Each 2D silhouette of a 3D unknown object O constrains O inside the volume obtained by back-projecting the silhouette from the corresponding viewpoint. A set of silhouettes specifies a boundary volume R obtained by intersecting the volumes due to each silhouette. R more or less closely approximates O, depending on the viewpoints and the object itself. This approach to the reconstruction of 3D objects is usually referred to as volume intersection. This correspondence addresses the problem of inferring the shape of the unknown object O from the reconstructed object R. For doing this, the author divides the points of the surface of R into hard points, which belong to the surface of any possible object originating R, and soft points, which may or may not belong to O. The author considers two cases: In the first case R is the closest approximation of O which can be obtained from its silhouettes, i.e., its visual hull; in the second case, R is a generic reconstructed object. In both cases the author supplies necessary and sufficient conditions for a point to be hard and gives rules for computing the hard surfaces. >

How far 3D shapes can be understood from 2D silhouettes

A widely used subpixel precision estimate of an object center is the weighted center of gravity (COG). We derive three maximum-likelihood estimators for the variance of the two-dimensional (2-D) COG as a function of the noise in the image. We assume that the noise is additive, Gaussian distributed and independent between neighboring pixels. Repeated experiments using 2500 generated 2-D bell-shaped markers superimposed with an increasing amount of Gaussian noise were performed, to compare the three approximations. The error of the most exact approximative variance estimate with respect to true variance was always less than 5% of the latter. This deviation decreases with increasing signal-to-noise ratio. Our second approximation to the variance estimate performed better than the third approximation, which was originally presented by Oron et al. by up to a factor /spl ap/10. The difference in performance between these two approximations increased with an increasing misplacement of the window in which the COG was calculated with respect to the real COG.

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Accurate object localization in gray level images using the center of gravity measure: accuracy versus precision

A novel automatic target tracking (ATT) algorithm for tracking targets in forward-looking infrared (FLIR) image sequences is proposed in this paper. The proposed algorithm efficiently utilizes the target intensity feature, surrounding background, and shape information for tracking purposes. This algorithm involves the selection of a suitable subframe and a target window based on the intensity and shape of the known reference target. The subframe size is determined from the region of interest and is constrained by target size, target motion, and camera movement. Then, an intensity variation function (IVF) is developed to model the target intensity profile. The IVF model generates the maximum peak value where the reference target intensity variation is similar to the candidate target intensity variation. In the proposed algorithm, a control module has been incorporated to evaluate IVF results and to detect a false alarm (missed target). Upon detecting a false alarm, the controller triggers another algorithm, called template model (TM), which is based on the shape knowledge of the reference target. By evaluating the outputs from the IVF and TM techniques, the tracker determines the real coordinates of one or more targets. The proposed technique also alleviates the detrimental effects of camera motion, by appropriately adjusting the subframe size. Experimental results using real-life long-wave and medium-wave infrared image sequences are shown to validate the robustness of the proposed technique.

Automatic target tracking in FLIR image sequences using intensity variation function and template modeling

In this paper we present a new technique for data association using multiassignment for tracking a large number of closely spaced (and overlapping) objects. The algorithm is illustrated on a biomedical problem, namely the tracking of a group of fibroblast (tissue) cells from an image sequence, which motivated this work. The algorithm presents a novel iterated approach to multiassignment using successive one-to-one assignments of decreasing size with modified costs. The cost functions, which are adjusted depending on the 'depth' of the current assignment level and on the tracking results, are derived. The resulting assignments are used to form, maintain and terminate tracks with a modified version of the probabilistic data association filter, which can handle the contention for a single measurement among multiple tracks in addition to the association of multiple measurements to a single track. Estimation results are given and compared with those of the standard 2-dimensional one-to-one assignment algorithm. It is shown that iterated multiassignment results in superior measurement-to- track association.

Multiassignment for tracking a large number of overlapping objects

In this paper we present a new technique for data association using multiassignment for tracking a large number of closely spaced (and overlapping) objects. The algorithm is illustrated on a biomedical problem, namely the tracking of a group of fibroblast (tissue) cells from an image sequence, which motivated this work. Because of their proximity to one another and due to the difficulties in segmenting the images accurately from a poor-quality image sequence, the cells are effectively closely spaced objects (CSOs). The algorithm presents a novel dichotomous, iterated approach to multiassignment using successive one-to-one assignments of decreasing size with modified costs. The cost functions, which are adjusted depending on the "depth" of the current assignment level and on the tracking results, are derived. The resulting assignments are used to form, maintain and terminate tracks with a modified version of the probabilistic data association (PDA) filter, which can handle the contention for a single measurement among multiple tracks in addition to the association of multiple measurements to a single track. Estimation results are given and compared with those of the standard 2D one-to-one assignment algorithm. It is shown that iterated multiassignment results in superior measurement-to-track association. The algorithms presented can be used for other general tracking problems, including dense air traffic surveillance and control.

Multiassignment for tracking a large number of overlapping objects [and application to fibroblast cells]

Precision target tracking based on data obtained from imaging sensors when the target is not fully visible during tracking is addressed. The image is divided into several layers of gray level intensities and thresholded. A binary image is obtained and grouped into clusters using image segmentation. The association of the various clusters to the track to be estimated relies on both the motion and pattern recognition characteristics of the target. The centroid measurements of the clusters and the probabilistic data association filter (PDAF) are employed for state estimation. Expressions for the single-frame-based centroid measurement noise variance of the target cluster and the optimal parameters for cluster segmentation are given. Simulation results validate the expressions for the measurement noise variance as well as the performance predictions of the tracking method. For a dim synthetic target with strong background noise, subpixel accuracy in the range of 0.3-0.4 pixel RMS error with moderate

Eliezer Oron

Papers

Precision tracking with segmentation for imaging sensors

Image Segmentation Based on Optimal Layering for Precision Tracking.