Part 1: Introduction to Displace
Skill level: Intermediate/Advanced
When I first got my hands on Photoshop, I headed for the filter menu to investigate some of the nifty things I could do with my images. As I worked my way down the available filter list, I eventually came to "Distort".
In there I found a list of goodies that looked very interesting. One by one I clicked to find out what each would do. Then I came to "Displace..."

Without hesitation, I clicked and was presented with a rather strange dialog box asking me to provide some completely foreign parameters.

OK!
Next I was presented with a standard file selection dialog asking me to "Choose a displacement map"!
"Huh? A displacement map? What's that?", I pondered.
CANCEL!
"I'll have to look into this Displace thing and come back to it later."
Eventually, that's exactly what I did and this is what I learned.
The Displace filter has been around ever since Photoshop 2.0. It's sole purpose is to move pixels within your image. It does this with the guidance of a "displacement map", a separate Photoshop document that essentially tells Displace which pixels to move as well as how far and in what direction to move them.
The tool itself hasn't changed much since it's introduction. There is no preview while working with it, making it a rather awkward tool to use. Arriving at a desired end is pretty much a trial and error affair. However, armed with a knowledge of it's inner workings, your chances of success will be greatly improved.
Conversely, you can conform an object to a texture. E.g., say you want to paint an American flag onto a brick wall.
(Note: I typically use Windows keyboard shortcuts, but for the most part, I will show CS5 menu commands herein for clarity.)
1. Open the brick wall image.
2. On a new layer, paste and fit the flag as desired. Mode: Multiply; Opacity: 70%.

To make the displacement map:
1. In a new document, open the same brick wall image.
2. Desaturate it.
3. To prevent pixel ripping when applying the map, apply a slight Gausian Blur (1-2 pixels should suffice).
4. Convert to grayscale mode. (Click Image > Mode > Grayscale.)
5. Save as a .PSD file (ensure Maximum Compatibility is enabled).

1. Back on your WIP image, with the flag layer selected, click Filter > Distort > Displace. In the parameter dialog, the default values of 10%, 10%, Stretch to fit and Repeat edge pixels will suffice in this case. OK
2. Locate the map you just made. OPEN

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