A method of graphically representing local activation time, the method comprising: receiving, at an electroanatomical mapping system, an LAT data set comprising a plurality of electrophysiology data points, wherein each EP data point of the plurality of EP data points includes localization information and an electrogram signal; computing, at the electroanatomical mapping system, a spatial gradient over a spatial kernel defined as a sphere of radius r centered at an EP data point of the plurality of EP data points of the LAT data set and further defined to include additional EP data points that are within the radius r; computing, at the electroanatomical mapping system, a respective temporal gradient for each of a plurality of temporal kernels, wherein each temporal kernel of the plurality of temporal kernels is defined to include an electrogram signal for the EP data point of the plurality of EP data points and further defined to include additional beats, over several beats, wherein the additional beats are morphologically similar to the electrogram signal for the EP data point of the plurality of EP data points; detecting, at the electroanatomical mapping system, a spatial outlier EP data point within the spatial kernel using the spatial gradient; detecting, at the electroanatomical mapping system, a temporal outlier EP data point using the plurality of temporal gradients; correcting, at the electroanatomical mapping system, the spatial outlier EP data point and the temporal outlier EP data point, thereby creating a corrected LAT map; and outputting, at the electroanatomical mapping system, a graphical representation of the corrected LAT map on a model of a cardiac surface on a display. receiving, at an electroanatomical mapping system, an LAT data set comprising a plurality of electrophysiology data points, wherein each EP data point of the plurality of EP data points includes localization information and an electrogram signal; computing, at the electroanatomical mapping system, a spatial gradient over a spatial kernel defined as a sphere of radius r centered at an EP data point of the plurality of EP data points of the LAT data set and further defined to include additional EP data points that are within the radius r; computing, at the electroanatomical mapping system, a respective temporal gradient for each of a plurality of temporal kernels, wherein each temporal kernel of the plurality of temporal kernels is defined to include an electrogram signal for the EP data point of the plurality of EP data points and further defined to include additional beats, over several beats, wherein the additional beats are morphologically similar to the electrogram signal for the EP data point of the plurality of EP data points; detecting, at the electroanatomical mapping system, a spatial outlier EP data point within the spatial kernel using the spatial gradient; detecting, at the electroanatomical mapping system, a temporal outlier EP data point using the plurality of temporal gradients; correcting, at the electroanatomical mapping system, the spatial outlier EP data point and the temporal outlier EP data point, thereby creating a corrected LAT map; and outputting, at the electroanatomical mapping system, a graphical representation of the corrected LAT map on a model of a cardiac surface on a display.