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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:

• http://docs.opencv.org/doc/tutorials/imgproc/imgtrans/sobel_derivatives/sobel_derivatives.html#sobel-derivatives
• http://docs.opencv.org/doc/tutorials/imgproc/imgtrans/laplace_operator/laplace_operator.html#laplace-operator
• http://docs.opencv.org/doc/tutorials/imgproc/imgtrans/canny_detector/canny_detector.html#canny-detector

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.

http://docs.opencv.org/doc/tutorials/imgproc/imgtrans/hough_lines/hough_lines.html#hough-lines

Try some stuff out and report back with questions.