M. Subbarao and A.M. Waxman. On the uniqueness of image flow solutions for planar surfaces in motion. Computer Vision, Graphics, and Image Processing, 36:208--228, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....1 1. Introduction The problem of determining rigid body motion and surface structure from image data has been the topic of many research papers in the area of machine vision [1 22] Many approaches based on, tracking feature points [5,11,19,20] or contours [9] using motion flow field [1,3,4,10,12,16,17,21,22], texture [2] or image intensity gradients [14,15] have been proposed in the literature. In the feature point matching schemes, information about a finite number of well seperated points is used to recover the motion (general 8 point 2 frame algorithms of Longuet Higgins [11] Tsai and Huang ....

....and Prazdny [11] suggested a method that uses the optical flow and its first and second derivatives at a single point. Later, Waxman and Ullman [21] developed this into an algorithm for recovering the struc ture and motion parameters from a set of nonlinear equations. Subbarao and Waxman [17] recently found a closed form solution to the original formulation in [21] for planar surfaces. These methods while mathematically elegant are very sensitive to errors in the optical flow data since second order derivatives of noisy data are used. At the expense of more computation, more robust ....

Subbarao, M., Waxman, A.M., "On the Uniqueness of Image Flow Solutions for Planar Surfaces in Motion," CAR-TR-114, Computer Vision Laboratory, Center for Automation Research, University of Maryland, College Park, MD, April 1985.

....stable. In order to demonstrate the true monotonic relation between the sensitivity and noise level, a larger number of trials have to be performed. In this case, the fact that the points in the scene are (almost) coplanar has to be incorporated in the designing of motion estimation algorithms [10, 19]. 3.4 Translation estimates v 0 versus v Further evaluation of the results and more extensive simulations are currently underway. We believe that thoroughly understanding the source of translational bias, we can obtain even better performance by utilizing additional information about the linear ....

M. Subbarao and A. M. Waxman. On the uniqueness of image flow solutions for planar surfaces in motion. Third IEEE workshop on computer vision: representation and control, pages 129--140, 1985.

....version of the problem. The differential version is important when the task is to control a dynamic mobile robot such as a UAV, since velocity estimates are necessary for the computation of control inputs. The differential planar ego motion estimation problem has been studied by many researchers [7, 12, 19, 22], each using a different approach. We here propose a new and unified geometric framework which provides motion estimation algorithms for the planar case in the same spirit of the general purpose 8 point algorithm: First minimize a planar discrete (differential) epipolar constraint based on image ....

....whereas if v T e 3 = 0 both solutions 2 and 4 are eliminated. For the case that v Theta n = 0, it is easy to see that solutions 1 and 2 are equivalent, and that imposing the positive depth constraint leads to a unique solution. The results for the ambiguities of solutions were also reported in [7, 19, 22]. In section 5.1 we give a method of disambiguating the solutions when the task is landing a UAV on a landing pad whose geometry is known a priori. 3.3 Implementation Issues For both the discrete and differential algorithms, the most computationally intensive task is the linear least squares ....

M. Subbarao and A.M. Waxman. On the uniqueness of image flow solutions for planar surfaces in motion. Computer Vision, Graphics, and Image Processing, 36:208--228, 1986.

....of fixed points in a plane. The differential version is important for the control of a dynamic mobile robot such as a UAV, since velocity estimates are necessary for the computation of control inputs. The differential structure from motion problem for a planar scene has also been studied in [2, 10]. We propose a new geometrical estimation scheme for the motion and structure parameters. Proposition 2 Suppose the camera undergoes a rigid motion with body linear and angular velocities v; Then the coordinates of coplanar points f q i g m i=1 in the instantaneous camera frame satisfy: q ....

M. Subbarao and A.M. Waxman. On the uniqueness of image flow solutions for planar surfaces in motion. In Third IEEE Workshop on Computer Vision: Representation and Control, pages 129--140, 1985.

....that two planes with distinct surface orientations that are engaged in different 3 d motions may have the same optical flow field. Waxman and Wohn [154] describe the dual nature of these motion and structure parameters: one set of parameters can be derived from the other. Subbarao and Waxman [141] demonstrate that these solutions are unique over time. Horn [68] proves that multiple interpretations of a single optical flow field generated by arbitrarily shaped surfaces occur only rarely. A number of planar motion techniques rely on normal velocity being available 10 . Waxman and Wohn s ....

M. Subbarao and A. M. Waxman. On the uniqueness of image flow solutions for planar surfaces in motion. In 3rd Workshop on Computer Vision: Representation and Control, pages 129--140, Bellaire, Michigan, October 1985.

....and other perceptual uncertainties. The problem of observing a moving agent was addressed in the literature extensively. It was discussed in the work addressing tracking of targets and determination of the optic flow [2,7,10,19] recovering 3 D parameters for different kinds of surfaces [6,14,17,18]; and also in the context of other problems [1,3,8,9] However, the need to recognize, understand, and report on different visual steps within a dynamic task was not sufficiently addressed. In particular, there is a need for high level symbolic interpretations of the actions of an agent. Those ....

....structure parameters. The system is linearized by either dividing the parameter space into three subspaces for the translational, rotational, and structure parameters and solving iteratively; or using other linearization techniques, and or assumptions to solve a linear system of random variables [4,5,6,17,18,20]. As an example, the recovered 3 D translational velocity cumulative density functions for an actual world motion, VX = 0 cm, V Y = 0 cm and VZ = 13 cm, is shown in figure 8.9. It should be noted that the recovered distributions represents a fairly accurate estimation of the actual 3 D motion. ....

M. Subbarao and A. M. Waxman, On The Uniqueness of Image Flow Solutions for Planar Surfaces in Motion, CAR--TR--113, Center for Automation Research, University of Maryland, April 1985.

....to singularities and breakdowns in general motion and structure algorithms [9] and hence one needs structure from motion algorithms specific to this case. The differential structure from motion problem for a planar scene has been studied by Longuet Higgins [4] Kanatani [3] and Subbarao et al. [8, 7], each using a different approach. We propose a new estimation scheme for the motion and structure parameters. 3.1 Formulating the Vision Problem Let P ae R 3 denote the fixed landing plane and nF 2 S 2 be the unit normal to P. Without loss of generality, we take the origin of the inertial ....

....of the three matrices B i B T i , and choose the B i that satisfies the eigenvalue constraint given by Lemma 4. 3.3 Decomposing the B Matrix We now address the task of decomposing B into its motion and structure parameters. The results for the ambiguities of solutions were also reported in [4, 8, 3]. The following constructive proof gives a new technique for the recovering the motion and structure parameters. Theorem 2 Given a matrix B 2 R 3 Theta3 in the form B = 1 d vn T , one can recover the motion and structure parameters f ; v d ; ng up to at most 2 physically possible ....

[Article contains additional citation context not shown here]

M. Subbarao and A.M. Waxman. On the uniqueness of image flow solutions for planar surfaces in motion. In Third IEEE Workshop on Computer Vision: Representation and Control, pages 129--140, 1985.

No context found.

M. Subbarao and A.M. Waxman. On the uniqueness of image flow solutions for planar surfaces in motion. Computer Vision, Graphics, and Image Processing, 36:208--228, 1986.

No context found.

M. Subbarao and A. M. Waxman, On The Uniqueness of Image Flow Solutions for Planar Surfaces in Motion, CAR--TR--113, Center for Automation Research, University of Maryland, April 1985.

No context found.

M. SUBBARAO and A. WAXMAN "On the uniqueness of image flow solutions for planar surfaces in motion" Proc. of the third IEEE Workshop on Computer Vision: Representation and Control, Oct. 1985,

No context found.

Subbarao, M. and A. Waxman (1985). On the uniqueness of image flow solutions for planar surfaces in motion. Proc. Third IEEE Workshop on Computer Vision: Representation and Control, 129--139, Bellaire, MI.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC