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morph surface

hi
i need to create an animation that will deform a flat wall into something similar to the next image >

ecf6d7869fa2b6b5e5223d9838506c60d0162802.jpeg

i need to control the animation with something similar to “lerp”
from flat (lerp 0.0) to the shape of the image (lerp 1.0)

Can you suggest how i could make this effect ?

previously i was trying to use tesellation on the material but that wont allow to have a convex shape ,
will this has to be done with morph target or does it exist a way to morph a plane into a complex shape ?