Edge detection using the local fractal dimension

Fractal Brownian noise is used as a model describing the local grey level change in digital images. At edges this model not truly reflects the reality, because edges add a deterministic component to the image which is not compatible with the notion of scale-independent self-similarity of fractal structures. Thus, the local degree of 'fractality' is used to differentiate edges from segment interiors and from noise. The concept is evaluated by comparing fractal edge detectors with conventional operators such as, e.g., a Sobel or Laplace operator. Results show a similar performance in a low-noise environment and superiority of the fractal operators in a high noise environment. The inclusion of the operators into an edge-based segmentation scheme revealed the same results for an application in image segmentation.