Expand point information to binary raster

Good day,

I've point information located arbitrarily and a binary raster. My aim is now to expand the point information, which is unique from point to point, to the extent of the ones of the binary raster. Two ideas came to my mind to expand the point information consistently and in some terms weighted.

Idea 1: Region Growing where the point information grows from neighbour to neighbour until it hits zeros (boundary) or already overwritten neighbours.

Idea 2: Voronoi of these points which separates the space weighted with subsequent filling of the regions

To illustrate the situation I append a doodle. The points are red and black is the boundary of the region with ones (actually it inner part should be black as well, but I think you get the idea)

My question is now, if there's an easier way to accomplish this task.

Thank you