Analytical Solution for Sparse Data Interpolation Using Geodesic Distance Affinity Space: Application to the Optical Flow Problem and 3D Reconstruction

Abstract

In this paper, we derive the analytic solution for sparse data interpolation using the geodesic distance affinity space of the known reference image associated with sparse data to be interpolated. We compare our method with the EpicFlow algorithm [1] that is intuitively motivated by almost the same geodesic distance principle. However, we found that our approach is more general, faster, and with clearer theoretical motivation. To test the accuracy of our approach, we applied our interpolation method to the sparse optical flow data obtained by the DCflow convolution neural network method [2] and compared our result with the EpicFlow interpolation result on the same sparse data set. The comparison shows that our algorithm is more accurate than the EpicFlow technique.