Kinect SDK 1.8 does not provide this feature itself (to my knowledge). Depending on the language which you use for coding, there most certainly are libraries which allow such an operation if you segment it into steps.
OpenCV for example is quite useful in image-processing. When I once worked with the Kinect for object recognition, I used AForge with C#.
I recommend to target the challenge as follows:
Edge Detection:
You will apply edge detection algorithms such as the Canny Filter onto the image. First you will probably - depending on the library - transform your depth picture into a greyscale picture. The resulting image will be greyscale as well and the intensity of a pixel correlates with the probability of it belonging to an edge. Using a threshold, you will binarize this picture to black/white.
Hough Transformation: is used to get the position and parameters of a line within a image, which allows further calculation. Hough Transformation is VERY sensistive to its parameters and you will spend a lot of time in tuning those to get good results.
Calculation of edge points: Assuming that your Hough Transformation was successful, you can now calculate all intersections or the given lines which will yield the points that you are looking for.
All of these steps (especially Edge Detection and Hough Transformation) have been asked/answered/discussed in this forum.
If you provide code and intermediate results or further question, you can get a more detailled answer.
p.s.
I remember that the kinect was not that accurate and that noise was a topic. Therefore you might consider using a filter before doing these operations.