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What you basically are telling us is that you probably have a school assignment to implement this stuff on your computer and you want us to provide you with a solution. Because I think that people learn more by actually trying, I will set you on the right way.

The orientation map is created by looking at the rough surface of the finger. You want to create a representation of the most specific edges in the image.

So have a look into edge detection algorithms:

After you have segmented out edges, create a binary image from that. You could use the binary image to match linear Hough Transforms to detects lines, straight parts and see if that gets you anywhere.

Try some stuff out and report back with questions.