# Comparing faces

#### Alexander (Sasha) Pastukhov

#### 2021-10-05

Tridimensional regression can be used to compare face similarity via R2 based on 3D landmarks.

    faces <-
      list("M010"=Face3D_M010,
           "M101"=Face3D_M101,
           "M244"=Face3D_M244,
           "M92"=Face3D_M92,
           "W070"=Face3D_W070,
           "W097"=Face3D_W097,
           "W182"=Face3D_W182,
           "W243"=Face3D_W243)

    face_comparison <-
      dplyr::as_tibble(t(combn(names(faces), 2))) %>%
      rename(Face1 = V1, Face2 = V2 ) %>%
      group_by(Face1, Face2) %>%
      nest() %>%
      mutate(Fit = purrr::map2(Face1,
                               Face2,
                               ~fit_transformation_df(faces[[.x]],
                                                      faces[[.y]],
                                                      transformation ='translation')))
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    face_R2 <-
      face_comparison %>%
      mutate(R2 = purrr::map(Fit, ~R2(.))) %>%
      select(Face1, Face2, R2) %>%
      unnest(cols=c(R2)) %>%
      arrange(desc(R2))

    knitr::kable(face_R2, digits = c(0, 0, 3, 3, 3))

Face1 | Face2 | R2 | R2_5.5 | R2_94.5
--- | --- | --- | --- | ---
W070 | W097 | 0.988 | 0.987 | 0.988
M010 | W243 | 0.984 | 0.984 | 0.985
M244 | W243 | 0.984 | 0.983 | 0.984
W182 | W243 | 0.980 | 0.980 | 0.981
M010 | M92 | 0.979 | 0.978 | 0.980
W097 | W243 | 0.978 | 0.978 | 0.979
M010 | M244 | 0.978 | 0.978 | 0.979
M92 | W243 | 0.975 | 0.975 | 0.976
W070 | W243 | 0.975 | 0.974 | 0.975
M010 | M101 | 0.975 | 0.974 | 0.975
M244 | W182 | 0.975 | 0.973 | 0.975
M92 | W182 | 0.973 | 0.972 | 0.974
M101 | W243 | 0.973 | 0.972 | 0.974
W070 | W182 | 0.972 | 0.971 | 0.973
W097 | W182 | 0.971 | 0.970 | 0.971
M244 | M92 | 0.969 | 0.967 | 0.969
M101 | M244 | 0.967 | 0.966 | 0.968
M010 | W182 | 0.967 | 0.965 | 0.968
M101 | W097 | 0.964 | 0.963 | 0.966
M101 | M92 | 0.962 | 0.961 | 0.963
M101 | W070 | 0.962 | 0.960 | 0.963
M010 | W070 | 0.962 | 0.960 | 0.963
M010 | W097 | 0.961 | 0.959 | 0.962
M244 | W097 | 0.961 | 0.959 | 0.962
M101 | W182 | 0.955 | 0.953 | 0.957
M244 | W070 | 0.955 | 0.953 | 0.956
M92 | W070 | 0.948 | 0.946 | 0.949
M92 | W097 | 0.946 | 0.944 | 0.948

    ggplot(data=face_R2, aes(x=Face1, y=Face2, size=R2, color=R2)) +
      geom_point()