Bottle outlines with elliptic Fourier transform coefficients

A dataset containing 40 bottle outlines that have been preprocessed and transformed using elliptic Fourier analysis. This dataset is used for demonstrating statistical methods in Momstats.

Usage

boteft

Format

A tibble with 40 rows and 5 variables:

• coo: List-column of class c("out", "coo", "list") containing outline coordinates (nx2 matrices). Outlines have been centered, scaled to unit centroid size, aligned using PCA, and rotated so the rightmost point is at 0 radians.

• coe: List-column of class c("eft", "coe", "list") containing elliptic Fourier transform coefficients. Each element is a named numeric vector with 24 coefficients (6 harmonics × 4 coefficients: A, B, C, D) representing the shape in Fourier space.

• type: Factor with 2 levels ("whisky", "beer") indicating bottle type.

• fake: Factor with 1 level ("a") - a dummy grouping variable for examples.

• price : Numeric with random prices

• length: Numeric vector containing the length of each outline along the major inertia axis (computed before standardization, also random because it ultimately depends on the size of original images in pixels...)

Source

Obtained with:

bot %>%
  mutate(length=unlist(get_length(coo))) %>%
  coo_center() %>% coo_scale() %>% coo_align() %>%
  coo_slide_direction("right") %>%
  eft(6) %>% relocate(coe, .after=coo) -> boteft

See also

• Momocs2::bot for the original unprocessed bottle outlines

• Momocs2::unfold() to expand coefficient columns for analysis

• Momocs2::fold() for the opposite transformation

Examples

# View structure
boteft
#> # A tibble: 40 × 7
#>    id           coo       coe   type   fake  price length
#>    <chr>        <out>     <eft> <fct>  <fct> <dbl>  <dbl>
#>  1 brahma       (138 x 2) <24>  whisky a       3    1088.
#>  2 caney        (168 x 2) <24>  whisky a       1.2   994.
#>  3 chimay       (189 x 2) <24>  whisky a       3.8   644.
#>  4 corona       (129 x 2) <24>  whisky a       2.6   806.
#>  5 deusventrue  (152 x 2) <24>  whisky a       1.1   886.
#>  6 duvel        (161 x 2) <24>  whisky a       3.1   606.
#>  7 franziskaner (124 x 2) <24>  whisky a       2.6   865.
#>  8 grimbergen   (126 x 2) <24>  whisky a       2.9   765.
#>  9 guiness      (183 x 2) <24>  whisky a       1.2   742.
#> 10 hoegardeen   (193 x 2) <24>  whisky a       3.6  1048.
#> # ℹ 30 more rows

# Examine coefficient structure
class(boteft$coe)
#> [1] "eft"  "coe"  "list"
class(boteft$coe[[1]])
#> [1] "eft"     "numeric"
boteft$coe[[1]]
#>            A1            A2            A3            A4            A5 
#>  1.3427539129  0.0090863444  0.1248632443  0.0183772998  0.0314900219 
#>            A6            B1            B2            B3            B4 
#>  0.0113182436  0.0469665913  0.0003981801  0.0136025769  0.0019011705 
#>            B5            B6            C1            C2            C3 
#>  0.0057056253  0.0022844660  0.0134712409 -0.0021381830  0.0126151941 
#>            C4            C5            C6            D1            D2 
#> -0.0139137033  0.0110247077  0.0084896655 -0.3943943267  0.0618459428 
#>            D3            D4            D5            D6 
#> -0.0694671431  0.0465708687 -0.0526203987 -0.0140823150 
#> attr(,"class")
#> [1] "eft"     "numeric"

# Unfold coefficients for statistical analysis
boteft_unfolded <- unfold(boteft, coe)

# Or without prefix
boteft_unfolded <- unfold(boteft, coe, .prefix = "")

# Principal component analysis on coefficients
# pca_result <- stat_pca(boteft)

# Linear discriminant analysis by bottle type
# lda_result <- stat_lda(boteft, type)