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11
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 1727 (7 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.
Optical flow estimation: an error analysis of gradientbased methods with local optimization
 IEEE Trans. PAMI
, 1987
"... AbstractMultiple views of a scene can provide important information about the structure and dynamic behavior of threedimensional objects. Many of the methods that recover this information require the determination of optical flowthe velocity, on the image, of visible points on object surfaces. An ..."
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Cited by 78 (1 self)
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AbstractMultiple views of a scene can provide important information about the structure and dynamic behavior of threedimensional objects. Many of the methods that recover this information require the determination of optical flowthe velocity, on the image, of visible points on object surfaces. An important class of techniques for estimating optical flow depend on the relationship between the gradients of image brightness. While gradientbased methods have been widely studied, little attention has been paid to accuracy and reliability of the approach. Gradientbased methods are sensitive to conditions commonly encountered in real imagery. Highly textured surfaces, large areas of constant brightness, motion boundaries, and depth discontinuities can all be troublesome for gradientbased methods. Fortunately, these problematic areas are usually localized can be identified in the image. In this paper we examine the sources of errors for gradientbased techniques that locally solve for optical flow. These methods assume that optical flow is constant in a small neighborhood. The consequence of violating in this assumption is examined. The causes of measurement errors and the determinants of the conditioning of the solution system are also considered. By understanding how errors arise, we are able to define the inherent limitations of the technique, obtain estimates of the accuracy of computed values, enhance the performance of the technique, and demonstrate the informative value of some types of error. Index TermsComputer vision, dynamic scene analysis, error analysis, motion, optical flow, timevarying imagery. I.
Production model based digital video segmentation
 JOURNAL OF MULTIMEDIA TOOLS AND APPLICATIONS
, 1995
"... Effective and efficient tools for segmenting and contentbased indexing of digital video are essential to allow easy access to videobased information. Most existing segmentation techniques do not use explicit models of video. The approach proposed here is inspired and influenced by well establishe ..."
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Cited by 58 (1 self)
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Effective and efficient tools for segmenting and contentbased indexing of digital video are essential to allow easy access to videobased information. Most existing segmentation techniques do not use explicit models of video. The approach proposed here is inspired and influenced by well established video production processes. Computational models of these processes are developed. The video models are used to classify the transition effects used in video and to design automatic edit effect detection algorithms. Video segmentation has been formulated as a production model based classification problem. The video models are also used to define segmentation error measures. Experimental results from applying the proposed technique to commercial cable television programming are presented.
A Tensor Framework for Multidimensional Signal Processing
 Linkoping University, Sweden
, 1994
"... ii About the cover The figure on the cover shows a visualization of a symmetric tensor in three dimensions, G = λ1ê1ê T 1 + λ2ê2ê T 2 + λ3ê3ê T 3 The object in the figure is the sum of a spear, a plate and a sphere. The spear describes the principal direction of the tensor λ1ê1ê T 1, where the lengt ..."
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Cited by 53 (8 self)
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ii About the cover The figure on the cover shows a visualization of a symmetric tensor in three dimensions, G = λ1ê1ê T 1 + λ2ê2ê T 2 + λ3ê3ê T 3 The object in the figure is the sum of a spear, a plate and a sphere. The spear describes the principal direction of the tensor λ1ê1ê T 1, where the length is proportional to the largest eigenvalue, λ1. The plate describes the plane spanned by the eigenvectors corresponding to the two largest eigenvalues, λ2(ê1ê T 1 + ê2ê T 2). The sphere, with a radius proportional to the smallest eigenvalue, shows how isotropic the tensor is, λ3(ê1ê T 1 + ê2ê T 2 + ê3ê T 3). The visualization is done using AVS [WWW94]. I am very grateful to Johan Wiklund for implementing the tensor viewer module used. This thesis deals with filtering of multidimensional signals. A large part of the thesis is devoted to a novel filtering method termed “Normalized convolution”. The method performs local expansion of a signal in a chosen filter basis which
Time, distance, and feature tradeoffs in visual apparent motion
 Psychological Review
, 1981
"... A model of visual apparent motion is derived from four observations on path selection in ambiguous displays in which apparent motion of illuminated dots could, in principle, be perceived along many possible paths: (a) Whereas motion over each path is clearly visible when its stimulus is presented in ..."
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Cited by 23 (2 self)
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A model of visual apparent motion is derived from four observations on path selection in ambiguous displays in which apparent motion of illuminated dots could, in principle, be perceived along many possible paths: (a) Whereas motion over each path is clearly visible when its stimulus is presented in isolation, motion is usually seen over only one path when two or more such stimuli are combined (competition), (b) Path selection is nearly independent of viewing distance (scale invariance). (c) At transition points between paths ( ' and j (where apparent motion is equally likely to be perceived along / and j), the time t and distance d between successive points along the paths are described by a log linear d/t relationship; that is, t = A B log (d/d,). (d) When successive elements along a path differ in orientation or size, the perceived motion along this path is not necessarily weaker than motion along a path composed entirely of identical elements. The model is a form of strength theory in which the path with greatest strength 5 becomes the dominant path. From scale invariance, we prove that the contributions of time and distance to stimulus strength are independent. From
Kinetic depth effect and optic flow  I. 3D shape from Fourier motion
 VISION RESEARCH
, 1989
"... Fiftythree different 3D shapes were defined by sequences of 2D views (frames) of dots on a rotating 3D surface. (1) Subjects ’ accuracy of shape identifications dropped from over 90 % to less than 10 % when either the polarity of the stimulus dots was alternated from lightongray to darkongray o ..."
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Cited by 4 (0 self)
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Fiftythree different 3D shapes were defined by sequences of 2D views (frames) of dots on a rotating 3D surface. (1) Subjects ’ accuracy of shape identifications dropped from over 90 % to less than 10 % when either the polarity of the stimulus dots was alternated from lightongray to darkongray on successive frames or when neutral gray interframe intervals were interposed. Roth manipulations interfere with motion extraction by spatiotemporal (Fourier) and gradient firstorder detectors. Secondorder (nonFourier) detectors that use fullwave rectification are unaffected by alternatingpolarity but disrupted by interposed gray frames. (2) To equate the accuracy of twoalternative forcedchoice (ZAFC) planar dir~tionofmotion ~~ri~nation in standard and zlotyalternated stimuli, standard contrast was reduced. 3D shape discrimination survived contrast reduction in standard stimuli whereas it failed completely with polarityalternation even at full contrast. (3) When individual dots were permitted to remain in the image sequence for only two frames, performance showed little loss compared to standard displays where individual dots had an expected lifetime of 20 frames, showing that 3D shape identification does not require continuity of stimulus tokens. (4) Performance in all discrimination tasks is predicted (up to a monotone transformation) by considering the quality of firstorder information (as given by a simple computation on Fourier power) and the number of locations at which motion information is required. Perceptual firstorder analysis of optic flow is the primary substrate for st~cturefrommotion computations in random dot displays because only it offers suBicient quality of perceptual motion at a sufficient number of locations. Kinetic depth effect Structure from motion Shape identification Fourier motion
Distributed Representation of Image Velocity
, 1992
"... We describe a new form of representation of image velocities, which does not rely on vector fields. For each local spatiotemporal region of the input image, we desire a function over the space of velocities describing the presence of a given velocity in that region. This function maybeinterpreted a ..."
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Cited by 2 (0 self)
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We describe a new form of representation of image velocities, which does not rely on vector fields. For each local spatiotemporal region of the input image, we desire a function over the space of velocities describing the presence of a given velocity in that region. This function maybeinterpreted as a probability distribution over velocity, although it is not necessary to do so. A primary advantage of this representation is that it is capable of representing more than one velocityat a given image location. A multimodal distribution indicates the presence of multiple motions. Such situations occur frequently in natural scenes near occlusion boundaries, and in situations of transparency. We develop an example of this type of representation through a series of modifications of current differential approaches to motion estimation. We define an angular version of the standard gradient constraint equation, and then extend this to representmultiple motions. The derivation is first d...
Cloud Motion Measurement from Radar Image Sequences
, 1987
"... The estimation of cloud motion is an active area of computer vision; it addresses the recovery of motion clues from a timevarying image sequence of a cloud cover, usually tracked by radar. Three major issues in this field are: (1)the choice of a measurement procedure and an area within the image wh ..."
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The estimation of cloud motion is an active area of computer vision; it addresses the recovery of motion clues from a timevarying image sequence of a cloud cover, usually tracked by radar. Three major issues in this field are: (1)the choice of a measurement procedure and an area within the image where the measurement constraint is guaranteed to achieve minimum error, (2)the choice of a topological constraint and an area where this constraint is guaranteed to achieve minimum error, and (3)the identification of a procedure of coupling the two constraints mentioned above in order to obtain an optimal approximation to the velocity field. In this paper, we show that the retrieval of a reliable motion clue is closely related to the manner in which the measurement and topological constraints are coupled. An example using the gradient vector as a measurement, smoothness as a topological constraint, and the temporal gradient as a coupling factor is given. As shown when this approach is compared against a correspondencebased technique, the differential approach measures only a local average of the true motion. The performance of this differential technique and a correspondencebased technique are compared using a real radar image sequence.
The Computation of Optical and Affine Flow
, 2005
"... In this note we review the computation of optical and affine flow. We will assume that the velocity within the considered neighbourhood is constant [7, 8]. An alternative formulation is to consider the motion within a neighbourhood (or entire image) as slowly varying [6]. The starting point is the a ..."
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In this note we review the computation of optical and affine flow. We will assume that the velocity within the considered neighbourhood is constant [7, 8]. An alternative formulation is to consider the motion within a neighbourhood (or entire image) as slowly varying [6]. The starting point is the assumption of brightness constancy [5], which assumes that the brightness structures of localtime varying image regions are unchanging under motion for a short period of time. Formally, this is defined as, I(x, y, t) = I(x − u, y − v, t − 1) (1) where (x, y) ⊤ represents image position in pixel coordinates, t represents the temporal coordinate, (u, v) ⊤ represents the motion at image position (x, y) ⊤ over the time t + 1 and I(x, y, t) represents the image brightness function. Using the leastsquares criteria, we seek the motion that minimizes the error ɛ over a region R of the image, formally, ɛ = ∑ x,t,∈R [I(x, y, t) − I(x − u, y − v, t − 1)] 2 Assuming that I(x, y, t) is approximately locally linear (2) is simplified by taking a Taylor series expansion and omitting terms higher than first order [5], ɛ ≈
Salient Stills, Inc. and
"... Salient Stills are a class of images that reflect the aggregation of the temporal changes that occur in a movingimage sequence with the salient features of individual frames preserved. They convey the intended expression of an entire series of moving frames—a visual summary of camera and object move ..."
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Salient Stills are a class of images that reflect the aggregation of the temporal changes that occur in a movingimage sequence with the salient features of individual frames preserved. They convey the intended expression of an entire series of moving frames—a visual summary of camera and object movements. The original frames, which may include variations in focal length or field of view, or moving objects, are combined to create a single still image. The still image may have multiresolution patches, a larger field of view, or higher overall resolution than any individual frame in the original image sequence. Salient Stills may also contain selected significant objects from individual or multiple video frames. Salient Stills attempt to retain much of the original content (detail) and spatial and temporal extent (context) of the original video or film sequence.