Characterization of arrhythmia complexity requires defining well behaved measures that respect the known signal symmetries. Multifractal analysis methods take into account the intermittency of the fluctuations observed in the cardiac electric potential. We present how singularity analysis provides a measure to robustly characterize complexity at a local level. This method is essentially nonlinear and it minimizes the effect of common artefacts on empirical signals such as finite size, noise and aliasing. The presented method aims at improving the understanding of arrhythmia mechanisms with minimal base hypotheses. In that sense, it highlights arrhythmogenic areas on electrocardiographic potential maps of the epicardium. From it, key descriptors could help in determining the prognosis of the arrhythmia, to forecast the outcome of ablation and resynchronization procedures, and to guide the surgical action in these operations.