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Visual Servoing with Trifocal Tensor

Kaixiang Zhang, Jian Chen, Francois Chaumette
2018 2018 IEEE Conference on Decision and Control (CDC)  
In this paper, a trifocal tensor-based approach is developed for 6 degrees-of-freedom visual servoing.  ...  The trifocal tensor model among the current, desired, and initial views is introduced to describe the geometric relationship.  ...  Then, we use geometric minimization algorithm to provide a geometrically valid tensor [19] . After obtaining the trifocal tensor, the auxiliary tensor variable can be computed with (4) .  ... 
doi:10.1109/cdc.2018.8618687 dblp:conf/cdc/ZhangCC18 fatcat:ohd4tx6rdfdxjmvd55jov65zma

Critical configurations of lines to geometry determination of three cameras

Ming Zhao, Ronald Chung
2008 Pattern Recognition (ICPR), Proceedings of the International Conference on  
We approach the question by looking into the trifocal tensor of the cameras, a quantity tightly related to the camera geometry.  ...  We offer a summary of by how much such families of line set are shy of the general enough structure for a unique determination of the tensor.  ...  Acknowledgement This research was partially supported by CAS/CUHK Shenzhen Inst. of Advanced Integration Technology, Shenzhen, China.  ... 
doi:10.1109/icpr.2008.4761368 dblp:conf/icpr/ZhaoC08 fatcat:ud3qb34v6bgmrmlzvlgff3d73i

Visual control through the trifocal tensor for nonholonomic robots

G. López-Nicolás, J.J. Guerrero, C. Sagüés
2010 Robotics and Autonomous Systems  
The contribution is a trifocal-based control law defined by an exact input-output linearization of the trifocal tensor model.  ...  The desired evolution of the system towards the target is directly defined in terms of the trifocal tensor elements by means of sinusoidal functions without needing metric or additional information from  ...  Later, we normalize the trifocal tensor to a fixed scale and it is denoted with T. The Trifocal Tensor Three perspective images can be geometrically linked by the trifocal tensor.  ... 
doi:10.1016/j.robot.2009.09.005 fatcat:xtjv3lbslbem7p524jq7bqxtoi

Trifocal motion modeling for object-based video compression and manipulation

Zhaohui Sun, A.M. Tekalp
1998 IEEE transactions on circuits and systems for video technology (Print)  
Trifocal transfer requires a trifocal tensor that is computed by matching image features across three views and a dense correspondence between two of the three views.  ...  We propose approximating the dense correspondence between two of the three views by a parametric model in order to apply the trifocal transfer for object-based video compression and background mosaic generation  ...  Then, is the projection of onto given the center of projection The projective geometric (trilinear) constraints across the three views and can be compactly expressed in terms of the trifocal tensor [8  ... 
doi:10.1109/76.718512 fatcat:edktgcwm6rdbrba4ljjzpt6vbi

Trifocal tensor as a tool for modeling an imperceptible structured light sensor

T. Molinier, D. Fofi, F. Meriaudeau, R. Seulin
2007 Journal of optical technology  
From the trifocal tensor, projective matrices can be estimated enabling the projective reconstruction of the scene.  ...  This article presents the first results for the estimation of the trifocal tensor which defines the relations of correspondence between the points pertaining to three image planes.  ...  Future work will deal with self-calibration of an imperceptible structured light sensor based on the geometrical information contained in the trifocal tensor: extract projection matrices, perform a projective  ... 
doi:10.1364/jot.74.000282 fatcat:q6kytfvmargabeabhom5ipsi3a

Trifocal tensor-based 6-DOF visual servoing

Kaixiang Zhang, François Chaumette, Jian Chen
2019 The international journal of robotics research  
The trifocal tensor model among the current, desired, and reference views is constructed to describe the geometric relationship of the system.  ...  This paper proposes a trifocal tensor-based approach for six-degree-of-freedom visual servoing.  ...  Considering the geometric connotation of trifocal tensor model, partial tensor elements were selected to define the visual features.  ... 
doi:10.1177/0278364919872544 fatcat:e7wmwlboafeuxldl7vmdwocw2q

Diagram techniques for multiple view geometry

Alberto Ruiz, Pedro E Lopez-de-Teruel
2009 2009 IEEE 12th International Conference on Computer Vision  
The advantages of this approach are illustrated in several constructions, including straightforward derivations of the standard multiview relations (Fundamental Matrix, Trifocal and Quadrifocal Tensors  ...  In this paper we adapt standard tensor diagrammatic techniques to the specific requirements of visual geometry, so that geometric relations are represented by circuits which can be manipulated using simple  ...  We thank the anonymous reviewers for their helpful comments.  ... 
doi:10.1109/iccv.2009.5459414 dblp:conf/iccv/RuizL09 fatcat:375vqvwgmjam3nxfrtbn4pecgq

Self-calibration of a 1D projective camera and its application to the self-calibration of a 2D projective camera

O. Faugeras, Long Quan, P. Strum
2000 IEEE Transactions on Pattern Analysis and Machine Intelligence  
The method requires the estimation of the trifocal tensor which can be achieved linearly with no approximation unlike the trifocal tensor of 2D images, and solving for the roots of a cubic polynomial in  ...  trifocal tensor of three 1D images.  ...  The same is true of the estimation of the 1D trifocal tensor [21] which is a linear process.  ... 
doi:10.1109/34.879801 fatcat:fdkilfvm5fdrrny2b7wyxci5cq

Three-View Multibody Structure from Motion

R. Vidal, R. Hartley
2008 IEEE Transactions on Pattern Analysis and Machine Intelligence  
We derive a rank constraint on the embedded correspondences from which one can estimate the number of independent motions, as well as linearly solve for the multibody trifocal tensor.  ...  which are natural generalizations of the trilinear constraint and the trifocal tensor to multiple motions.  ...  and the ICT Research Centre of Excellence programs.  ... 
doi:10.1109/tpami.2007.1179 pmid:18084054 fatcat:zb4z4eeptnatxat5mia7rmqik4

A new characterization of the trifocal tensor [chapter]

Théodore Papadopoulo, Olivier Faugeras
1998 Lecture Notes in Computer Science  
The paper contains two new results. First a new, simpler, set of algebraic constraints that characterizes the set of trifocal tensors is presented.  ...  Second, we give a new parametrization of the trifocal tensor based upon those constraints which is also simpler than previously known parametrizations.  ...  Any tensor of the form (2) is a trifocal tensor.  ... 
doi:10.1007/bfb0055662 fatcat:5dafxbj63jaoraaki7ocg7355a

Tensor Embedding of the Fundamental Matrix [chapter]

Shai Avidan, Amnon Shashua
1998 Lecture Notes in Computer Science  
The bifocal and trifocal tensors share the same form and share the same contraction properties.  ...  The motivation is to establish a common terminology that bridges between the fundamental matrix F associated with the bilinear constraint and the trifocal tensor T jk i associated with the trilinearities  ...  In particular, as is the case with the trifocal tensor, contractions of the bifocal tensor into reduced forms matrices have a geometric significance.  ... 
doi:10.1007/3-540-49437-5_4 fatcat:t3dgehlunzawzc4saqyfmsec3i

Constrained planar motion analysis by decomposition

Long Quan, Yichen Wei, Le Lu, Heung-Yeung Shum
2004 Image and Vision Computing  
Finally, we demonstrate both in theory and experiments the advantage of the decomposition method over the general SFM methods by incorporating the constrained motion into the earliest stage of motion analysis  ...  Next, we describe new subspace reconstruction methods, and apply these methods to the images captured by concentric mosaics, which undergo a special case of constrained planar motion.  ...  The work has also been partly supported by the Hong Kong RGC grant HKUST6188/02E.  ... 
doi:10.1016/j.imavis.2003.11.010 fatcat:ynsimllynfdgfe4wqodt2j6654

An Efficient Point-Matching Method Based on Multiple Geometrical Hypotheses

Miguel Carrasco, Domingo Mery, Andrés Concha, Ramiro Velázquez, Roberto De Fazio, Paolo Visconti
2021 Electronics  
Point matching in multiple images is an open problem in computer vision because of the numerous geometric transformations and photometric conditions that a pixel or point might exhibit in the set of images  ...  The main strength and novelty of this method is the determination of the point-to-point geometric correspondence through the intersection of multiple geometrical hypotheses weighted by the maximum likelihood  ...  Multiple Trifocal Tensors This section presents a similar analysis now considering three views.  ... 
doi:10.3390/electronics10030246 fatcat:6ax7pn4mbbg6xotz3wnjpd3kl4

On Weighting and Choosing Constraints for Optimally Reconstructing the Geometry of Image Triplets [chapter]

Wolfgang Förstner
2000 Lecture Notes in Computer Science  
Results of an image sequence with 800 images and an Euclidean parametrization of the trifocal tensor demonstrate the feasibility of the approach.  ...  Motivation and Problem Image triplets reveal quite some advantage over image pairs for geometric image analysis.  ...  However, the analysis confirms the direct 6-point solution of [21] to be a solution for the minimal number of points, as the number of free parameters of the trifocal tensor is 18 [16] .  ... 
doi:10.1007/3-540-45053-x_43 fatcat:ury3ulf3jbgspb4pml57enf45u

A novel 1D trifocal tensor-based control for differential-drive robots

H. M. Becerra, C. Sagues
2009 2009 IEEE International Conference on Robotics and Automation  
We use for the first time the elements of the 1D trifocal tensor directly in the control law.  ...  1D trifocal tensor.  ...  In order to overcome the drawbacks of the typical geometric constraints, we propose a novel approach based on the 1D trifocal tensor.  ... 
doi:10.1109/robot.2009.5152308 dblp:conf/icra/BecerraS09 fatcat:vacpucfmdba43jl6jjocbny6qq
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