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Recovery of EgoMotion Using Image Stabilization
, 1994
"... A method for computing the 3D camera motion #the egomotion# in a static scene is introduced, which is based on computing the 2D image motion of a single image region directly from image intensities. The computed image motion of this image region is used to register the images so that the detected i ..."
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Cited by 63 (9 self)
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A method for computing the 3D camera motion #the egomotion# in a static scene is introduced, which is based on computing the 2D image motion of a single image region directly from image intensities. The computed image motion of this image region is used to register the images so that the detected image region appears stationary. The resulting displacement #eld for the entire scene between the registered frames is affected only by the 3D translation of the camera. After canceling the e#ects of the camera rotation by using such 2D image registration, the 3D camera translation is computed by #nding the focusofexpansion in the translationonly set of registered frames. This step is followed by computing the camera rotation to complete the computation of the egomotion.
Recovery of EgoMotion Using Region Alignment
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1997
"... A method for computing the 3D camera motion (the egomotion) in a static scene is described, where initially a detected 2D motion between two frames is used to align corresponding image regions. We prove that such a 2D registration removes all effects of camera rotation, even for those image regions ..."
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Cited by 62 (8 self)
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A method for computing the 3D camera motion (the egomotion) in a static scene is described, where initially a detected 2D motion between two frames is used to align corresponding image regions. We prove that such a 2D registration removes all effects of camera rotation, even for those image regions that remain misaligned. The resulting residual parallax displacement field between the two regionaligned images is an epipolar field centered at the FOE (Focusof Expansion). The 3D camera translation is recovered from the epipolar field. The 3D camera rotation is recovered from the computed 3D translation and the detected 2D motion. The decomposition of image motion into a 2D parametric motion and residual epipolar parallax displacements avoids many of the inherent ambiguities and instabilities associated with decomposing the image motion into its rotational and translational components, and hence makes the computation of egomotion or 3D structure estimation more robust.
Projective Structure from Uncalibrated Images: Structure from Motion and Recognition
, 1994
"... We address the problem of reconstructing 3D space in a projective framework from two or more views, and the problem of artificially generating novel views of the scene from two given views (reprojection). We describe an invariance relation which provides a new description of structure, we call proj ..."
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Cited by 62 (14 self)
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We address the problem of reconstructing 3D space in a projective framework from two or more views, and the problem of artificially generating novel views of the scene from two given views (reprojection). We describe an invariance relation which provides a new description of structure, we call projective depth, which is captured by a single equation relating image point correspondences across two or more views and the homographies of two arbitrary virtual planes. The framework is based on knowledge of correspondence of features across views, is linear, extremely simple, and the computations of structure readily extends to overdetermination using multiple views. Experimental results demonstrate a high degree of accuracy in both tasks  reconstruction and reprojection. KeywordsVisual Recognition, 3D Reconstruction from 2D Views, Projective Geometry, Algebraic and Geometric Invariants. I. Introduction The geometric relation between objects (or scenes) in the world and their imag...
Relative Affine Structure: Theory and Application to 3D Reconstruction From Perspective Views
 In IEEE Conference on Computer Vision and Pattern Recognition
, 1994
"... We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewercentered invariant we call relative affine structure. Via a number of corollaries of our main results we show that our framework unifies previous work  including Euclidean, proje ..."
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Cited by 58 (12 self)
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We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewercentered invariant we call relative affine structure. Via a number of corollaries of our main results we show that our framework unifies previous work  including Euclidean, projective and affine  in a natural and simple way. Finally, the main results were applied to a real image sequence for purpose of 3D reconstruction from 2D views. 1 Introduction The introduction of affine and projective tools into the field of computer vision have brought increased activity in the fields of structure from motion and recognition by alignment in the recent few years. The emerging realization is that nonmetric information, although weaker than the information provided by depth maps and rigid camera geometries, is nonetheless useful in the sense that the framework may provide simpler algorithms, camera calibration is not required, more freedom in picturetaking is allowed  ...
Relative Affine Structure: Canonical Model for 3D from 2D Geometry and Applications
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewercentered invariant we call relative affine structure. Via a number of corollaries of our main results we show that our framework unifies previous work  including Euclidean, projec ..."
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Cited by 57 (9 self)
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We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewercentered invariant we call relative affine structure. Via a number of corollaries of our main results we show that our framework unifies previous work  including Euclidean, projective and affine  in a natural and simple way, and introduces new, extremely simple, algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications.
Projective Structure from two Uncalibrated Images: Structure from Motion and Recognition
 A.I. MEMO
, 1992
"... This paper addresses the problem of recovering relative structure, in the form of an invariant, from two views of a 3D scene. The invariant structure is computed without any prior knowledge of camera geometry, or internal calibration, and with the property that perspective and orthographic project ..."
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Cited by 32 (3 self)
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This paper addresses the problem of recovering relative structure, in the form of an invariant, from two views of a 3D scene. The invariant structure is computed without any prior knowledge of camera geometry, or internal calibration, and with the property that perspective and orthographic projections are treated alike, namely, the system makes no assumption regarding the existence of perspective distortions in the input images. We show that
On Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views
 In Proceedings of the 2nd European Workshop on Invariants, Ponta Delagada, Azores
, 1993
"... Part I of this paper investigates the differences  conceptually and algorithmically  between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. It is shown that an affine invariant exists between any view and a fixed view chosen as a ..."
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Cited by 23 (8 self)
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Part I of this paper investigates the differences  conceptually and algorithmically  between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. It is shown that an affine invariant exists between any view and a fixed view chosen as a reference view. This implies that for tasks for which a reference view can be chosen, such as in alignment schemes for visual recognition, projective invariants are not really necessary. The projective extension is then derived, showing that it is necessary only for tasks for which a reference view is not available  such as happens when updating scene structure from a moving stereo rig. The geometric difference between the two proposed invariants are that the affine invariant measures the relative deviation from a single reference plane, whereas the projective invariant measures the relative deviation from two reference planes. The affine invariant can be computed from three correspondin...
Recursive Estimation of Motion and Planar Structure
 In Proceedings of the Conference on Computer Vision and Pattern Recognition, Hilton Head Island, South
, 2000
"... A specialized formulation of Azarbayejani and Pentland's framework for recursive recovery of motion, structure and focal length from feature correspondences tracked through an image sequence is presented. The specialized formulation addresses the case where all tracked points lie on a plane. This pl ..."
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Cited by 12 (1 self)
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A specialized formulation of Azarbayejani and Pentland's framework for recursive recovery of motion, structure and focal length from feature correspondences tracked through an image sequence is presented. The specialized formulation addresses the case where all tracked points lie on a plane. This planarity constraint reduces the dimension of the original state vector, and consequently the number of feature points needed to estimate the state. Experiments with synthetic data and real imagery illustrate the system performance. The experiments confirm that the specialized formulation provides improved accuracy, stability to observation noise, and rate of convergence in estimation for the case where the tracked points lie on a plane.
Image Sequence Description Using Spatiotemporal Flow Curves: Toward MotionBased Recognition
, 1991
"... Recovering a hierarchical motion description of a long image sequence is one way to recognize objects and their motions. Intermediatelevel and highlevel motion analysis, i.e., recognizing a coordinated sequence of events such as walking and throwing, has been formulated previously as a process tha ..."
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Cited by 11 (1 self)
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Recovering a hierarchical motion description of a long image sequence is one way to recognize objects and their motions. Intermediatelevel and highlevel motion analysis, i.e., recognizing a coordinated sequence of events such as walking and throwing, has been formulated previously as a process that follows highlevel object recognition. This thesis develops an alternative approach to intermediatelevel and highlevel motion analysis. It does not depend on complex object descriptions and can therefore be computed prior to object recognition. Toward this end, a new computational framework for low and intermediatelevel processing of long sequences of images is presented. Our new computational framework uses spatiotemporal (ST) surface flow and ST flow curves. As contours move, their projections into the image also move. Over time, these projections sweep out ST surfaces. Thus, these surfaces are direct representations of object motion. ST surface flow is defined as the natural extensio...
An Integrated Approach for Segmentation and Estimation of Planar Structures
, 2000
"... Standard structure from motion algorithms recover 3D structure of points. If a surface representation is desired, for example a piecewise planar representation, then a twostep procedure typically follows: in the first step the planemembership of points is first determined manually, and in a subse ..."
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Cited by 3 (0 self)
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Standard structure from motion algorithms recover 3D structure of points. If a surface representation is desired, for example a piecewise planar representation, then a twostep procedure typically follows: in the first step the planemembership of points is first determined manually, and in a subsequent step planes are fitted to the sets of points thus determined, and their parameters are recovered. This paper presents an approach for automatically segmenting planar structures from a sequence of images, and simultaneously estimating their parameters. In the proposed approach the planemembership of points is determined automatically, and the planar structure parameters are recovered directly in the algorithm rather than indirectly in a postprocessing stage. Simulated and real experimental results show the efficacy of this approach.