T. Brodsky, C. Fermuller, and Y. Aloimonos. Directions of motion fields are hardly ever ambiguous. IJCV, 26(1):5--24, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the motion according to the observer s center [15] One of the major problems in motion recovery is the ambiguity problem. Multiple kinds of motion induce similar optical flow fields and it is difficult to determine the motion from the observed optical flow field. Horn [20] and Brodsky et al. [21] stated that the motion fields and their directions are hardly ever ambiguous, but the ambiguity problem arises if the camera s field of view is small and the variation of the relative depth in the field of view is also small [22,23,5] In the application of vehicle navigation, for example, ....

Tomas Brodsky, Cornelia Fermuller, and Yiannis Aloimonos, "Directions of motion fields are hardly ever ambiguous", International Journal of Computer Vision, vol. 26, no. 1, pp. 5--24, 1998.

....is necessary because we assume that the sequence is all the time dense enough. The most general problem of the motion analysis uncalibrated camera and scene camera motion with more degrees of freedom leads to the well known and often discussed problem of the motion field analysis ( VGT89] [BFA96], or [Nal93] for example) The most primitive case one degree of freedom scene camera motion (pure translation of perspective camera or pure rotation of orthographic camera) leads to the problem of tracking correspondences in a rectified sequence, i.e. correspondences are tracked along ....

Tomas Brodsky, Cornelia Fernmuller, and Yiannis Aloimonos. Directions of motion fields are hardly ever ambiguous. In Bernard Buxton and Roberto Cipolla, editors, Proceedings of the European Conference in Computer Vision, volume 2 of LNCS 1065, pages 119--128, Cambridge, UK, April 1996. Springer.

....restricts the theory explained in this paper to this class of motion problems. However, the theory will still be useful for motion problems encountered when dealing with mobile robots. In the past, research on motion estimation has concentrated mainly on issues of existence and uniqueness [1] 2] [4] [9] 13] Since most uniqueness aspects of the problem are now well understood motion estimation research has shifted its focus on the robustness issue. The motion interpretation part of the motion algorithms appears to be very sensitive for errors introduced in the motion estimation part [7] ....

T. Brodsky, C. Fermuller, and Y. Aloimonos. Directions of motion fields are hardly ever ambiguous. Int. J. of Computer Vision, 26(1):5--24, 1998.

.... of 3D motion does not necessarily require the prior computation of exact correspondence [11, 12, 13, 20, 29] Flow measurements, or even their signs, along some direction in the image, such as for example the one provided by the spatial gradient, are sufficient for recovering 3D motion [3]. Such measurements can be computed by even the simplest systems biological or artificial using, for example, Reichardt detectors or equivalent energy models [32, 33, 31, 43] In this paper an approach that is independent of any algorithm or estimator is taken. Due to the geometry of image ....

T. Brodsky, C. Fermuller, and Y. Aloimonos. Directions of motion fields are hardly ever ambiguous. Technical Report CAR-TR-780, Center for Automation Research, University of Maryland, 1995.

....A does not represent a real camera. 2.2 Projections of affine motion fields Some interesting properties of motion fields become apparent when the flow vectors are projected onto certain carefully chosen directions. Such projections have been used not only to facilitate the theoretical analysis [5, 15], but also to design robust egomotion estimation algorithms [9, 10] The extension to affine fields is quite natural and will be used several times in this paper. Of particular interest throughout the paper, especially for the study of uniqueness in Section 3, are the copoint projections [9] ....

....6 and scene surfaces, the so called critical surfaces, that lead to ambiguities in motion estimation [15, 18, 20] Since here we are dealing with a problem that is more general, certain ambiguities are unavoidable. We consider ambiguities of affine motion fields, applying the method used in [5, 15]. Note that both components of the motion field vectors are used, but the results can be easily adapted to the case of normal flow input. Let the two motions be ( t 1 , A 1 ) and ( t 2 , A 2 ) where t i is the apparent translation K i t i . The two scene depths are denoted by Z 1 and Z 2 . ....

T. Brodsky, C. Fermuller, and Y. Aloimonos. Directions of motion fields are hardly ever ambiguous. International Journal of Computer Vision, 26:5--24, 1998.

.... of 3D motion does not necessarily require the prior computation of exact correspondence [11, 12, 13, 20, 29] Flow measurements, or even their signs, along some direction in the image, such as for example the one provided by the spatial gradient, are sufficient for recovering 3D motion [3]. Such measurements can be computed by even the simplest systems biological or artificial using, for example, Reichardt detectors or equivalent energy models [32, 33, 31, 43] In this paper an approach that is independent of any algorithm or estimator is taken. Due to the geometry of image ....

T. Brodsky, C. Fermuller, and Y. Aloimonos. Directions of motion fields are hardly ever ambiguous. Technical Report CAR-TR-780, Center for Automation Research, University of Maryland, 1995.

....A does not represent a real camera. 2.2 Projections of affine motion fields Some interesting properties of motion fields become apparent when the flow vectors are projected onto certain carefully chosen directions. Such projections have been used not only to facilitate the theoretical analysis [5, 15], but also to design robust egomotion estimation algorithms [9, 10] The extension to affine fields is quite natural and will be used several times in this paper. Of particular interest throughout the paper, especially for the study of uniqueness in Section 3, are the copoint projections [9] ....

....and scene surfaces, the so called critical surfaces, that lead to ambiguities in motion estimation [15, 18, 20] Since here we are dealing with a problem that is more general, certain ambiguities are unavoidable. We consider ambiguities of affine motion fields, applying the method used in [5, 15]. Note that both components of the motion field vectors are used, but the results can be easily adapted to the case of normal flow input. Let the two motions be ( t 1 , A 1 ) and ( t 2 , A 2 ) where t i is the apparent translation K i t i . The two scene depths are denoted by Z 1 and Z 2 . ....

T. Brodsky, C. Fermuller, and Y. Aloimonos. Directions of motion fields are hardly ever ambiguous. International Journal of Computer Vision, 26:5--24, 1998.

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T. Brodsky, C. Fermuller, and Y. Aloimonos. Directions of motion fields are hardly ever ambiguous. IJCV, 26(1):5--24, 1998.

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