@article {14237,
	title = {Noise causes slant underestimation in stereo and motion},
	journal = {Vision Research},
	volume = {46},
	year = {2006},
	month = {2006/10//},
	pages = {3105 - 3120},
	abstract = {This paper discusses a problem, which is inherent in the estimation of 3D shape (surface normals) from multiple views. Noise in the image signal causes bias, which may result in substantial errors in the parameter estimation. The bias predicts the underestimation of slant found in psychophysical and computational experiments. Specifically, we analyze the estimation of 3D shape from motion and stereo using orientation disparity. For the case of stereo, we show that bias predicts the anisotropy in the perception of horizontal and vertical slant. For the case of 3D motion we demonstrate the bias by means of a new illusory display. Finally, we discuss statistically optimal strategies for the problem and suggest possible avenues for visual systems to deal with the bias.},
	keywords = {Bias, Partial bias correction, shape estimation, Shape from motion, Stereo orientation disparity},
	isbn = {0042-6989},
	doi = {10.1016/j.visres.2006.04.010},
	url = {http://www.sciencedirect.com/science/article/pii/S0042698906002124},
	author = {Hui Ji and Ferm{\"u}ller, Cornelia}
}
@conference {14224,
	title = {Integration of motion fields through shape},
	booktitle = {IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005. CVPR 2005},
	volume = {2},
	year = {2005},
	month = {2005/06/20/25},
	pages = {663- 669 vol. 2 - 663- 669 vol. 2},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {Structure from motion from single flow fields has been studied intensively, but the integration of information from multiple flow fields has not received much attention. Here we address this problem by enforcing constraints on the shape (surface normals) of the scene in view, as opposed to constraints on the structure (depth). The advantage of integrating shape is two-fold. First, we do not need to estimate feature correspondences over multiple frames, but we only need to match patches. Second, the shape vectors in the different views are related only by rotation. This constraint on shape can be combined easily with motion estimation, thus formulating motion and structure estimation from multiple views as a practical constrained minimization problem using a rank-3 constraint. Based on this constraint, we develop a 3D motion technique, which locates through color and motion segmentation, planar patches in the scene, matches patches over multiple frames, and estimates the motion between multiple frames and the shape of the selected scene patches using the image gradients. Experiments evaluate the accuracy of the 3D motion estimation and demonstrate the motion and shape estimation of the technique by super-resolving an image sequence.},
	keywords = {3D motion estimation, Automation, CAMERAS, computational geometry, Computer vision, constrained minimization problem, decoupling translation from rotation, Educational institutions, image colour analysis, image gradients, image resolution, Image segmentation, image sequence, Image sequences, integration of motion fields, Layout, minimisation, Motion estimation, motion field integration, motion segmentation, parameter estimation, planar patches, rank-3 constraint, scene patches, SHAPE, shape and rotation, shape estimation, structure estimation},
	isbn = {0-7695-2372-2},
	doi = {10.1109/CVPR.2005.190},
	author = {Ji,H. and Ferm{\"u}ller, Cornelia}
}
@conference {12047,
	title = {Which shape from motion?},
	booktitle = {Sixth International Conference on Computer Vision, 1998},
	year = {1998},
	month = {1998/01/04/7},
	pages = {689 - 695},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {In a practical situation, the rigid transformation relating different views is recovered with errors. In such a case, the recovered depth of the scene contains errors, and consequently a distorted version of visual space is computed. What then are meaningful shape representations that can be computed from the images? The result presented in this paper states that if the rigid transformation between different views is estimated in a way that gives rise to a minimum number of negative depth values, then at the center of the image affine shape can be correctly computed. This result is obtained by exploiting properties of the distortion function. The distortion model turns out to be a very powerful tool in the analysis and design of 3D motion and shape estimation algorithms, and as a byproduct of our analysis we present a computational explanation of psychophysical results demonstrating human visual space distortion from motion information},
	keywords = {3D motion estimation, affine shape, Algorithm design and analysis, Computer vision, distorted version, distortion function, human visual space distortion, HUMANS, Image motion analysis, image representation, Information analysis, Layout, Motion analysis, Motion estimation, motion information, Psychology, rigid transformation, SHAPE, shape estimation, shape representations, State estimation, visual space},
	isbn = {81-7319-221-9},
	doi = {10.1109/ICCV.1998.710792},
	author = {Ferm{\"u}ller, Cornelia and Aloimonos, J.}
}
@conference {14264,
	title = {The confounding of translation and rotation in reconstruction from multiple views},
	booktitle = {, 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1997. Proceedings},
	year = {1997},
	month = {1997/06/17/19},
	pages = {250 - 256},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {If 3D rigid motion is estimated with some error a distorted version of the scene structure will in turn be computed. Of computational interest are these regions in space where the distortions are such that the depths become negative, because in order to be visible the scene has to lie in front of the image. The stability analysis for the structure-from-motion problem presented in this paper investigates the optimal relationship between the errors in the estimated translational and rotational parameters of a rigid motion, that results in the estimation of a minimum number of negative depth values. The input used is the value of the flow along some direction, which is more general than optic flow or correspondence. For a planar retina it is shown that the optimal configuration is achieved when the projections of the translational and rotational errors on the image plane are perpendicular. Furthermore, the projection of the actual and the estimated translation lie on a line passing through the image center. For a spherical retina given a rotational error, the optimal translation is the correct one, while given a translational error. The optimal rotational error is normal to the translational one at an equal distance from the real and estimated translations. The proofs, besides illuminating the confounding of translation and rotation in structure from motion, have an important application to ecological optics, explaining differences of planar and spherical eye or camera designs in motion and shape estimation},
	keywords = {3D rigid motion, CAMERAS, ecological optics, Error correction, Image motion analysis, Image reconstruction, Layout, Motion analysis, Motion estimation, multiple views, Optical distortion, optimal configuration, optimal rotational error, planar retina, RETINA, rigid motion, ROTATION, scene structure, shape estimation, spherical retina, Stability analysis, structure-from-motion problem, translation},
	isbn = {0-8186-7822-4},
	doi = {10.1109/CVPR.1997.609328},
	author = {Ferm{\"u}ller, Cornelia and Aloimonos, J.}
}
