Evolving Estimators of the Pointwise Holder Exponent with Genetic Programming

The analysis of image regularity using Holder exponents can be used to characterize singular structures contained within an image, and provide a compact description of local shape and appearance. However, estimating the Holder exponent is not a trivial task and current methods tend to be slow and complex. Therefore, the goal in this work is to automatically synthesize image operators that can be used to estimate the Holder regularity of an image. We pose this task as an optimization problem and use Genetic Programming (GP) to search for operators that can approximate a traditional estimator, the oscillations method. In our experiments, GP was able to evolve estimators that achieve a low error and a high correlation with the ground truth estimation. Furthermore, most of the GP estimators are faster than the traditional approaches, in some cases their runtime is orders of magnitude smaller. This result allowed us to implement a real-time estimation of the Holder exponent on a live video signal, the first such implementation in current literature. Moreover, the evolved estimators are used to generate local descriptors of salient image regions, a task for which we obtain a stable and robust matching that is comparable with state-of-the-art methods. In conclusion, the evolved estimators produced by GP could help expand the application domain of Holderian regularity within the fields of image analysis and signal processing