Line-Based Recognition Using A Multidimensional Hausdorff Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
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We have developed a method, using the minimum Hausdorff distance, for visually locating an object in an image. This method is very reliable, and fast enough for real-world applications. A visual recognition system takes an image and a model of an object which may occur in that image; these images and models are composed of features (points, line segments, etc.). The system locates instances of the model in the image by determining transformations of the model which bring a large number of model features close to image features. One of the unique strengths of the Hausdorff distance is the reverse distance which reduces the frequency of erroneous matching between a model and a cluttered portion of the image. The Hausdorff distance is a measure defined between two point sets representing a model and an image. Its properties make it attractive for model-based recognition; one of these properties is that the Hausdorff distance is a metric. The minimum Hausdorff distance is used to find a transformation of the model which brings it into closest correspondence with the image. This can be done by searching over a space of allowable transformations. In some cases, the minimum Hausdorff distance is also a metric. The Hausdorff distance can be modified so that it is reliable even when the image contains multiple objects, noise, spurious features, and occlusions. We construct lower bounds which show that finding the exact transformation that minimises the Hausdorff distance may be quite expensive. We develop a rasterised approach to the search and a number of techniques which allow this search to be performed efficiently. The principal search technique used is transformation space subdivision. The space of transformations is searched in a tree-like fashion: a large region is examined as a unit, and if the results of this examination are good, it is subdivided and each of the subregions examined in turn; if the results are not good, then the region is discarded. We discuss some implementations of this approach, together with their applications to practical problems such as motion tracking and mobile robot navigation.