1. A touch sensing system, comprising: a two-dimensional capacitive sense array including a plurality of capacitive sensors, wherein each capacitive sensor is assigned a respective location type based on proximity to edges of the capacitive sense array; a capacitance measurement circuit coupled to the capacitive sense array and configured to measure capacitance changes at each capacitive sensor of the capacitive sense array; a processing unit coupled to the capacitance measurement circuit, wherein the processing unit is configured for: performing a scan of the capacitive sense array to measure capacitance for at least a plurality of the capacitive sensors; identifying a first capacitive sensor whose measured capacitance is a local peak; identifying a local rectangular array of capacitive sensors around the first capacitive sensor; for each column of the local rectangular array, summing measured capacitances for the capacitive sensors in the column to form a respective column sum; and determining an x-coordinate of the touch, including: determining whether the local peak is proximate in an x-direction to a transition point on the capacitive sense array, wherein the transition point is a point of transition between distinct location types on the capacitive sense array; in accordance with a determination that the local peak is not proximate in the x-direction to a transition point on the capacitive sense array, computing the x-coordinate of a touch using a plurality of the column sums; and in accordance with a determination that the local peak is proximate in the x-direction to a transition point on the capacitive sense array, applying a smoothing algorithm, including computing the x-coordinate of the touch as an average of two x-coordinate calculations, wherein each of the two x-coordinate calculations conditionally performs a horizontal shift of the local rectangular array based on comparing the peak measured capacitance of the first capacitive sensor to an adjacent measured capacitance and computes a respective x-coordinate using a respective plurality of the column sums.