Local mode filtering

Linear filters have two major drawbacks. First, edges in the image are smoothed with increasing filter size. Second, by extending the filters to multi-channel data, correlation between the channels is lost. Only a few researchers have explored the possibilities of mode filtering to overcome these problems. Mode filtering is motivated from both a local histogram with tonal scale and a robust statistics point of view. The tonal scale is proved to be equal to the scale of the error norm function within the robust statistics framework. Instead of the more commonly studied global mode, our focus is on the local mode. It preserves edges and details and is easily extensible to multi-channel data. A generalization of the spatial Gaussian filtering to a spatial and tonal Gaussian filter is used to iterate to the local mode. Results on color images include successful noise attenuation while preserving edges and detail by local mode filtering.