Linear, transfinite and weighted method for interpolation from grid lines applied to OCT images

When performing a line scan using optical coherence tomography (OCT), the distance between the successive scan lines is often large compared to the resolution along each scan line. If two sets of such line scans are acquired orthogonal to each other, intensity values are known along the lines of a square grid, but are unknown inside each square. 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. The linear method does not preserve the known values along the grid lines. The transfinite method, known from mesh generation, preserves the known values but might cause artifacts further away from the grid lines. The weighted method, which we propose, is designed to combine the desired properties of the transfinite method close to grid lines and the stability of the linear method further away. An important parameter influencing the performance of the interpolation methods is the upsampling rate. We perform an extensive evaluation of the three interpolation methods across a range of upsampling rates. Our statistical analysis shows 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 upsampling rates typically used in practice. On the basis of these findings we propose an approach for combining two OCT scans, acquired such that the lines of the second scan are orthogonal to the first.