Estimating three-dimensional motion parameters of a rigid planar patch, II: Singular value decomposition

Tsai, Roger Y.; Huang, Thomas S.; Zhu, Wei

doi:10.1109/tassp.1982.1163931

Cited by 200 publications

(81 citation statements)

References 10 publications

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“…The most common approach to monocular reconstruction involves solving (generally nonlinear) systems of equations relating image velocity (or image displacement) to a set of motion and structure parameters [Adiv 1984;Bruss and Horn 1983;Buxton et al 1984;Dreschler and Nagel 1982;Kanatani 1985;Lawton 1983;Prazdny 1979;Roach and Aggarwal 1980;Tsai et al 1982;Tsai and Huang 1984;Webb and Aggarwal 1981]. Some of the issues that arise for these algorithms are the need for good initial guesses of the solution, the possibility of multiple solutions, and the need for accurate input.…”

Section: Literature Surveymentioning

confidence: 99%

The feasibility of motion and structure from noisy time-varying image velocity information

Barron

Jepson

Tsotsos

1990

Int J Comput Vision

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This research addresses the problem of noise sensitivity inherent in motion and structure algorithms. The motion and structure paradigm is a two-step process. First, we measure image velocities and, perhaps, their spatial and temporal derivatives, are obtained from time-varying image intensity data and second, we use these data to compute the motion of a moving monocular observer in a stationary environment under perspective projection, relative to a single 3-D planar surface. The first contribution of this article is an algorithm that uses time-varying image velocity information to compute the observer's translation and rotation and the normalized surface gradient of the 3-D planar surface. The use of time-varying image velocity information is an important tool in obtaining a more robust motion and structure calculation. The second contribution of this article is an extensive error analysis of the motion and structure problem. Any motion and structure algorithm that uses image velocity information as its input should exhibit error sensitivity behavior compatible with the results reported here. We perform an average and worst case error analysis for four types of image velocity information: full and normal image velocities and full and normal sets of image velocity and its derivatives. (These derivatives are simply the coefficients of a truncated Taylor series expansion about some point in space and time.) The main issues we address here are: just how sensitive is a motion and structure computation in the presence of noisy input, or alternately, how accurate must our image velocity information be, how much and what type of input data is needed, and under what circumstances is motion and structure feasible? That is, when can we be sure that a motion and structure computation will produce usable results? We base our answers on a numerical error analysis we conduct for a large number of motions.

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Section: Literature Surveymentioning

confidence: 99%

The feasibility of motion and structure from noisy time-varying image velocity information

Barron

Jepson

Tsotsos

1990

Int J Comput Vision

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“…Although many plane motion algorithms have been developed (e.g., [9], [11], [6], [3], [7], and [1] ), the conditions obtained for a unique solution of motion and structure of a planar surface (1911,1171, I11], [1], 113]) are restricted to only two and three views. Even for two and three views, the existing conditions are not complete in the sense that some rare sitttalions have been ignored, as will be discussed here.…”

Section: Introductionmentioning

confidence: 99%

“…Matrix K can be estimated to within a scalar from Equation (2-4) with four correspondences of points if and only if no three of the points are colinear in the space ( [9], [11], [3]). The scalar can be determined by the rigidity condition ( [9], [11], [3], [11).…”

Section: Introductionmentioning

confidence: 99%

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Necessary and sufficient conditions for a unique solution of plane motion and structure

Ahuja

1993

Computer Analysis of Images and Patterns

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ABSTRACT. First, we show an uncertain situation for tile two-view plane motion problem in which an infinite number of solutions may result. Then, we present necessary and sufficient conditions Ior a unique solution of plane motion and structure from any number of views. These algorithm-independent conditions enhance our understanding about the problem of estimating plane motion and structure from image sequences and may be incorporated in any practical algorithms for estimating the motion and slructme of a planar surface.

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“…Reference [11] shows that, if the camera is calibrated (that is, A is known), it is possible to obtain from 2 H two valid solutions for 2 R , 2 t , λ and n , up to a scale factor.…”

Section: A Theoretical Issuesmentioning

confidence: 99%

A visual odometer without 3D reconstruction for aerial vehicles. Applications to building inspection

Caballero¹,

Merino²,

Ferruz

et al.

Proceedings of the 2005 IEEE International Conference on Robotics and Automation

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-This paper presents a vision-based method to estimate the *real motion of a single camera from views of a planar patch. Projective techniques allow to estimate camera motion from pixel space apparent motion without explicit 3-D reconstruction. In addition, the paper will present the HELINSPEC project, the framework where the proposed method has been tested, and will detail some applications in external building inspection that make use of the proposed techniques.Index Terms -feature matching, homography, visual odometer, UAV, building inspection.

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Estimating three-dimensional motion parameters of a rigid planar patch, II: Singular value decomposition

Cited by 200 publications

References 10 publications

The feasibility of motion and structure from noisy time-varying image velocity information

The feasibility of motion and structure from noisy time-varying image velocity information

Necessary and sufficient conditions for a unique solution of plane motion and structure

A visual odometer without 3D reconstruction for aerial vehicles. Applications to building inspection

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