An approach is presented for the estimation of object motion parameters based on a sequence of noisy images. The problem considered is that of a rigid body undergoing unknown rotational and translational motion. The measurement data consists of a sequence of noisy image coordinates of two or more object correspondence points. By modeling the object dynamics as a function of time, estimates of the model parameters (including motion parameters) can be extracted from the data using recursive and/or batch techniques. This permits a desired degree of smoothing to be achieved through the use of an arbitrarily large number of images. Some assumptions regarding object structure are presently made. Results are presented for a recursive estimation procedure: the case considered here is that of a sequence of one dimensional images of a two dimensional object. Thus, the object moves in one transverse dimension, and in depth, preserving the fundamental ambiguity of the central projection image model (loss of depth information). An iterated extended Kalman filter is used for the recursive solution. Noise levels of 5-10 percent of the object image size are used. Approximate Cramer-Rao lower bounds are derived for the model parameter estimates as a function of object trajectory and noise level. This approach may be of use in situations where it is difficult to resolve large numbers of object match points, but relatively long sequences of images (10 to 20 or more) are available.

Estimation of Object Motion Parameters from Noisy Images

The goal of this paper is to offer a structured synopsis of the problems in image motion computation and analysis, and of the methods proposed, exposing the underlying models and supporting assumptions. A sufficient number of pointers to the literature will be given, concentrating mostly on recent contributions. Emphasis will be on the detection, measurement and segmentation of image motion. Tracking, and deformable motion issues will be also addressed. Finally, a number of related questions which could require more investigations will be presented.

Computation and analysis of image motion: a synopsis of current problems and methods

This paper introduces a novel semantic video object extraction system using mathematical morphology and a perspective motion model. Inspired by the results from the study of the human visual system, we intend to solve the semantic video object extraction problem in two separate steps: supervised I-frame segmentation, and unsupervised P-frame tracking. First, the precise semantic video object boundary can be found using a combination of human assistance and a morphological segmentation tool. Second, the semantic video objects in the remaining frames are obtained using global perspective motion estimation and compensation of the previous semantic video object plus boundary refinement as used for I frames.

Semiautomatic segmentation and tracking of semantic video objects

We propose a new method for object tracking in image sequences using template matching. To update the template, appearance features are smoothed temporally by robust Kalman filters, one to each pixel. The resistance of the resulting template to partial occlusions enables the accurate detection and handling of more severe occlusions. Abrupt changes of lighting conditions can also be handled, especially when photometric invariant color features are used, The method has only a few parameters and is computationally fast enough to track objects in real time.

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Fast occluded object tracking by a robust appearance filter

The determination of moving edges in an image sequence is discussed An approach is proposed that relies on modeling principles and likely hypothesis testing techniques A spatiotemporal edge in an image sequence is modeled as a surface patch in a 3-D spatiotemporal space A likelihood ratio test enables its detection as well as simultaneous estimation of its related attributes It is shown that the computation of this test leads to convolving the image sequence with a set of predetermined masks The emphasis is on a restricted but widely relevant and useful case of surface patch, namely the planar one In addition, an implementation of the procedure whose computation cost is merely equivalent to a spatial gradient operator is presented This method can be of interest for motion-analysis schemes, not only for supplying spatiotemporal segmentation, but also for extracting local motion information Moreover, it can cope with occlusion contours and important displacement magnitude Experiments have been carried out with both synthetic and real images >

A maximum likelihood framework for determining moving edges

A mathematical model using an operator formulation for a moving object in a sequence of images is presented. Time-varying translation and rotation operators are derived to describe the motion. A variational estimation algorithm is developed to track the dynamic parameters of the operators. The occlusion problem is alleviated by using a predictive Kalman filter to keep the tracking on course during severe occlusion. The tracking algorithm (variational estimation in conjunction with Kalman filter) is implemented to track moving objects with occasional occlusion in computer-simulated binary images.

A Mathematical Model for Computer Image Tracking

Binary random variables are regarded as random vectors in a binary-field (modulo-2) linear vector space. A characteristic function is defined and related results derived using this formulation. Minimax estimation of probability distributions using an entropy criterion is investigated, which leads to an A-distribution and bilinear discriminant functions. Nonparametric classification approaches using Hamming distances and their asymptotic properties are discussed. Experimental results are presented.

Statistical Pattern Classification with Binary Variables

Very Large Scale Integration (VLSI) computing arrays for pattern recognition and image processing have received increasing attention in recent years. The computation speed of an array is often limited by the I/O bandwidth of the host system or the VLSI array. Reconfiguration techniques are used to restructure a computing array, so that successive functional computation steps can be carried out without the data leaving the array. Computation time is reduced, since with reconfiguration the limited I/O bandwidth affects only the first and last phases of the necessary computations.

VLSI Arrays for Pattern Recognition and Image Processing: I/O Bandwidth Considerations

Publisher Summary Pictorial pattern analysis and image processing have applications in many areas, including character recognition, remote sensing, target tracking, biomedical image analysis, fingerprint analysis, industrial automation, and robotics. There are two approaches to very large-scale integration (VLSI) design for image processing, parallel-processing cellular arrays, and special-purpose image-processing chips. LSI/VLSI cellular arrays are being developed and implemented for image processing. The arrays are flexible and programmable, and each processing element (PE) in an array is connected to its neighboring PEs to perform neighbor-dependent operations. Parallel streams of pixel values are piped into the array and computed results flow out of the array synchronously without branching. In the future, hierarchical and reconfigurable general-purpose image-processing and pattern-recognition systems would be implemented using VLSI components. The lowest level would be the cellular array or the systolic array to handle low-level and parallel-image-processing tasks. The second level could be a number of multiprocessors that handle intermediate- and high-level processing tasks and call upon the first-level processors to perform the necessary low-level operations.

Tzay Y. Young

Papers

A Mathematical Model for Computer Image Tracking

Statistical Pattern Classification with Binary Variables

VLSI Arrays for Pattern Recognition and Image Processing: I/O Bandwidth Considerations

Impact of VLSI on Pattern Recognition and Image Processing

Vlsi arrays and conrol structure for image processing.