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Bilateral / anisotropic filtering of gradient field

Source: R/utils_gradients.R
smooth_field.Rd

Gradient fields are smoothed using bilateral filtering, in which the smoothed gradient of each point is computed as the weighted average of the neighbors' gradients, considering both distance in space and also similarity in gradients.

Usage

smooth_field(
  coords,
  field,
  adj,
  include_self = TRUE,
  distance = "euclidean",
  similarity = "euclidean"
)

Arguments

coords

A N x 2 matrix of cell coordinates.

field

A 2 x D x N array in column-major ordering containing the spatial gradient in expression for each of D latent variables at every point in space.

adj

A N x N sparse adjacency matrix in dgCMatrix format.

include_self

A boolean whether or not to include the each point's gradient in its own smoothed value. Defaults to TRUE.

distance

Method for computing distance score in weighted average. See description for details. Defaults to 'euclidean'.

similarity

Method for computing similarity score in weighted average. See description for details. Defaults to 'euclidean'.

Value

A 2 x D x N array in column-major ordering containing the smoothed spatial gradient in expression for each of D latent variables at every point in space.

Details

The weight of each neighbor is computed from the product of two scores:

  • distance score: Generally, closer neighbors have greater weight.

    • if 'euclidean': Gaussian transformation of the Euclidean distance of a cell from its neighbor, so that more distant neighbors have less weight.

    • if 'projected': An anisotropic filter that accounts for expected change in expression along the direction of the neighbor. The expected change in expression is calculated from the gradient field as the total derivative in the direction of the neighbor. This change in expression is then Gaussian transformed so that neighbors that are more distant along the direction of greatest change have less weight.

    • if 'constant': All neighbors have equal distance weights

  • similarity score: Generally, neighbors with more similar gradients have greater weight

    • if 'euclidean': Gaussian transformation of the Euclidean distance between a cell's gradient field and its neighbor's gradient field.

    • if 'projected': Gaussian transformation of the cosine distance between a cell's gradient field and its neighbor's gradient field.

    • if 'constant': All neighbors have equal similarity weights