Model the agar background and correct uneven illumination

Estimates the colour of the agar, removes the spatial illumination gradient (vignetting, oblique light) by flat-field correction, and flags every dish pixel that differs significantly from agar.

Usage

model_background(
  plate,
  flat_field = TRUE,
  degree = 2L,
  max_clipped_fraction = 0.02,
  min_delta_e = 3,
  texture_z = 4,
  shadow_texture_z = 2.5,
  smooth_mm = 0.08,
  feature_smooth_mm = 0.25,
  reference = NULL,
  reference_lab = c(50, 0, 0)
)

Arguments

plate: A funmel_plate with a detected dish.
flat_field: Logical; request the illumination correction. The fitted correction is applied only if it passes the max_clipped_fraction check below; plate$bg$flat_field records whether it was actually applied.
degree: Polynomial degree of the illumination surface (1 or 2).
max_clipped_fraction: Largest fraction of dish pixels whose fitted gain may reach the correction limits (0.5x-2x) before the whole correction is judged degenerate and withheld. A correction that saturates over a substantial part of the dish is not a mild illumination gradient: it rescales colonies by a position-dependent factor and shifts MI by several units, which would be read as a melanization difference. This can occur with reflections or strongly nonuniform backgrounds. Gain saturation alone does not identify the cause of the failed fit. Use Inf to apply the correction unconditionally, and inspect flat_field_status in the plate summary either way.
min_delta_e: Minimum CIE76 colour difference from agar for a pixel to be considered object.
texture_z: Robust z-score of log local texture (relative to agar) above which a pixel is an object even if its colour matches the agar.
shadow_texture_z: Pixels darker than agar, with agar-like chromaticity and texture z below this value are cast shadows of raised colonies and are excluded (set -Inf to disable).
smooth_mm: Gaussian smoothing (mm) of colour used for object detection (measurements always use unsmoothed pixels).
feature_smooth_mm: Gaussian smoothing (mm) of colour used as classification feature; averages over hyphal ridges and valleys so a wrinkled colony is described by its mean colour.
reference: Optional exposure / white-balance reference applied after flat-field correction: a grey-card region c(x, y, r) in relative image coordinates (see calibrate_color()), or "agar" to scale the image so that the agar takes the colour reference_lab (only valid when all plates use the same medium batch and the agar is not tinted).
reference_lab: Known CIELAB of the reference.

Value

The plate with corrected rgb/lab and an element bg.

Details

1. Agar colour by mode seeking. The agar is the most frequent colour inside the dish even on crowded confrontation plates, because agar pixels are concentrated in colour space while colonies, bacteria and hyphae are spread along gradients. The mode of the (smoothed) $L^*a^*b^*$ distribution of low-texture pixels is found with a coarse 3-D histogram followed by mean-shift refinement (Comaniciu & Meer 2002). It works on dark and on light agar.

2. Flat-field correction. Illumination acts multiplicatively on linear light. For each linear RGB channel c a quadratic surface $\log I_c(x, y) = \beta_0 + \beta_1 x + \beta_2 y + \beta_3 x^2 + \beta_4 xy + \beta_5 y^2$ is fitted to agar pixels with iterative 3-MAD trimming, and every pixel is multiplied by $\exp(\hat\ell_c(x_0, y_0) - \hat\ell_c(x, y))$, i.e. normalised to the illumination at the dish centre. Because the correction is estimated from agar around the colonies and applied to the colonies, colony lightness is adjusted for the fitted spatial surface. This does not prove that remaining lighting or exposure differences have been removed.

3. Object detection. After correction the agar has a spatially constant colour $\mu$ with per-channel robust SD $\sigma$ (MAD). A pixel is object (non-agar) if its standardised distance $D^2 = \sum_c ((x_c - \mu_c)/\sigma_c)^2$ exceeds the 0.999 quantile of $\chi^2_3$ and its colour difference exceeds min_delta_e (default 3, just above the ~2.3 just-noticeable difference), so that neither sensor noise nor imperceptible tints are called objects. In addition, a pixel is object when its local texture (SD of $L^*$ in a ~0.2 mm window, log scale) exceeds the agar texture by more than texture_z robust standard deviations: strongly melanized, wrinkled colonies can have almost the mean colour of a dark agar but are far rougher. Cast shadows of raised colonies (darker than agar, agar-like chromaticity, smooth) are removed from the objects: under directional light they would otherwise be counted as melanized tissue on one side of every colony.

Examples

sim <- simulate_plate(width = 300, height = 400, seed = 3, vignetting = 0.3)
p <- detect_plate(read_plate(sim$image))
p <- model_background(p)
p$bg$agar_lab
#>          L          a          b 
#> 22.2716888 -0.9644315 -3.8346218 
p$bg$illumination_range_pct
#> [1] 28.25772