Computation of partial derivatives from an image

Partial derivatives are easily computed analytically assuming that all the geometric information is known. However, there are computational difficulties in getting accurate partial derivatives directly from a range image since an image is a discrete version of continuous data contaminated with some noise. In this paper, we develop a general window function to compute partial derivatives based on the least square surface fitting method. A dynamic selective surface fitting method is introduced to make the window less sensitive to noise. Any degree of partial derivative can be obtained by a simple convolution between an image and window functions.