Image-based 3D reconstruction remains a competitive field of research as state-of-the-art algorithms continue to improve. This paper presents a voxel-based algorithm that adapts the earliest space-carving methods and utilises a minimal surface technique to obtain a cleaner result. Embedded Voxel Colouring is built in two stages: (a) progressive voxel carving is used to build a volume of embedded surfaces and (b) the volume is processed to obtain a surface that maximises photo-consistency data in the volume. This algorithm combines the strengths of classical carving techniques with those of minimal surface approaches. We require only a single pass through the voxel volume, this significantly reduces computation time and is the key to the speed of our approach. We also specify three requirements for volumetric reconstruction: monotonic carving order, causality of carving and water-tightness. Experimental results are presented that demonstrate the strengths of this approach.