Compute Functional Gradient from Feature Matrix

Calculates the functional gradient for each voxel as the average dissimilarity to its spatial neighbors in feature space. Low gradient values indicate stable, homogeneous regions (good seed locations); high values indicate boundaries.

Usage

compute_functional_gradient(feature_mat, coords, k_neighbors = 26)

Arguments

feature_mat

Numeric matrix (N x M) of features (voxels x dimensions).

coords

Numeric matrix (N x 3) of spatial coordinates.

k_neighbors

Integer; number of nearest spatial neighbors to use. Default: 26.

Value

Numeric vector of length N containing gradient values for each voxel.

Details

For each voxel i, the functional gradient is: $$grad(i) = \frac{1}{k} \sum_{j \in N_k(i)} (1 - f_i \cdot f_j)$$

where \(N_k(i)\) are the k nearest spatial neighbors and \(f_i \cdot f_j\) is the dot product (cosine similarity for unit-length vectors).

Examples

if (FALSE) { # \dontrun{
features <- matrix(rnorm(500 * 15), 500, 15)
features <- t(apply(features, 1, function(x) x / sqrt(sum(x^2))))
coords <- matrix(rnorm(500 * 3), 500, 3)

grad <- compute_functional_gradient(features, coords, k_neighbors = 26)
hist(grad, breaks = 50, main = "Functional Gradient Distribution")
} # }