). A toolbox for automatic calibration of range and camera sensors using a single shot. In International conference on robotics and automation (ICRA).Google Scholar
- Haralick, R. M., Lee, D., Ottenburg, K., & Nölle, M. (1991). Analysis and solutions of the three point perspective pose estimation problem. In Computer vision and pattern recognition (CVPR).Google Scholar
- Harker, M., & O’Leary, P. (2005). Computation of homographies. In British computer vision conference (BMVC).Google Scholar
- Hesch, J. A., & Roumeliotis, S. I. (2011). A direct least-squares (DLS) method for PnP. In International conference on computer vision (ICCV).Google Scholar
- Hilsmann, A., Schneider, D., & Eisert, P. (2011). Template-free shape from texture with perspective cameras. In British machine vision conference (BMVC).Google Scholar
- Hung, Y., Harwood, D., & Yeh, P.-S., (1984). Passive ranging to known planar point sets. Technical Report. College Park, MD: University of Maryland.Google Scholar
- Kato, H., & Billinghurst, M. (1999). Marker tracking and HMD calibration for a video-based augmented reality conferencing system. In International workshop on augmented reality (IWAR).Google Scholar
- Li, S., Xu, C., & Xie, M. (2012). A robust O(n) solution to the perspective-n-point problem. Pattern Analysis and Machine Intelligence (PAMI).Google Scholar
- Lobay, A., & Forsyth, D. A. (2004). Recovering shape and irradiance maps from rich dense texton fields. In Computer vision and pattern recognition (CVPR).Google Scholar
- Munoz-Salinas, R. ArUco: Augmented reality library from the university of cordoba. http://www.uco.es/investiga/grupos/ava/node/26. Accessed May 2013.
- Ohta, Y., Maenobu, K., & Sakai, T. (1981). Obtaining surface orientation from texels under perspective projection. In International joint conferences on artificial intelligence (IJCAI).Google Scholar
- Poelman, C., & Kanade, T. (1993). A paraperspective factorization method for shape and motion recovery. Technical Report.Google Scholar
- Quan, L., & Lan, Z. (1999). Linear n-point camera pose determination. In Pattern analysis and machine intelligence (PAMI). Google Scholar
- Sturm, P. (2000). Algorithms for plane-based pose estimation. In Computer vision and pattern recognition (CVPR).Google Scholar
- Triggs, B. (1999). Camera pose and calibration from 4 or 5 known 3D points. In International conference on computer vision (ICCV).Google Scholar
- Vedaldi, A., & Fulkerson, B. VLFeat: An open and portable library of computer vision algorithms. http://www.vlfeat.org/. Accessed May 2013.