Azriel Rosenfeld

Prof. Rosenfeld's research has dealt with many aspects of image analysis and computer vision. This report summarizes recent work on geometry, motion, and facial features.

Digital Geometry

Classical digital geometry deals with sets of cubical voxels (or square pixels) that can share faces, edges, or vertices; but basic parts of digital geometry can be generalized to sets S of convex voxels (or pixels) that can have arbitrary intersections. In particular, it can be shown that if each voxel P of S has only finitely many neighbors (voxels of S that intersect P), and if any nonempty intersection of neighbors of P intersects P (we call such a set of voxels ìstrongly normalî), then the neighborhood N(P) of every voxel P is simply connected, and if the topology of N(P) does not change when P is deleted, then P is a ìsimpleî voxelói.e., deletion of P does not change the topology of S. This may not be true if the set of voxels is not strongly normal; and even if it is strongly normal, P may be simple even if deletion of P does not preserve the topology of N(P). Tessellations of R2 or R3 into convex polygons or polyhedra may not be strongly normal; for example, the square and hexagonal regular tessellations of R2 are, but the triangular regular tessellation is not.

Digital Knots

Digital (6-)knots in Z3 are topologically equivalent to isothetic polygonal knots in R3. With respect to topology-preserving ìsimple deformationsî (SD) of digital images, it can be shown that equivalent knots have digitizations that differ by SD. Conversely, we can define a general concept of knottedness for ìK-setsî (sets that can be obtained from digital knots by SD), and show that SD preserves the knottedness types of K-sets. We can also define ìregular positionî for isothetic knots and digital knots, and show that SD can be used to put any digital knot into such a position and to perform ìReidemeister movesî on the resulting projection.

Motion Fields

If we histogram the normal flow vectors in images of a scene viewed by a moving observer, we can use the time-varying histogram to derive qualitative information about the observer's motionófor example, whether it is (primarily) translational or rotational, and whether the direction of translation or axis of rotation is (roughly) parallel or perpendicular to the camera axis. This can be demonstrated using flow histograms obtained from a variety of real image sequences. If the motion is translational, qualitative information about the scene depth can also be obtained from the flow histogramsófor example, whether the scene depth is unimodal or bimodal. This has been demonstrated for real scenes containing a layer of vegetation seen against a textured background, or two layers of vegetation.

Vehicular Motion

Autonomous operation of a vehicle on a road calls for understanding of various events involving the motions of the vehicles in its vicinity. We have shown that a moving vehicle which is carrying a camera can estimate the relative motions of nearby vehicles. We define a model for the motion of the observing vehicle, and show how to ìstabilizeî it, i.e. to correct the image sequence so that transient motions resulting from bumps, etc. are removed and the sequence corresponds more closely to the sequence that would have been collected if the motion had been smooth. We also model the motions of nearby vehicles and show how to detect their motions relative to the observing vehicle.The effectiveness of our approach has been demonstrated for several road image sequences.

Facial Features

We have developed two methods of detecting the eyes in color images of human faces. The face is detected as a large flesh-colored region, and anthropometric data are then used to estimate the size and separation of the eyes. Our first method of eye detection uses a linear filtering approach applied to the gray-level image of the face; our second method uses non-linear filters, applied to the color face image, to detect the corners of the eyes. Both methods have been tested on two datasets. The first method had a good detection rate, but also gave many false alarms; the second method had a 90% detection rate with no false alarms. An example is shown in Figure 1.

Figure 1. Eye corner detection.

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November 1999