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 does not truly reflect 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