Combine multiple distorted images with Image Magick to create a final rendering IM ImageMagick

Task: Build a software where a user can post an image to our API and return a render via an API call. This task can be accomplished with 3 layers: 1) The first layer is the bottom-most base layer. We will provide a rendering of a white/raw product in ordinary light. 2) The second layer is the middle layer. We will paint an absolute displacement map on a product that with only diffuse (ambient) light, so the rendering doesn't change the colours of the absolute displacement map. 3) Lastly, the third layer is the top layer. We will provide a rendering of the product with the specular reflections (if any), and a mask. We then need Image Magick to distort the image according to the displacement mapping and combine it with the other renderings.