How Succolarity could be used as another fractal measure in image analysis

Three aspects of texture are distinguished by fractal geometry: Fractal Dimension (FD), Lacunarity and Succolarity. Although, FD has been well studied and Lacunarity has been more and more used, Succolarity, until now, has not been considered. This work presents a method to compute Succolarity. The proposed approach, for this computation, is based on the evaluation of a proposed equation that employ the FD Box Counting idea adapted to the concept of Succolarity. Simple examples, on 2D and 3D images, are considered to easily explain, step by step, how to compute the Succolarity. To illustrate this approach examples are shown, they range form satellite to ultrasound images. The proposed form of Succolarity evaluation is a unique feature usable whether it is relevant differentiate images with some directional or flow information associated with it. Therefore it could be used as a new feature in pattern recognition processes for the identification of natural textures. Furthermore, it works very well when is relevant differentiate images with some characteristics (e.g. directional information) that can not be discriminate by FD or Lacunarity.