Convert simple isometric image to 3D

Question

I'm curious how one would deduce 3D coordinates in simple isometric images. The only approach I could come up with is to do depth-first searches to find the vertices of each face and then use complex branching logic to figure out the vertex position from all the possibilities there are for how faces can be partially hidden. What would be a better approach to go about this?

This is just for hobby, so I'm fine with simplifying the problem further (say by requiring the scene to be composed of only unit voxels or by giving the solution only as coordinates of the midpoints of individual voxels instead of giving the coordinates and their face indices in counter-clockwise order).

I'd assume the input to be given as a matrix of the five different colors I use in the picture. As output I'd expect a list of 3D coordinates, possibly accompanied by a list of coordinate indices for the faces.

Answer 1

I assume that you are able to detect all edges and their direction (among six possilbe). Also if they are complete or occluded. And detect the vertices, so that you get a 2D graph.

Assign the coordinates (0, 0, 0) to some point, such as the lowest vertex. Then following every complete edge from the already known points, you will obtain the coordinates of the endpoints by considering the edge direction (and possibly length) and you will know which coordinate to increment/decrement.

In the end, you will get all coordinates of the endpoints of the complete edges, tell the complete faces, and be able to tell the occluded faces.