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Mirror symmetry⇒2-view stereo geometry

Alexandre R.J. François, Gérard G. Medioni, Roman Waupotitsch
2003 Image and Vision Computing  
All traditional tools of classical 2-view stereo can then be applied, and the concepts of fundamental/essential matrix, epipolar geometry, rectification and disparity hold.  ...  We address the problem of 3-D reconstruction from a single perspective view of a mirror symmetric scene.  ...  from a single perspective view using traditional 2-view stereo geometry.  ... 
doi:10.1016/s0262-8856(02)00149-x fatcat:u3w4uwnphfbtzldvjcsrm2ijle

Dense 3D Reconstruction of Symmetric Scenes from a Single Image [chapter]

Kevin Köser, Christopher Zach, Marc Pollefeys
2011 Lecture Notes in Computer Science  
This naturally creates a symmetry in the matching costs for dense stereo. Alternatively, we also show how to enforce the 3D symmetry in dense depth estimation for the original image.  ...  Given this symmetry plane a second camera is hallucinated that serves as a virtual second image for dense 3D reconstruction, where the point of view for reconstruction can be chosen on the symmetry plane  ...  Camera geometry Since we are aiming at dense stereo, some baseline is required to reconstruct the scene geometry. We will now construct a second virtual camera to perform the stereo.  ... 
doi:10.1007/978-3-642-23123-0_27 fatcat:ivl6fe7l7jfjdh3omid3bssfdm

Mirrors in Computer Graphics, Computer Vision and Time-of-Flight Imaging [chapter]

Ilya Reshetouski, Ivo Ihrke
2013 Lecture Notes in Computer Science  
On the other side, mirrors, with their unique reflective properties, can be used to improve our sensing modalities, enabling applications such as surround, stereo and light field imaging.  ...  Surfaces often cause specular reflection, making it necessary to design robust geometry recovery algorithms for many practical situations.  ...  Fig. 16 : 16 Design for a four mirror stereo camera or viewing device [4] (left). The Sokkia MS27 commercial stereo viewer for aerial imagery (right).  ... 
doi:10.1007/978-3-642-44964-2_5 fatcat:as7vcxgwr5ao3jczlnb2nw3dpi

3-D Shape Representation by Contours

Isaac Weiss
1985 International Joint Conference on Artificial Intelligence  
Figure 1 : 1 Figure 1: Viewing geometry.  ...  on surface and viewing geometry Certain assumptions about the geometries are made, for the sake of mathematical simplicity Then the equations are inverted so that, given viewing geometry and disparities  ... 
dblp:conf/ijcai/Weiss85 fatcat:m5grof7pvnd6pe5umgeqbfw2pm

Binocular 3D Object Recovery Using a Symmetry Prior

Aaron Michaux, Vikrant Kumar, Vijai Jayadevan, Edward Delp, Zygmunt Pizlo
2017 Symmetry  
There has been a small amount of persistent interest in using mirror symmetry to perform 3D recovery; however, almost no attempts use both mirror symmetry and two-view geometry at the same time.  ...  The advantage of combining mirror symmetry with two-view geometry is that each problem disambiguates the other, making it simpler to solve both simultaneously.  ...  The content of this paper is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.  ... 
doi:10.3390/sym9050064 fatcat:it3mgfnnzvefrp7q5bmdyb6z2e

Detecting and Reconstructing 3D Mirror Symmetric Objects [chapter]

Sudipta N. Sinha, Krishnan Ramnath, Richard Szeliski
2012 Lecture Notes in Computer Science  
Our detection stage is based on matching mirror symmetric feature points and descriptors and then estimating the symmetry direction using RANSAC.  ...  This allows the algorithm to reconstruct lightly textured objects, which are problematic for traditional feature-based and intensity-based stereo matchers.  ...  We begin with a review of previous work in Section 2. In Section 3, we describe the imaging geometry when viewing a bilaterally symmetric 3D object from both a canonical and general viewpoint.  ... 
doi:10.1007/978-3-642-33709-3_42 fatcat:m6fqwn2fwjdkzcyoahajqkt5l4

Catadioptric Omni-directional Stereo Vision and Its Applications in Moving Objects Detection [chapter]

Xiong Zhihui, Chen Wang, Zhang Maoju
2008 Computer Vision  
No. 60773023), Postdoctor Science Foundation of China project "Research on key techniques of stereo omni-directional panorama system" (Fund.  ...  No. 60705013), National Natural Science Foundation of China (NSFC) project "Research on virtual environment construction methods based on stereo parallel mosaicing" (Fund.  ...  Epipolar geometry of two views can be formalized as follows. Let p v1 , p v2 denote positions of a scene point in viewpoint coordinate of V 1 and V 2 .  ... 
doi:10.5772/6159 fatcat:kb2ilhlgtvc7xbnkeposlkwmte

Figure-ground organization based on three-dimensional symmetry

Aaron Michaux, Vijai Jayadevan, Edward Delp, Zygmunt Pizlo
2016 Journal of Electronic Imaging (JEI)  
Therefore, we present a general purpose method for finding 3-D symmetry correspondence by pairing the problem with the two-view geometry of the binocular correspondence problem.  ...  No general purpose approach is known for solving 3-D symmetry correspondence in two-dimensional (2-D) camera images, because few invariants exist.  ...  The content of this paper is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.  ... 
doi:10.1117/1.jei.25.6.061606 fatcat:zsgk2t6fjjcbdlyo6giy6xcmim

Planar Catadioptric Stereo: Single and multi-view geometry for calibration and localization

G.L. Mariottini, S. Scheggi, F. Morbidi, D. Prattichizzo
2009 2009 IEEE International Conference on Robotics and Automation  
In this paper we present a rigorous analytical treatment of the imaging geometry of PCS, propose new mirror calibration algorithms and introduce new multi-view properties that can be used for eye-in-hand  ...  Planar Catadioptric Stereo vision sensors (PCS) combine a pinhole camera with two or more planar mirrors.  ...  SINGLE AND MULTI-VIEW GEOMETRY FOR PCS A. Single-view geometry In this section we will assume to have two planar mirrors n 1 and n 2 as in Fig. 3 .  ... 
doi:10.1109/robot.2009.5152609 dblp:conf/icra/MariottiniSMP09 fatcat:amgci7hdcffflk5iq2ice6neuu

Depth From Water Reflection

Linjie Yang, Jianzhuang Liu, Xiaoou Tang
2015 IEEE Transactions on Image Processing  
This problem can be regarded as a special case of two-view stereo vision.  ...  We then present a stereo matching algorithm to obtain the disparity map of the real scene.  ...  The keypoints in the real scene are marked in red and those in the mirror scene are marked in yellow. Better viewed on the screen with enlarged images.  ... 
doi:10.1109/tip.2015.2397591 pmid:25643408 fatcat:5d2jwbnzsbctdeylv2kylvsc6y

Design of Vertically Aligned Binocular Omnistereo Vision Sensor

Yi-ping Tang, Qing Wang, Ming-li Zong, Jun Jiang, Yi-hua Zhu
2010 EURASIP Journal on Image and Video Processing  
The catadioptric mirror design uses the method of increasing the resolution of the view field and the scope of the image in the vertical direction.  ...  Using the collinearity of two view points, the binocular stereo ODVS is able to easily align the azimuth, while the camera calibration, feature points match, and other cumbersome steps have been simplified  ...  The resulting surface therefore always has azimuthally symmetry.  ... 
doi:10.1155/2010/624271 fatcat:rvxcwtnhsnhsdmyz364g4hvteu

Environmental Perception for Intelligent Vehicles Using Catadioptric Stereo Vision Systems

Miriam Schönbein, Bernd Kitt, Martin Lauer
2011 European Conference on Mobile Robots  
Both stereo camera systems consist of at least one catadioptric camera, which combines a lens with a hyperbolic mirror and provides a panoramic view of the surrounding.  ...  We discuss the advantages of both camera systems for stereo vision and 3D reconstruction.  ...  Field of View of the catadioptric stereo camera systems. Fig. 2 . 2 Fig. 2.  ... 
dblp:conf/ecmr/SchonbeinKL11 fatcat:w5zh65wwyrhxlknojfc74infnu

Analysis and optimization of the stereo-system with a four-mirror adapter

Rong Wang, Xiaoyan Li, Yang Zhang
2008 Journal of the European Optical Society-Rapid Publications  
The stereo system with a four-mirror adapter in particular is analyzed, whereafter an improvement is made to achieve the maximum field of view (FOV) of the stereo system with the four-mirror adapter.  ...  In the diagnostic procedure two views are used to provide in-depth information of the observing object.  ...  A simple and an illustrative geometry of a four-mirror stereo adapter with the camera lenses is displayed in Figure 11 .  ... 
doi:10.2971/jeos.2008.08033 fatcat:pmhuxyotkjamlgshw7wvi4suoq

Catadioptric Stereo with Planar Mirrors: Multiple-view Geometry and Camera Localization [chapter]

Gian Luca Mariottini, Stefano Scheggi, Fabio Morbidi, Domenico Prattichizzo
2010 Lecture notes in control and information sciences  
PCS systems have recently received an increasing attention in computer vision and have a promising applicability in robotics, since the use of mirrors allows to obtain a stereo view without the need of  ...  Planar catadioptric stereo (PCS) vision sensors consist of a pinhole camera and two or more planar mirrors.  ...  Single and multiple view geometry for PCS sensors Single view geometry In this section we assume that a camera c observes a set of 3-D points reflected by two planar mirrors (see Fig. 4 ).  ... 
doi:10.1007/978-1-84996-089-2_1 fatcat:uezhaq3qvbdmrk767xy6556n5y

Multiview panoramic cameras using mirror pyramids

Kar-Han Tan, Hong Hua, N. Ahuja
2004 IEEE Transactions on Pattern Analysis and Machine Intelligence  
A mirror pyramid consists of a set of planar mirror faces arranged around an axis of symmetry and inclined to form a pyramid.  ...  view (FOV), using simulations to illustrate the concepts.  ...  Fig. 2 . The geometry of a mirror pyramid. pyramid. More recently, Nalwa [2] , [3] discussed the possibility of placing multiple viewpoints at arbitrary locations in the same pyramid.  ... 
doi:10.1109/tpami.2004.33 pmid:18579952 fatcat:637awxpzqzdcnmjbj2vos22t6i
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