Scale space classification using area morphology

We explore the application of area morphology to image classification. From the input image, a scale space is created by successive application of an area morphology operator. The pixels within the scale space corresponding to the same image location form a scale space vector. A scale space vector therefore contains the intensity of a particular pixel for a given set of scales, determined in this approach by image granulometry. Using the standard k-means algorithm or the fuzzy c-means algorithm, the image pixels can be classified by clustering the associated scale space vectors. The scale space classifier presented here is rooted in the novel area open-close and area close-open scale spaces. Unlike other scale generating filters, the area operators affect the image by removing connected components within the image level sets that do not satisfy the minimum area criterion. To show that the area open-close and area close-open scale spaces provide an effective multiscale structure for image classification, we demonstrate the fidelity, causality, and edge localization properties for the scale spaces. The analysis also reveals that the area open-close and area close-open scale spaces improve classification by clustering members of similar objects more effectively than the fixed scale classifier. Experimental results are provided that demonstrate the reduction in intra-region classification error and in overall classification error given by the scale space classifier for classification applications where object scale is important. In both visual and objective comparisons, the scale space approach outperforms the traditional fixed scale clustering algorithms and the parametric Bayesian classifier for classification tasks that depend on object scale.