From flat image to pseudo-3D, how to manage a texture/depth map couple ?

Hello everybody,

I read Unity forums for a long time now, getting almost all of my questions answered by a topic after few researches. However, my last issue is a dead-end in terms of documentation, certainly limited by my relative recent experience with Unity.

This is my simple (according to me) problem: I have a flat image I want to use as texture on a basic plane. Following an transparent/diffuse effect to make the transparent background of the texture disappear, I'd like to add a 3D effect to the image..! For that, I thought that a depth map (greyscale image) of the same texture would be enough to bring some 3D reliefs in the image... I tried to do that by using Render Texture + another camera different from my main one but couldn't achieve to have any effect... Is my thinking path correct ? Does someone already performed these kind of effects for a single image ? Basically and to sum up, the desired effect would be close to a height map applied to a terrain but without the squared limitation as well as the orientation one..!

Thanks in advance for your help ;)