Scale cauchy loss to approximate r^2 in inlier region

[theartful]

This PR scales cauchy loss by threshold^2 so that it approximates the squared error in the inlier region.

I also added some missing std includes (algorithm for std::min, cmath for std::log1p, limits for std::numeric_limits).

Fixes #142

[vlarsson]

Thanks for implementing this. If possible, could you run through the posebench suite https://github.com/vlarsson/posebench with and without the fix to confirm there is no regression? Otherwise I can run it too once I find the time.

Thanks again!

[theartful]

Sure, here are the results before:

Datasets: eth3d_130_dusmanu,7scenes_heads,7scenes_stairs,cambridge_landmarks_GreatCourt,cambridge_landmarks_ShopFacade,cambridge_landmarks_KingsCollege,cambridge_landmarks_StMarysChurch,cambridge_landmarks_OldHospital,megadepth1500_sift,megadepth1500_spsg,megadepth1500_splg,megadepth1500_roma,megadepth1500_dkm,megadepth1500_aspanformer,scannet1500_sift,scannet1500_spsg,scannet1500_roma,scannet1500_dkm,scannet1500_aspanformer,imc_british_museum,imc_london_bridge,imc_piazza_san_marco,imc_florence_cathedral_side,imc_milan_cathedral,imc_sagrada_familia,imc_lincoln_memorial_statue,imc_mount_rushmore,imc_st_pauls_cathedral,barath_Alamo,barath_NYC_Library

                AUC0   AUC1   AUC5   med_rot   med_pos   avg_rt   med_rt 
PnP (poselib)  50.51  89.72  96.95   3.3E-01       0.1   12.7ms   11.5ms 
PnP (COLMAP)   50.65  89.70  96.87   3.4E-01       0.1   24.8ms   23.4ms 

              AUC5   AUC10   AUC20   avg_rt   med_rt 
E (poselib)  49.14   63.49   74.70   35.0ms   31.6ms 
E (COLMAP)   42.39   58.69   71.87   46.7ms   39.8ms 
F (poselib)  34.04   47.86   60.51   31.5ms   27.1ms 
F (COLMAP)   29.36   43.16   56.55   20.7ms   15.1ms 

              AUC5   AUC10   AUC20   avg_rt   med_rt 
H (poselib)   0.86    2.54    7.15  583.8us  398.2us 
H (COLMAP)    0.73    2.39    6.82    2.2ms    2.1ms 

after:

Datasets: eth3d_130_dusmanu,7scenes_heads,7scenes_stairs,cambridge_landmarks_GreatCourt,cambridge_landmarks_ShopFacade,cambridge_landmarks_KingsCollege,cambridge_landmarks_StMarysChurch,cambridge_landmarks_OldHospital,megadepth1500_sift,megadepth1500_spsg,megadepth1500_splg,megadepth1500_roma,megadepth1500_dkm,megadepth1500_aspanformer,scannet1500_sift,scannet1500_spsg,scannet1500_roma,scannet1500_dkm,scannet1500_aspanformer,imc_british_museum,imc_london_bridge,imc_piazza_san_marco,imc_florence_cathedral_side,imc_milan_cathedral,imc_sagrada_familia,imc_lincoln_memorial_statue,imc_mount_rushmore,imc_st_pauls_cathedral,barath_Alamo,barath_NYC_Library

                AUC0   AUC1   AUC5   med_rot   med_pos   avg_rt   med_rt 
PnP (poselib)  50.51  89.72  96.95   3.3E-01       0.1   13.9ms   12.6ms 
PnP (COLMAP)   50.65  89.70  96.87   3.4E-01       0.1   27.3ms   25.8ms 

              AUC5   AUC10   AUC20   avg_rt   med_rt 
E (poselib)  49.14   63.49   74.70   35.4ms   32.0ms 
E (COLMAP)   42.39   58.69   71.87   47.1ms   40.2ms 
F (poselib)  34.05   47.86   60.50   31.3ms   27.0ms 
F (COLMAP)   29.36   43.16   56.55   20.9ms   15.2ms 

              AUC5   AUC10   AUC20   avg_rt   med_rt 
H (poselib)   0.86    2.54    7.15  562.7us  383.5us 
H (COLMAP)    0.73    2.39    6.82    2.1ms    2.1ms 

[vlarsson]

LGTM. Thanks for setting this up.