Recent research in image sensors has produced cameras with very large fields of view. An area of computer vision research which will benefit from this technology is the computation of camera motion (ego-motion) from a sequence of images. Traditional cameras suffer from the problem that the direction of translation may lie outside of the field of view, making the computation of camera motion sensitive to noise. In this paper, we present a method for the recovery of ego-motion using omnidirectional cameras. Noting the relationship between spherical projection and wide-angle imaging devices, we propose mapping the image velocity vectors to a sphere, using the Jacobian of the transformation between the projection model of the camera and spherical projection. Once the velocity vectors are mapped to a sphere, we show how existing ego-motion algorithms can be applied and present some experimental results. These results demonstrate the ability to compute egomotion with omnidirectional cameras....

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 methods---gradient-based, energy-based, and correlation methods, and it analyzes different ways of compounding one-dimensional motio...

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 ...

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: NSF-IIS-0083209, NSF-IIS-0121293, NSF-

Computing a camera's ego-motion 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.

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 one-dimensional motion signals into two-dimensional 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.

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...

A computational explanation of the illusory movement experienced upon extended viewing of Enigma, a static figure painted by Leviant, is presented. The explanation relies on a model for the interpretation of three-dimensional motion information contained in retinal motion measurements. This model shows that the Enigma figure is a special case of a larger class of figures exhibiting the same illusory movement and these figures are introduced here. Our explanation supports the view that higher-level processes are the cause of these illusions [29] and suggests a number of new experiments to unravel the functional structure of the motion pathway.

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.

We address the problem of egomotion estimation for a monocular observer moving under arbitrary translation and rotation, in an unknown environment. The method we propose is uniquely based on the spatio-temporal image derivatives, or the normal flow. We introduce a search paradigm which is based on geometric properties of the normal flow field, and consists in considering a family of search subspaces to estimate the egomotion parameters. Various algorithms are proposed within this framework. In order to decrease the noise sensitivity of the estimation methods, we use statistical tools, based on robust regression theory. Finally, we present and discuss a wide variety of experiments with synthetic and real images, for various kinds of camera motion. Index Terms: motion analysis, egomotion, optical flow, normal flow. 1 Introduction We address the problem of egomotion estimation for a monocular moving observer. The problem consists in determining the 3D motion parameters, by observing an ...