Multifractal Anomaly Detection in Images via Space-Scale Surrogates

Multifractal analysis provides a global description for the spatial fluctuations of the strengths of the pointwise regularity of image amplitudes. A global image characterization leads to robust estimation, but is blind to and corrupted by small regions in the image whose multifractality differs from that of the rest of the image. Prior detection of such zones with anomalous multifractality is thus crucial for relevant analysis, and their delineation of central interest in applications, yet has never been achieved so far. The goal of this work is to devise and study such a multifractal anomaly detection scheme. Our approach combines three original key ingredients: i) a recently proposed generic model for the statistics of the multiresolution coefficients used in multifractal estimation (wavelet leaders), ii) an original surrogate data generation procedure for simulating a hypothesized global multifractality and iii) a combination of multiple hypothesis tests to achieve pixel-wise detection. Numerical simulations using synthetic multifractal images show that our procedure is operational and leads to good multifractal anomaly detection results for a range of target sizes and parameter values of practical relevance.