Hi, I have surface slope data which is in the form of a rectangular matrix and i have to integrate the surface slopes to obtain topography

4 views (last 30 days)
In the earlier cases surface slope(partial derivative of Z direction displacement with respect x and partial derivative of Z direction displacement with respect y) measured in 66*99 matrix was integrated along X direction using trapezoidal rule and the same was done with Y direction. This operation helped me to obtain deformation in Z direction. The above procedure was possible because the slopes in the boundaries was zero. In the current problem i do not have boundary conditions well defined and hence the surface slopes at the boundary is not zero. Is there a method i could use to obtain Topography from surface slopes without knowing the boundary conditions?
This is my first experience with posting a question, hence if my question is not clear please let me know.
Thanks.

Answers (1)

Image Analyst
Image Analyst on 22 Aug 2014
I don't know what "obtain Topography" means. If you want the volume under the surface, why not just sum the image:
volume = sum(grayImage(:));
You don't have to take slopes. Imagine that your surface is in 2.5D like the city of Manhattan (NYC). If you want the volume of the city, you could add up the volume of all the square buildings (pixels) in it. Or you could put pieces of plywood from the center of the roof of each building to the centers of rooves on the 4 buildings on adjacent sides, and calculate the area under the slanted pieces of plywood. Obviously this is a lot harder than just assuming flat-topped buildings and summing the building heights. The two methods will give different volumes. Is one necessarily more correct than the other? No. Either one may suit you well with whatever you want to do with the volume number - it's up to you.
  2 Comments
amith
amith on 22 Aug 2014
Thank you.
Let me rephrase my question for better understanding. My experiments involve digital image co-relation techniques to measure surface slopes(2D). Hence I am looking for a way to integrate these slope values which is in the form of a matrix to obtain the surface deformation.
Integration of surface slopes will give me deformation when the boundary conditions are known. But in this particular case boundary conditions are not known hence integration is a bit tricky.
Thanks.
Image Analyst
Image Analyst on 22 Aug 2014
Sorry - I've never heard of the "digital image co-relation technique to measure surface slopes". I don't know how it works or what it expects for boundary conditions. Good luck.

Sign in to comment.

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!