I need to do vertex displacements using a texture map in Three.js.
Vertex displacements using a texture map are supported by THREE.ShaderTerrain[ "terrain" ]
and THREE.ShaderLib[ "normalmap" ]
.
Examples of their use can be found in http://threejs.org/examples/webgl_terrain_dynamic.html and http://threejs.org/examples/webgl_materials_normalmap.html.
If these do not suit your needs, then you will have to write your own shader. Doing so is not easy. It is best to modify an existing shader.
three.js r.61