@conference {11982,
	title = {Global rigidity constraints in image displacement fields},
	booktitle = {Proceedings of Fifth International Conference on Computer Vision, 1995},
	year = {1995},
	month = {1995/06/20/23},
	pages = {245 - 250},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {Image displacement fields-optical flow fields, stereo disparity fields, normal flow fields-due to rigid motion possess a global geometric structure which is independent of the scene in view. Motion vectors of certain lengths and directions are constrained to lie on the imaging surface at particular loci whose location and form depends solely on the 3D motion parameters. If optical flow fields or stereo disparity fields are considered, then equal vectors are shown to lie on conic sections. Similarly, for normal motion fields, equal vectors lie within regions whose boundaries also constitute conics. By studying various properties of these curves and regions and their relationships, a characterization of the structure of rigid motion fields is given. The goal of this paper is to introduce a concept underlying the global structure of image displacement fields. This concept gives rise to various constraints that could form the basis of algorithms for the recovery of visual information from multiple views},
	keywords = {3D motion parameters, algorithms, Automation, Computer science, Computer vision, conic sections, curves, equal vectors, Fluid flow measurement, global geometric structure, global rigidity constraints, image displacement fields, Image motion analysis, Image segmentation, Image sequences, imaging surface, Laboratories, Layout, Motion estimation, Motion measurement, motion vectors, multiple views, normal flow fields, optical flow fields, regions, rigid motion, stereo disparity fields, Stereo vision, vectors, visual information recovery},
	isbn = {0-8186-7042-8},
	doi = {10.1109/ICCV.1995.466779},
	author = {Ferm{\"u}ller, Cornelia and Aloimonos, J.}
}
@conference {14168,
	title = {Global rigidity constraints in image displacement fields},
	booktitle = {, Fifth International Conference on Computer Vision, 1995. Proceedings},
	year = {1995},
	month = {1995/06/20/23},
	pages = {245 - 250},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {Image displacement fields-optical flow fields, stereo disparity fields, normal flow fields-due to rigid motion possess a global geometric structure which is independent of the scene in view. Motion vectors of certain lengths and directions are constrained to lie on the imaging surface at particular loci whose location and form depends solely on the 3D motion parameters. If optical flow fields or stereo disparity fields are considered, then equal vectors are shown to lie on conic sections. Similarly, for normal motion fields, equal vectors lie within regions whose boundaries also constitute conics. By studying various properties of these curves and regions and their relationships, a characterization of the structure of rigid motion fields is given. The goal of this paper is to introduce a concept underlying the global structure of image displacement fields. This concept gives rise to various constraints that could form the basis of algorithms for the recovery of visual information from multiple views},
	keywords = {3D motion parameters, algorithms, Automation, Computer science, Computer vision, conic sections, curves, equal vectors, Fluid flow measurement, global geometric structure, global rigidity constraints, image displacement fields, Image motion analysis, Image segmentation, Image sequences, imaging surface, Laboratories, Layout, Motion estimation, Motion measurement, motion vectors, multiple views, normal flow fields, optical flow fields, regions, rigid motion, stereo disparity fields, Stereo vision, vectors, visual information recovery},
	isbn = {0-8186-7042-8},
	doi = {10.1109/ICCV.1995.466779},
	author = {Ferm{\"u}ller, Cornelia and Aloimonos, J.}
}
@conference {14171,
	title = {The information in the direction of image flow},
	booktitle = {, International Symposium on Computer Vision, 1995. Proceedings},
	year = {1995},
	month = {1995/11/21/23},
	pages = {461 - 466},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {If instead of the full motion field, we consider only the direction of the motion field due to a rigid motion, what can we say about the information regarding the three-dimensional motion? In this paper it is shown that considering as the imaging surface the whole sphere, independently of the scene in view, two different rigid motions cannot give rise to the same directional motion field. If we restrict the image to half of a sphere (or an infinitely large image plane) two different rigid motions with instantaneous translational and rotational velocities (t1, ω1) and (t2, ω2) cannot give rise to the same directional motion field unless the plane through t1 and t2 is perpendicular to the plane through ω1 and ω2 (i.e., (t1{\texttimes}t2){\textperiodcentered}(ω1 {\texttimes}ω2)=0). In addition, in order to give a practical significance to these uniqueness results for the case of a limited field of view we also characterize the locations on the image where the motion vectors due to the different motions must have different directions. If (ω1{\texttimes}ω2){\textperiodcentered}(t1 {\texttimes}t2)=0 and certain additional constraints are met, then the two rigid motions could produce motion fields with the same direction. For this to happen the depth of each corresponding surface has to be within a certain range, defined by a second and a third order surface},
	keywords = {Automation, CAMERAS, Computer vision, Educational institutions, image flow, Image motion analysis, Image sequences, imaging surface, Laboratories, Layout, Motion analysis, Motion estimation, motion field, motion vectors, Optical imaging, rigid motion, rigid motions, three-dimensional motion},
	isbn = {0-8186-7190-4},
	doi = {10.1109/ISCV.1995.477071},
	author = {Brodsky, T. and Ferm{\"u}ller, Cornelia and Aloimonos, J.}
}
