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347
Determining Optical Flow
 ARTIFICIAL INTELLIGENCE
, 1981
"... Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent veloc ..."
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Cited by 2180 (8 self)
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Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.
The Computation of Optical Flow
, 1995
"... Twodimensional image motion is the projection of the threedimensional motion of objects, relative to a visual sensor, onto its image plane. Sequences of timeordered images allow the estimation of projected twodimensional image motion as either instantaneous image velocities or discrete image dis ..."
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Cited by 274 (10 self)
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Twodimensional image motion is the projection of the threedimensional motion of objects, relative to a visual sensor, onto its image plane. Sequences of timeordered images allow the estimation of projected twodimensional image motion as either instantaneous image velocities or discrete image displacements. These are usually called the optical flow field or the image velocity field. Provided that optical flow is a reliable approximation to twodimensional image motion, it may then be used to recover the threedimensional motion of the visual sensor (to within a scale factor) and the threedimensional surface structure (shape or relative depth) through assumptions concerning the structure of the optical flow field, the threedimensional environment and the motion of the sensor. Optical flow may also be used to perform motion detection, object segmentation, timetocollision and focus of expansion calculations, motion compensated encoding and stereo disparity measurement. We investiga...
The Fundamental matrix: theory, algorithms, and stability analysis
 International Journal of Computer Vision
, 1995
"... In this paper we analyze in some detail the geometry of a pair of cameras, i.e. a stereo rig. Contrarily to what has been done in the past and is still done currently, for example in stereo or motion analysis, we do not assume that the intrinsic parameters of the cameras are known (coordinates of th ..."
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Cited by 263 (13 self)
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In this paper we analyze in some detail the geometry of a pair of cameras, i.e. a stereo rig. Contrarily to what has been done in the past and is still done currently, for example in stereo or motion analysis, we do not assume that the intrinsic parameters of the cameras are known (coordinates of the principal points, pixels aspect ratio and focal lengths). This is important for two reasons. First, it is more realistic in applications where these parameters may vary according to the task (active vision). Second, the general case considered here, captures all the relevant information that is necessary for establishing correspondences between two pairs of images. This information is fundamentally projective and is hidden in a confusing manner in the commonly used formalism of the Essential matrix introduced by LonguetHiggins [40]. This paper clarifies the projective nature of the correspondence problem in stereo and shows that the epipolar geometry can be summarized in one 3 \Theta 3 ma...
Epipolarplane image analysis: An approach to determining structure from motion
 INTERN..1. COMPUTER VISION
, 1987
"... We present a technique for building a threedimensional description of a static scene from a dense sequence of images. These images are taken in such rapid succession that they form a solid block of data in which the temporal continuity from image to image is approximately equal to the spatial conti ..."
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Cited by 248 (3 self)
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We present a technique for building a threedimensional description of a static scene from a dense sequence of images. These images are taken in such rapid succession that they form a solid block of data in which the temporal continuity from image to image is approximately equal to the spatial continuity in an individual image. The technique utilizes knowledge of the camera motion to form and analyze slices of this solid. These slices directly encode not only the threedimensional positions of objects, but also such spatiotemporal events as the occlusion of one object by another. For straightline camera motions, these slices have a simple linear structure that makes them easier to analyze. The analysis computes the threedimensional positions of object features, marks occlusion boundaries on the objects, and builds a threedimensional map of "free space." In our article, we first describe the application of this technique to a simple camera motion, and then show how projective duality is used to extend the analysis to a wider class of camera motions and object types that include curved and moving objects.
Kalman Filterbased Algorithms for Estimating Depth from Image Sequences
, 1989
"... Using known camera motion to estimate depth from image sequences is an important problem in robot vision. Many applications of depthfrommotion, including navigation and manipulation, require algorithms that can estimate depth in an online, incremental fashion. This requires a representation that ..."
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Cited by 246 (25 self)
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Using known camera motion to estimate depth from image sequences is an important problem in robot vision. Many applications of depthfrommotion, including navigation and manipulation, require algorithms that can estimate depth in an online, incremental fashion. This requires a representation that records the uncertainty in depth estimates and a mechanism that integrates new measurements with existing depth estimates to reduce the uncertainty over time. Kalman filtering provides this mechanism. Previous applications of Kalman filtering to depthfrommotion have been limited to estimating depth at the location of a sparse set of features. In this paper, we introduce a new, pixelbased (iconic) algorithm that estimates depth and depth uncertainty at each pixel and incrementally refines these estimates over time. We describe the algorithm and contrast its formulation and performance to that of a featurebased Kalman filtering algorithm. We compare the performance of the two approaches by analyzing their theoretical convergence rates, by conducting quantitative experiments with images of a flat poster, and by conducting qualitative experiments with images of a realistic outdoorscene model. The results show that the new method is an effective way to extract depth from lateral camera translations. This approach can be extended to incorporate general motion and to integrate other sources of information, such as stereo. The algorithms we have developed, which combine Kalman filtering with iconic descriptions of depth, therefore can serve as a useful and general framework for lowlevel dynamic vision.
Model of human visualmotion sensing
, 1985
"... We propose a model of how humans sense the velocity of moving images. The model exploits constraints provided by human psychophysics, notably that motionsensing elements appear tuned for twodimensional spatial frequency, and by the frequency spectrum of a moving image, namely, that its support li ..."
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Cited by 220 (3 self)
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We propose a model of how humans sense the velocity of moving images. The model exploits constraints provided by human psychophysics, notably that motionsensing elements appear tuned for twodimensional spatial frequency, and by the frequency spectrum of a moving image, namely, that its support lies in the plane in which the temporal frequency equals the dot product of the spatial frequency and the image velocity. The first stage of the model is a set of spatialfrequencytuned, directionselective linear sensors. The temporal frequency of the response of each sensor is shown to encode the component of the image velocity in the sensor direction. At the second stage, these components are resolved in order to measure the velocity of image motion at each of a number of spatial locations and spatial frequencies. The model has been applied to several illustrative examples, including apparent motion, coherent gratings, and natural image sequences. The model agrees qualitatively with human perception.
Passive navigation
 Computer Vision, Graphics, and Image Processing
, 1983
"... A method is proposed for determining the motion of a body relative to a fixed environment using the changing image seen by a camera attached to the body. The optical flow in the image plane is the input, while the instantaneous rotation and translation of the body are the output. If optical flow cou ..."
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Cited by 193 (8 self)
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A method is proposed for determining the motion of a body relative to a fixed environment using the changing image seen by a camera attached to the body. The optical flow in the image plane is the input, while the instantaneous rotation and translation of the body are the output. If optical flow could be determined precisely, it would only have to be known at a few places to compute the parameters of the motion. In practice, however, the measured optical flow will be somewhat inaccurate. It is therefore advantageous to consider methods which use as much of the available information as possible. We employ a leastsquares approach which minimizes some measure of the discrepancy between the measured flow and that predicted from the computed motion parameters. Several different error norms are investigated. In general, our algorithm leads to a system of nonlinear equations from which the motion parameters may be computed numerically. However, in the special cases where the motion of the camera is purely translational or purely rotational, use of the appropriate norm leads to a system of equations from which these parameters can be determined in closed form. 1.
Relative Orientation
 International Journal of Computer Vision
, 1990
"... Abstract: Before corresponding points in images taken with two cameras can be used to recover distances to objects in a scene, one has to determine the position and orientation of one camera relative to the other. This is the classic photogrammetric problem of relative orientation, central to the in ..."
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Cited by 144 (2 self)
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Abstract: Before corresponding points in images taken with two cameras can be used to recover distances to objects in a scene, one has to determine the position and orientation of one camera relative to the other. This is the classic photogrammetric problem of relative orientation, central to the interpretation of binocular stereo information. Iterative methods for determining relative orientation were developed long ago; without them we would not have most of the topographic maps we do today. Relative orientation is also of importance in the recovery of motion and shape from an image sequence when successive frames are widely separated in time. Workers in motion vision are rediscovering some of the methods of photogrammetry. Described here is a simple iterative scheme for recovering relative orientation that, unlike existing methods, does not require a good initial guess for the baseline and the rotation. The data required is a pair of bundles of corresponding rays from the two projection centers to points in the scene. It is well known that at least five pairs of rays are needed. Less appears to be known about the existence of multiple solutions and their interpretation. These issues are discussed here. The unambiguous determination of all of the parameters of relative orientation is not possible when the observed points lie on a critical surface. These surfaces and their degenerate forms are analysed as well.
A unified approach to moving object detection in 2d and 3d scenes
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1998
"... The detection of moving objects in important in many tasks. Previous approaches to this problem can be broadly divided into two classes: 2D algorithms which apply when the scene can be approximated by a at surface and/or when the camera is only undergoing rotations and zooms, and 3D algorithms which ..."
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Cited by 116 (5 self)
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The detection of moving objects in important in many tasks. Previous approaches to this problem can be broadly divided into two classes: 2D algorithms which apply when the scene can be approximated by a at surface and/or when the camera is only undergoing rotations and zooms, and 3D algorithms which work well only when significant depth variations are present in the scene and the camera is translating. In this paper, we describe a unified approach to handling moving object detection in both 2D and 3D scenes, with a strategy to gracefully bridge the gap between those two extremes. Our approach is based on a stratification of the moving object detection problem into scenarios which gradually increase in their complexity. We present a set of techniques that match the above strati cation. These techniques progressively increase in their complexity, ranging from 2D techniques to more complex 3D techniques. Moreover, the computations required for the solution to the problem at one complexity level become the initial processing step for the solution at the next complexity level. We illustrate these techniques using examples from real image sequences.