Of course as always there are more ways to do this in any software especially in Houdini. A simple way to do Texture Based Polygon Deformation in Houdini:
In Houdini we can have UVs for vertices (default in any software) but also for Points as well. That’s the key.
Import or create any geometry
Check the attributes If you have UVs that is for the Vertex Attributes part. If you don’t have create some UV (for example UV Unwrap)
Create an Attribute Promote node (you can tell Houdini to get those Vertex UVs and use as Point UVs.)
Original Name: uv
Original Class: Vertex
New Class: Point
Create a Point VOP node (Thats why we need UV coordinates for points)
Inside the Point VOP:
Create a Displace Along Normal node
Create a Texture node, choose your Texture Map (usually you have to change the Source Color Space to Linear)
Create an Add Constant node (you need this to offset the deformation, usually -0.5).
Create a Normal node (put the focus on this to see a better preview when you changing the Point VOP)
Finally you have to copy back the vertex UVs from the original object.
Attribute to Copy: Texture UV
You may want to smooth the normals with a Smooth node to get better deformation.
Constrained Boundary: None
Strength: something high maybe 500 (this could be slow but very useful)
Filter Quality: 1
You can promote a parameter to its parent node by click with the MMB on the name of the parameter (for example the displacement scale inside the Point VOP)
You can use a simple Add node instead the Add Constant and promote the second value parameter for better control.
You can blur your deformation texture (Texture node).
You may want to change the scale of the UV (use a UV Transform node after you get the UVs for Attribute Copy)