Interpolation from Grid Lines: Linear, Transfinite and Weighted Method

When two sets of line scans are acquired orthogonal to each other, intensity values are known along the lines of a grid. To view these values as an image, intensities need to be interpolated at regularly spaced pixel positions. In this paper we evaluate three methods for interpolation from grid lines: linear, transfinite and weighted. Linear method does not preserve the known values along the grid lines. Transfinite method, known from mesh generation, preserves the known values but might cause overshoot. The weighted method, which we propose, is designed to combine the desired properties of transfinite method close to grid lines, and the stability of the linear method. We perform an extensive evaluation of the three interpolation methods across a range of upsampling rates for two data sets. Depending on the upsampling rate, we show significant difference in the performance of the three methods. We find that the transfinite interpolation works well for small upsampling rates and the proposed weighted interpolation method performs very well for all relevant upsampling rates.