This paper introduces a unified approach to the problem of verifying alignment hypotheses in the presence of substantial amounts of uncertainty in the predicted locations of projected model features. Our approach is independent of whether the uncertainty is distributed or bounded, and, moreover, incorporates information about the domain in a formally correct manner. Information which can be incorporated includes the error model, the distribution of background features, and the positions of the data features near each predicted model feature. Experiments are described that demonstrate the improvement over previously used methods. Furthermore, our method is efficient in that the number of operations is on the order of the number of image features that lie nearby the predicted model features.

The Saliency Network proposed by Shashua and Ullman (1988) is a well-known approach to the problem of extracting salient curves from images while performing gap completion. This paper analyzes the Saliency Network. Although the network is attractive for a number reasons, our analysis reveals certain weaknesses with the method. In particular, we show cases in which the most salient element does not lie on the perceptually most salient curve. Furthermore, the saliency measure may change its preferences when curves are scaled uniformly. Also, for certain fragmented curves the measure prefers large gaps over a few small gaps of the same total size. We analyze the time complexity required by the method and discuss problems due to coarse sampling of the range of possible orientations. We show that with proper sampling the complexity of the network becomes cubic in the size of the network. Finally, we consider the possibility of using the Saliency Network for grouping. We show that the Saliency Network recovers the most salient curve efficiently, but it has problems with identifying any salient curve other than the most salient one.

Robust recognition systems require a careful understanding of the effects of error in sensed features. Error in these image features results in uncertainty in the possible image location of each additional model feature. We present an accurate, analytic approximation for this uncertainty when model poses are based on matching three image and model points. This result applies to objects that are fully three-dimensional, where past results considered only two-dimensional objects. Further, we introduce a linear programming algorithm to compute this uncertainty when poses are based on any number of initial matches.>

This correspondence discusses computing the pose of a model from three matching point pairs under weak-perspective projection. A new approach to the problem that is motivated geometrically is described. Like previous methods, the method here involves solving a biquadratic equation, but here the biquadratic's solutions, comprised of an actual and a false solution, are interpreted graphically. The final equations take a new form, which leads to a simple expression for the image position of any unmatched model point.>

Alignment is a common approach for recognizing 3-D objects in 2-D images. Current implementations handle image uncertainty in ad hoc ways. These errors, however, can propagate and magnify through the alignment computations, such that the ad hoc approaches may not work. The authors give a technique for tightly bounding the propagated error, which can be used to make the recognition robust while still being efficient. Previous analyses of alignment have demonstrated a sensitivity to false positives. But these analyses applied only to point features, whereas alignment systems often rely on extended features for verifying the presence of a model in the image. A new formula is derived for the selectivity of a line feature. It is experimentally demonstrated using the technique for computing error bounds that the use of line segments significantly reduces the expected false positive rate. The extent of the improvement is that an alignment system that correctly handles propagated error is expected to remain reliable even in substantially cluttered scenes.>

Object recognition systems that use a small number of pairings of data and model features to compute the 3D transformation from model to sensor coordinates are considered. The effects of 2D sensor uncertainty on such computations are examined. The uncertainty in transformation parameters is bounded, and the effect of this uncertainty on false positive recognition rates is analyzed.>