1. A touch-sensitive apparatus comprising: a panel; a plurality of light emitters and a plurality of light detectors arranged at a periphery of the panel, wherein the plurality of light emitters are configured to transmit light signals to a plurality of light detectors to define detection lines that extend across a non-circular touch surface on the panel between pairs of the plurality of light emitters and the plurality of light detectors, and wherein the plurality of light detectors are configured to generate an output signal based on the transmitted light signals; and a hardware processor configured to: generate a set of observed values for at least a subset of the detection lines based on the output signal, wherein the observed values correspond to sampling points in a two-dimensional sample space, in which a first dimension is defined by an angle parameter that represents a rotation angle of the detection line in a plane of the panel and a second dimension is defined by a distance parameter that represents a distance of the detection line in the plane of the panel from a predetermined origin; generate estimated values for matched sampling points in the two-dimensional sample space based on interpolation of the observed values, wherein the matched sampling points are arranged to form a plurality of columns of matched sampling points in the two-dimensional sample space, wherein the plurality of columns of matched sampling points extend in the second dimension and include a spacing between immediately adjacent columns in the first dimension, and wherein the spacing between the immediately adjacent columns is variable in the plurality of columns of matched sampling points, and wherein at least some of the plurality of columns of matched sampling points are arranged to coincide with alignment lines that are defined by locations of the sampling points in the two-dimensional sample space; execute a tomographic reconstruction function on the estimated values for the matched sampling points; and generate a two-dimensional representation of touch interaction on the touch surface based on the executed tomographic reconstruction function.