Locating objects using the Hausdorff distance

The Hausdorff distance is a measure defined between two point sets representing a model and an image. In the past, it has been used to search images for instances of a model that has been translated or translated and scaled by finding transformations that bring a large number of model features close to image features, and vice versa. The Hausdorff distance is reliable even when the image contains multiple objects, noise, spurious features, and occlusions. We apply it to the task of locating an affine transformation of a model in an image; this corresponds to determining the pose of a planar object that has undergone weak perspective projection. We develop a rasterised approach to the search and a number of techniques that allow us to quickly locate all transformations of the model that satisfy two quality criteria; we can also quickly locate only the best transformation. We discuss an implementation of this approach, and present some examples of its use