using a patch size of $9\times 9$ pixels and $m=5000$ sample warps, we compare our proposed approach with the IC-LK and ESM methods. The results are shown in Table \[tab:compare\_lp\_with\_energy\], where we also show timing results for our approach where the learning step is done on a GPU. As expected, energy-based methods exhibit faster training time on a CPU but they also suffer from a longer refinement time as well as slightly lower accuracy compared to our approach. However, note that on a GPU, the learning step is almost as efficient as energy-based methods for our approach.

  ----------- ----------- ------------ ------
  Method       Training    Refinement   RMSE
               time (ms)   time (ms)   
  ESM          **0.10**       3.26      0.12
  IC-LK          0.19         0.99      0.16
  Sym (CPU)      3.75                  
  Sym (GPU)      0.41                  
  ----------- ----------- ------------ ------

  : Comparison with energy-based methods.[]{data-label="tab:compare_lp_with_energy"}

![Thumbnails of images used for real data experiment.[]{data-label="fig:hannover_dataset"}](RealDatSetThumbs.pdf){width="\columnwidth"}

Still Image Pairs Experiment {#subsec:real_experiment}
----------------------------

  -- ----- -------- ------------ ------------ ------------ ---------- ------------ ------------ ------------ ------------ ------------
                                                                                                                          
            IC-LK       ESM           hp        hpdct-25    hpdct-49     dct-25       dct-49         jd          sym       symdct-25
      1,2   0.2433     0.1946       0.3164       0.3142      0.2433    **0.1409**     0.1677       0.1677       0.1677     **0.1409**
      2,3   0.2519   **0.2151**     0.3748       0.3731      0.3748      0.2375       0.2747       0.2747       0.2747       0.2375
      3,4   0.4459     0.4185       0.5871       0.6343      0.5871    **0.3323**     0.3411       0.3411       0.3411     