The authors present an iterative algorithm for the recovery of 2-D motion, i.e., for the determination of a transformation that maps one image onto another. The local ambiguity in measuring the motion of contour segments (the aperture problem) implies a reliance on measurements along the normal direction. Since the measured normal flow does not agree with the actual normal flow, the full flow recovered from this erroneous flow also possesses substantial error, and any attempt to recover the 3-D motion from such full flow fails. The proposed method is based on the observation that a polynomial approximation of the image flow provides sufficient information for 3-D motion computation. The use of an explicit flow model results in improved normal flow estimates through an iterative process. The authors discuss the adequacy and the convergence of the algorithm. The algorithm was tested on some synthetic and some simple natural time-varying images. The image flow recovered from this scheme is sufficiently accurate to be useful in 3-D structure and motion computation.>

In our previous analysis reported elsewhere, we have shown that 3D velocity of a single point up to a scale factor could be recovered from its 2D trajectory under the perspective projection. We developed a batch method to solve the non-linear regression relation between motion parameters and measurements of projected position. The algorithm was tested on the simulated data and the real images. In this paper, we further extend our work along two directions. First, in order to facilitate the speed of the estimation process we took the recursive approach to estimate the motion parameters. Second, we investigate the performance degradation due to two classes of model mismatch: parameter jumping and undermodeling. Then we propose the Finite Lifetime Alternately Triggered Multiple Model Filter (FLAT MMF), as a solution. A number of experiments are conducted to illustrate the performance degradation due to the model mismatches and the performance improvement as the proposed FLAT MMF is used.

The authors propose a new state formulation to analyze object motion with arbitrary orders of translation and rotation from a sequence of video images. An extended Kalman filter is used to find the estimates sequentially from noisy images. Simulations showed that the proposed formulation was quite effective for estimating nonconstant rigid body motion.>

Abstract Time-varying imagery is often described in terms of image flow fields (i.e., image motion), which correspond to the perceptive projection of feature motions in three dimensions (3D). In the case of multiple moving objects with smooth surfaces, the image flow possesses an analytic structure that reflects these 3D properties. This paper describes the analytic structure of image flow fields in the image space-time domain, and its use for segmentation and 3D motion computation. First we discuss thelocal flow structure as embodied in the concept ofneighborhood deformation. The local image deformation is effectively represented by a set of 12 basis deformations, each of which is responsible for an independent deformation. This local representation provides us with sufficient information for the recovery of 3D object structure and motion, in the case of relative rigid body motions. We next discuss theglobal flow structure embodied in the partitioning of the entire image plane intoanalytic regions separated byboundaries of analyticity, such that each small neighborhood within the analytic region is described in terms of deformation bases. This analysis reveals an effective mechanism for detecting the analytic boundaries of flow fields, thereby segmenting the image into meaningful regions. The notion ofconsistency which is often used in the image segmentation is made explicit by the mathematical notion ofanalyticity derived from the projection relation of 3D object motion. The concept of flow analyticity is then extended to the temporal domain, suggesting a more robust algorithm for recovering image flow from multiple frames. Finally, we argue that the process of flow segmentation can be understood in the framework of grouping process. The general concept ofcoherence orgrouping through local support (such as the second-order flows in our case) is discussed.

The authors present an iterative algorithm for the recovery of 2D motion, i.e. an algorithm for the determination of a transformation which maps one image onto another. The local ambiguity in measuring the motion of contour segments (called the aperture problem) makes it necessary to rely on measurements along the normal direction. Since the measured normal flow itself does not agree with the actual normal flow, the full flow recovered from this erroneous normal flow possesses substantial error too, and any attempt to recover the 3D motion from such full flow is doomed to failure. The present method is based on the observation that a polynomial approximation of image flow provides sufficient information for 3D motion computation. The use of an explicit flow model makes it possible to improve normal flow estimates through an iterative process. The algorithm has been tested on synthetic and simple natural time-varying images. The image flow recovered from this scheme was sufficiently accurate as to be useful in 3D structure and motion computation.>

A method is presented for depth recovery through the analysis of scene sharpness across changing focus position. Modeling a defocused image as the application of a low pass-filter on a properly focused image of the same scene, the authors can compare the high spatial frequency content of regions in each image and determine the correct focus position. Recovering depth in this manner is inherently a local operation, and can be done efficiently using a pipelined image processor. Laplacian and Gaussian pyramids are used to calculate maps which are collected and compared to find the focus position that maximizes high spatial frequencies for each region.>