Voronoi Label N

Tool for drawing a Voronoi label matrix given a set of centroids. Creates an N-D Voronoi diagram label matrix from input centroid coordinates. May be used directly on pixel coordinate centroids, or used on arbitrary numeric coordinate centroids with args 2-4.

Two methods are available:

1. "coordinates" - uses a compute- and memory-intensive direct computation of nearest centroid to each element. Labels all elements, biased towards smaller valued labels when there is a tie. Complexity is O(M*N*P) where M is the number of centroids, N is the number of dimensions, P is the number of elements in the output image. Suitable if Image Processing Toolbox is not available.
2. "watershed" - uses a faster, less-memory-intensive computation using optimized image processing algorithms bwdist() and watershed(). Prefer this method if Image Processing Toolbox is available, it is about twice as fast.

Usage:

1. Pixel coordinates, call with 1st arg only, or with 1st and 5th (args 2-4 empty arrays).
2. Arbitrary coordinates, call with 2nd arg to give shape, 3rd to give origin and 4th to scale pixels/voxels.

% direct
labels = voronoi_labeln(centroids) % implied shape
labels = voronoi_labeln(centroids, shape) % explicit shape
labels = voronoi_labeln(centroids, shape, [], px_len) % scale
labels = voronoi_labeln(centroids, shape, origin, []) % translate
labels = voronoi_labeln(centroids, shape, origin, px_len) % both

% watershed
labels = voronoi_labels(centroids, [], [], [], "watershed")
labels = voronoi_labels(centroids, shape, [], [], "watershed")
% ... etc.