Hausdorff Distance with k-Nearest Neighbors

Hausdorff distance (HD) is an useful measurement to determine the extent to which one shape is similar to another, which is one of the most important problems in pattern recognition, computer vision and image analysis. Howeverm, HD is sensitive to outliers. Many researchers proposed modifications of HD. HD and its modifications are all based on computing the distance from each point in the model image to its nearest point in the test image, collectively called nearest neighbor based Hausdorff distances (NNHDs). In this paper, we propose modifications of Hausdorff distance measurements by using k-nearest neighbors (kNN). We use the average distance from each point in the model image to its kNN in the test image to replace the NN procedures of NNHDs and obtain the Hausdorff distance based on kNN, named kNNHDs. When k=1, kNNHDs are equal to NNHDs. kNNHDs inherit the properties of outliers tolerance from the prototypes in NNHDs and are more tolerant to noise.