A Comparative analysis of Green’s functions of 1D matching equations for motion synthesis

Motion Blur and Deblur Through Green's Matrices

“…Since x = x U is a singular point of the Green's operator, we found it necessary to use stratified sampling for its discretization, with the sampling frequency increasing as we approach x U (Ferreira Júnior et al, 2009). We consider this below.…”

“…In this case, we need to compute the Green's function samples only once, and a single matrix product per line is required for yielding the transformed image. The complexity of the original filtering process, as described in (Ferreira Júnior et al, 2008;2009) , is of order O(M.N 2 ) per each image line, and since the filtering along the image columns is also required, we have a total complexity of order O(M.N 2 )+O(N.M 2 ). With the matrix approach, this will be reduced to O(M)+O(N).…”

“…When implementing consecutive horizontal and vertical filterings, as in (Ferreira Júnior et al, 2009), separate kernels can be used, such that…”

“…For the video interpolation experiments, we take the output of a motion estimation algorithm as input parameters to the Green's function, similarly as in (Ferreira Júnior et al, 2009). The general 2D affine model for motion estimation can be expressed as…”

“…Also, in (Ferreira Júnior et al, 2009), the second-order matching model of Eq. (3) has been compared to first-order variants, having been shown to generally yield more realistic motion effects.…”