Image Segmentation Using Fractal Dimension

The task of object recognition in image processing and machine vision problems relies on nding good algorithms for one particular low-level processing task: image segmentation. In this report, we apply the concept of fractal dimension to this problem. In particular, we introduce the notion of a local fractal operator that can \measure" the fractal dimension of a single pixel; we investigate three simple examples of such operators. We then use histograms of the computed fractal dimensions of all the pixels to recolor the image in bins; the result is the segmented image. We illustrate the use of our methods on several images and discuss the various shortcomings of the technique. For an image ofm pixels, we show that our basic algorithm with operators can execute in O(m) steps, which is faster than traditional approaches using transform methods which are O m 2 log(m) ; however, despite this attractive feature, numerous problems remain.