Color optical flow

Artificial intelligence in perspective, 1994

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.

Lecture Notes in Computer Science, 1994

The computation of the optical flow field from an image sequences requires the definition of constraints on the temporal change of image features. In general, these constraints limit the motion of the body in space and/or of the features on the image plane. In this paper the implications in the use of multiple constraints in the computational schema are considered. It is shown that differential constraints correspond to an implicit feature tracking. Consequently, the results strictly depend upon the local gray level structure. The best results (either in terms of measurement accuracy and speed in the computation) are obtained by selecting and applying the constraints which are best "tuned" to the particular image feature under consideration. Several experiments are presented both from a synthetic scene and from real image sequences.

Accurate and high density estimation of optical flow vectors in an image sequence is accomplished by a method that estimates the velocity distribution function for small overlapping regions of the image. Because the distribution is multimodal, the method can accurately estimate the change in velocity near motion contrast borders. Large spatiotemporal support without sacrificing spatial resolution is a feature of the method, so it is not necessary to smooth the resulting flow vectors in a subsequent operation, and there is a certain degree of resistance to aperture and aliasing effects. Spatial support also provides for the accurate estimation of long-range displacements, and subpixel accuracy is achieved by a simple maximum likelihood estimation of the velocity distribution function. A confidence value is also estimated, which can help to predict flow ambiguities. The method is demonstrated using image sequences obtained from the analysis of ceramic and metal materials under stress.

Handbook of Mathematical Methods in Imaging, 2015

Motions of physical objects relative to a camera as observer naturally occur in everyday live and in many scientific applications. Optical flow represents the corresponding motion induced on the image plane. This paper describes the basic problems and concepts related to optical flow estimation together with mathematical models and computational approaches to solve them. Emphasis is placed on common and different modelling aspects and to relevant research directions from a broader perspective. The state of the art and corresponding deficiencies are reported along with directions of future research. The presentation aims at providing an accessible guide for practitioners as well as stimulating research work in relevant fields of mathematics and computer vision.

2009

The quantitative evaluation of optical flow algorithms by led to significant advances in performance. The challenges for optical flow algorithms today go beyond the datasets and evaluation methods proposed in that paper. Instead, they center on problems associated with complex natural scenes, including nonrigid motion, real sensor noise, and motion discontinuities. We propose a new set of benchmarks and evaluation methods for the next generation of optical flow algorithms. To that end, we contribute four types of data to test different aspects of optical flow algorithms: (1) sequences with nonrigid motion where the ground-truth flow is determined by tracking hidden fluorescent texture, (2) realistic synthetic sequences, (3) high frame-rate video used to study interpolation error, and (4) modified stereo sequences of static scenes. In addition to the average angular error used by Barron et al., we compute the absolute flow endpoint error, measures for frame interpolation error, improved statistics, and results at motion discontinuities and in textureless regions. In October 2007, we published the performance of several well-known methods on a preliminary version of our data to establish the current state of the art. We also made the data freely available on the web at http://vision.middlebury.edu/flow/. Subsequently a number of researchers have uploaded their results to our website and published papers using the data. A significant improvement in performance has already been achieved. In this paper we analyze the results obtained to date and draw a large number of conclusions from them.

1995

time-varying 2D projection. Hence as an intermediate The use of color images for motion estimation is investigated stage in the 3D motion estimation process we need to in this work. Beyond the straightforward approach of using find the 2D projection of a motion field onto the image the color components as separate images of the same scene, a plane. This 2D field of velocities is called image flow. new method, based on exploiting color invariance under motion, Then we could attempt to recover the 3D motion field is discussed. Two different sets of color-related, locally computfrom its 2D projection. To do this, however, seems able motion ''invariants'' are analyzed and tested in this paper, impossible without additional information about the and the results of motion estimation based on them are commotion field. Instead, we can extract the so-called pared to the direct use of the RGB brightness functions. © 1997 optical flow, which is a 2D field of velocities associated Academic Press with the variation of brightness patterns of the image [7, 17].

International Journal of Computer Vision, 1998

In this paper, we present two very efficient and accurate algorithms for computing optical flow. The first is a modified gradient-based regularization method, and the other is an SSD-based regularization method. For the gradient-based method, to amend the errors in the discrete image flow equation caused by numerical differentiation as well as temporal and spatial aliasing in the brightness function, we propose to selectively combine the image flow constraint and a contour-based flow constraint into the data constraint by using a reliability measure. Each data constraint is appropriately normalized to obtain an approximate minimum distance (of the data point to the linear flow equation) constraint instead of the conventional linear flow constraint. These modifications lead to robust and accurate optical flow estimation. We propose an incomplete Cholesky preconditioned conjugate gradient algorithm to solve the resulting large and sparse linear system efficiently. Our SSD-based regularization method uses a normalized SSD measure (based on a similar reasoning as in the gradient-based scheme) as the data constraint in a regularization framework. The nonlinear conjugate gradient algorithm in conjunction with an incomplete Cholesky preconditioning is developed to solve the resulting nonlinear minimization problem. Experimental results on synthetic and real image sequences for these two algorithms are given to demonstrate their performance in comparison with competing methods reported in literature.

2009

Abstract—Motion detection is very important in image processing. One way of detecting motion is using optical flow. 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. The method used for finding the optical flow in this project is assuming that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image.

International Journal of Computer Vision, 1992

The primary goal in motion vision is to extract information about the motion and shape of an object in a scene that is encoded in the optic flow. While many solutions to this problem, both iterative and in closed form, have been proposed, practitioners still view the problem as unsolved, since these methods, for the most part, cannot deal with some important aspects of realistic scenes. Among these are comlex unsegmented scenes, nonsmooth objects, and general motion of the camera. In addition, the performance of many methods degrades ungracefully as the quality of the data deteriorates.

The original optical flow algorithm [1] dealt with a flow field that could vary from place to place in the image, as would typically occur when a camera is moved through a three-dimensional environment-or if objects moved in front of a fixed camera. A related, but simpler problem, is that of recovering the motion of an image, all parts of which move with the same velocity (section 4.3 in [2]). The solution of this problem enables "optical mice," as well as motion compensation in hand-held video cameras-critical to their operation. We provide here background on moving images, a method for the estimation of image velocity using least squares applied to brightness derivatives, and an analysis of the sensitivity of the estimated image velocity to noise in brightness measurement.