A computer-assisted method for quantitatively characterizing atrial fibrillation in a patient includes recording time series of bipolar atrial fibrillation signals at multiple sites in a patient's atria using two or more electrodes, calculating a similarity index vector by a computer system based on the bipolar atrial fibrillation signal between a first site and its neighboring sites, constructing an similarity-index vector field based on similarity-index vectors at different sites, calculating Curl and Divergence of the similarity-index vector field, calculating Rotor Identification using Curl and Divergence, calculating Focal Identification using Divergence, and determining one or more critical regions in the patient's atria if Rotor Identification is above a first predetermined threshold and Focal Identification is above a second predetermined threshold.
