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42
Catadioptric Omnidirectional Camera
 Proc. of IEEE Computer Vision and Pattern Recognition, (CVPR
, 1997
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The Statistics of Optical Flow
 Computer Vision and Image Understanding
, 1999
"... When processing image sequences some representation of image motion must be derived as a first stage. The most often used such representation is the optical flow field, which is a set of velocity measurements of image patterns. It is well known that it is very difficult to estimate accurate optical ..."
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Cited by 34 (6 self)
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When processing image sequences some representation of image motion must be derived as a first stage. The most often used such representation is the optical flow field, which is a set of velocity measurements of image patterns. It is well known that it is very difficult to estimate accurate optical flow at locations in an image which correspond to scene discontinuities. What is less well known, however, is that even at the locations corresponding to smooth scene surfaces, the optical flow field often cannot be estimated accurately. Noise in the data causes many optical flow estimation techniques to give biased flow estimates. Very often there is consistent bias: the estimate tends to be an underestimate in length and to be in a direction closer to the majority of the gradients in the patch. This paper studies all three major categories of flow estimation methodsgradientbased, energybased, and correlation methods, and it analyzes different ways of compounding onedimensional motio...
Observability of 3D Motion
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2000
"... This paper examines the inherent difficulties in observing 3D rigid motion from image sequences. It does so without considering a particular estimator. Instead, it presents a statistical analysis of all the possible computational models which can be used for estimating 3D motion from an image sequen ..."
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Cited by 22 (13 self)
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This paper examines the inherent difficulties in observing 3D rigid motion from image sequences. It does so without considering a particular estimator. Instead, it presents a statistical analysis of all the possible computational models which can be used for estimating 3D motion from an image sequence. These computational models are classified according to the mathematical constraints that they employ and the characteristics of the imaging sensor (restricted field of view and full field of view). Regarding the mathematical constraints, there exist two principles relating a sequence of images taken by a moving camera. One is the "epipolar constraint," applied to motion fields, and the other the "positive depth" constraint, applied to normal flow fields. 3D motion estimation amounts to optimizing these constraints over the image. A statistical modeling of these constraints leads to functions which are studied with regard to their topographic structure, specifically as regards the errors ...
Aloimonos, Ambiguity in structure from motion: Sphere versus plane
 Internat. J. Comput. Vision
, 1998
"... Abstract. If 3D rigid motion can be correctly estimated from image sequences, the structure of the scene can be correctly derived using the equations for image formation. However, an error in the estimation of 3D motion will result in the computation of a distorted version of the scene structure. Of ..."
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Cited by 21 (6 self)
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Abstract. If 3D rigid motion can be correctly estimated from image sequences, the structure of the scene can be correctly derived using the equations for image formation. However, an error in the estimation of 3D motion will result in the computation of a distorted version of the scene structure. Of computational interest are these regions in space where the distortions are such that the depths become negative, because in order for the scene to be visible it has to lie in front of the image, and thus the corresponding depth estimates have to be positive. 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 through the center. For a spherical retina, given a rotational error, the optimal translation is the correct one; given a translational error, the optimal rotational error depends both in direction and value on the actual and estimated translation as well as the scene in view. The proofs, besides illuminating the confounding of translation and rotation in structure from motion, have an important application to ecological optics. The same analysis provides a computational explanation of why it is
Rotation recovery from spherical images without correspondences
 IEEE Transactions on Pattern Analysis and Machine Intelligence
"... This paper addresses the problem of rotation estimation directly from images defined on the sphere and without correspondence. The method is particularly useful for the alignment of large rotations and has potential impact on 3D shape alignment. The foundation of the method lies in the fact that the ..."
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Cited by 18 (2 self)
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This paper addresses the problem of rotation estimation directly from images defined on the sphere and without correspondence. The method is particularly useful for the alignment of large rotations and has potential impact on 3D shape alignment. The foundation of the method lies in the fact that the spherical harmonic coefficients undergo a unitary mapping when the original image is rotated. The correlation between two images is a function of rotations and we show that it has an SO(3)Fourier transform equal to the pointwise product of spherical harmonic coefficients of the original images. The resolution of the rotation space depends on the bandwidth we choose for the harmonic expansion and the rotation estimate is found through a direct search in this 3D discretized space. A refinement of the rotation estimate can be obtained from the conservation of harmonic coefficients in the rotational shift theorem. A novel decoupling of the shift theorem with respect to the Euler angles is presented and exploited in an iterative scheme to refine the initial rotation estimates. Experiments show the suitability of the method for large rotations and the dependence of the method on bandwidth and the choice of the spherical harmonic coefficients. ∗ The authors are grateful for support through the following grants: NSFIIS0083209, NSFIIS0121293, NSF
A General Approach for Egomotion Estimation with Omnidirectional Images
 In IEEE Workshop on Omnidirectional Vision
, 2002
"... Computing a camera's egomotion from an image sequence is easier to accomplish when a spherical retina is used, as opposed to a standard retinal plane. On a spherical field of view both the focus of expansion and contraction are visible, whereas for a planar retina that is not necessarily the c ..."
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Cited by 16 (1 self)
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Computing a camera's egomotion from an image sequence is easier to accomplish when a spherical retina is used, as opposed to a standard retinal plane. On a spherical field of view both the focus of expansion and contraction are visible, whereas for a planar retina that is not necessarily the case.
Visual Space Distortion
 Biological Cybernetics
, 1997
"... We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics and computational vision. In many of the computational models employed in the past, it has been assumed that a metr ..."
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Cited by 13 (12 self)
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We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics and computational vision. In many of the computational models employed in the past, it has been assumed that a metric representation of physical space can be derived by visual means. Psychophysical experiments, as well as computational considerations, can convince us that the perception of space and shape has a much more complicated nature, and that only a distorted version of actual, physical space can be computed. This paper develops a computational geometric model that explains why such distortion might take place. The basic idea is that, both in stereo and motion, we perceive the world from multiple views. Given the rigid transformation between the views and the properties of the image correspondence, the depth of the scene can be obtained. Even a slight error in the rigid transformation parameters c...
The Ouchi illusion as an artifact of biased flow estimation
, 2000
"... A pattern by Ouchi has the surprising property that small motions can cause illusory relative motion between the inset and background regions. The effect can be attained with small retinal motions or a slight jiggling of the paper and is robust over large changes in the patterns, frequencies and bou ..."
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Cited by 13 (8 self)
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A pattern by Ouchi has the surprising property that small motions can cause illusory relative motion between the inset and background regions. The effect can be attained with small retinal motions or a slight jiggling of the paper and is robust over large changes in the patterns, frequencies and boundary shapes. In this paper, we explain that the cause of the illusion lies in the statistical difficulty of integrating local onedimensional motion signals into twodimensional image velocity measurements. The estimation of image velocity generally is biased, and for the particular spatial gradient distributions of the Ouchi pattern the bias is highly pronounced, giving rise to a large difference in the velocity estimates in the two regions. The computational model introduced to describe the statistical estimation of image velocity also accounts for the findings of psychophysical studies with variations of the Ouchi pattern and for various findings on the perception of moving plaids. The insight gained from this computational study challenges the current models used to explain biological vision systems and to construct robotic vision systems. Considering the statistical difficulties in image velocity estimation in conjunction with the problem of discontinuity detection in motion fields suggests that theoretically the process of optical flow computations should not be carried out in isolation but in conjunction with the higher level processes of 3D motion estimation, segmentation and shape computation.
Families of stationary patterns producing illusory movement: Insights into the visual system
 Proceedings of Royal Society of London. B. Biological Sciences
, 1997
"... insights into the visual system ..."
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PulseBased 2D Motion Sensors
 IEEE TRANS. ON CIRCUITS AND SYSTEMS 2: ANALOG AND DIGITAL SIGNAL PROCESSING
, 1999
"... We present two compact CMOS integrated circuits for computing the 2D local direction of motion of an image focused directly onto the chip. These circuits incorporate onboard photoreceptors and focal plane motion processing. With fully functional 14 x 13 and 12 x 13 implementations consuming less tha ..."
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Cited by 11 (3 self)
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We present two compact CMOS integrated circuits for computing the 2D local direction of motion of an image focused directly onto the chip. These circuits incorporate onboard photoreceptors and focal plane motion processing. With fully functional 14 x 13 and 12 x 13 implementations consuming less than 50 W per pixel, we conclude that practical pixel resolutions of at least 64 x 64 are easily achievable. Measurements characterizing the elementary 1D motion detectors are presented along with a discussion of 2D performance and example 2D motion vector fields. As an example application of the sensor, it is shown that the array as fabricated can directly compute the focus of expansion of a 2D motion vector field.