Local activation time (LAT) mapping of cardiac chambers is vital for targeted treatment of cardiac arrhythmias in catheter ablation procedures. Current methods require many LAT observations for an accurate interpolation of the LAT signal extracted from intracardiac electrograms (EGMs). Additionally, conventional performance metrics do not accurately measure the quality of interpolated maps. We propose, first, a novel graph-based method for spatial interpolation of the LAT signal with respect to the manifold; second, a realistic sub-sampling protocol for LAT interpolation testing; and third, a new color-based metric for evaluation of interpolation quality that quantifies perceived differences in LAT maps. We evaluate our approach on a dataset consisting of seven LAT maps from four patients obtained by the CARTO electroanatomic mapping system during premature ventricular complex (PVC) ablations. Our results show excellent accuracy for relatively few observations, achieving on average 6% lower error than state-of-the-art techniques for only 100 observations.