Identification of Riccati dynamics under perspective and orthographic observations

@article{Ghosh2000IdentificationOR,
  title={Identification of Riccati dynamics under perspective and orthographic observations},
  author={Bijoy Kumar Ghosh and Hiroshi Inaba and Satoru Takahashi},
  journal={IEEE Trans. Autom. Control.},
  year={2000},
  volume={45},
  pages={1267-1278}
}
The problem of identifying motion and shape parameters of a planar object undergoing a Riccati motion, from the associated optical flow generated on the image plane of a single CCD camera, is studied. The optical flow is generated by projecting feature points on the object onto the image plane via perspective and orthographic projections. An important result we show is that, under perspective projection, the parameters of a specific Riccati dynamics that extend the well-known "rigid motion" can… 
Modeling and Estimation of the Dynamics of Planar Algebraic Curves via Riccati Equations
TLDR
It is shown that rigid or affine motion of an algebraic curve can be described using the dynamics of line factors obtained from a unique decomposition of the curve, and each individual line dynamics can be description by a Riccati equation.
Motion and shape identification with vision and range
TLDR
In this paper, the problem of motion and shape estimation using a camera and a laser range finder is considered using a plane which is undergoing a Riccati motion and the results are characterized as an orbit of a suitable group.
Perspective observation based motion recovery
  • Xinkai Chen, H. Kano, R. Abdursul
  • Mathematics, Computer Science
    2004 International Conference on Intelligent Mechatronics and Automation, 2004. Proceedings.
  • 2004
TLDR
The recovery of motion for a class of movements in the space by using the perspective observation of one point is considered in this paper and the algorithm is modified to deal with the occlusion phenomenon.
MOTION RECOVERY BY USING DYNAMIC VISION
Abstract The recovery of motion for a class of movements in the space by using the perspective observation of one point is considered in this paper. The motion equation can cover a wide class of
An Optical Flow-Based Solution to the Problem of Range Identification in Perspective Vision Systems
TLDR
A globally exponentially stable observer is synthesized, where optical flow estimates are derived from tracking feature trajectory on the image plane over successive camera frames, to yield asymptotic estimates of feature depth at a desired convergence rate.
Range identification for perspective dynamic systems with 3D imaging surfaces
Range identification using image sequence via observations from a traditional camera-type vision system has been discussed in the literature. In this paper, the camera-type planar imaging surface is
Motion recovery for a class of movements under perspective observation
  • Xinkai Chen, H. Kano
  • Mathematics
    Proceedings of the 2004 IEEE International Symposium on Intelligent Control, 2004.
  • 2004
The recovery of motion for a class of movements in the space by using the perspective observation of one point is considered In this work. The motion equation can cover a wide class of practical
Range identification for perspective vision systems
In this note, a new observer is developed to determine range information (and, hence, the three-dimensional (3-D) coordinates) of an object feature moving with affine motion dynamics (or the more
Provably stable nonlinear and adaptive observers for dynamic structure and motion estimation
TLDR
This paper proposes a novel approach based on nonlinear and adaptive observers based on a dynamic model of the motion that provides an estimate of structure and motion at each time instance, which is then updatedbased on a novel image in the sequence.
Range identification of a mobile robot with a monocular camera system
Range identification is a classical problem in the field of machine vision, which aims to recover the depth information of a moving object/camera from 2D image space for perspective dynamic systems
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 27 REFERENCES
A Perspective Theory for Motion and Shape Estimation in Machine Vision
In this paper, we consider the problem of motion and shape estimation of a moving body with the aid of a monocular camera. We show that the estimation problem reduces to a specific parameter
Surface Structure and Three-Dimensional Motion from Image Flow Kinematics
TLDR
An approach is suggested by which the kine matic variables may be extracted from evolving contours in an image sequence by extracting the instantaneous motion and local structure of the object along the line of sight from an evolving image sequence.
Motion and Structure From Two Perspective Views: Algorithms, Error Analysis, and Error Estimation
TLDR
The presented approach to error estimation applies to a wide variety of problems that involve least-squares optimization or pseudoinverse and shows, among other things, that the errors are very sensitive to the translation direction and the range of field view.
Theory of Reconstruction from Image Motion
"Theory of Reconstruction from Image Motion" presents the mathematics underlying the reconstruction of camera motion from the movements of points in the camera image. The author describes recent work
Recovery of the Three-Dimensional Shape of an Object from a Single View
  • T. Kanade
  • Mathematics, Computer Science
    Artif. Intell.
  • 1981
TLDR
The purpose of this paper is to identify some of these assumptions about the world and the image formation process by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape-recovery method.
Estimating three-dimensional motion parameters of a rigid planar patch
We present a new direct method of estimating the three-dimensional motion parameters of a rigid planar patch from two time-sequential perspective views (image frames). First, a set of eight pure
Uniqueness and Estimation of Three-Dimensional Motion Parameters of Rigid Objects with Curved Surfaces
  • R. Tsai, Thomas S. Huang
  • Mathematics, Computer Science
    IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 1984
TLDR
It is shown that seven point correspondences are sufficient to uniquely determine from two perspective views the three-dimensional motion parameters (within a scale factor for the translations) of a rigid object with curved surfaces.
Algebraic methods in 3‐d motion estimation from two‐view point correspondences
TLDR
This work considers the problem of determining motion (3‐D rotation and translation) of rigid objects from their images taken at two time instants, and derives a variety of necessary and sufficient conditions a solution must satisfy, and uses algebraic geometry to derive the bound on the number of solutions.
A realization theory for perspective systems with applications to parameter estimation problems in machine vision
TLDR
The notion of perspective observability is introduced and under a special case a necessary and sufficient condition that would guarantee observability of the initial condition of the linear dynamical system up to a one-parameter magnitude scaling is obtained.
A computer algorithm for reconstructing a scene from two projections
A simple algorithm for computing the three-dimensional structure of a scene from a correlated pair of perspective projections is described here, when the spatial relationship between the two
...
1
2
3
...