# Integrating An Arbirtary Field inside a Circle (Formulation Only)

I have a 2D mapping of some field that is parametrized by $$x$$ & $$y$$, $$F(x,y)$$. I want to integrate the values of the field that lie within a circle of radius $$r$$ and centered at $$(x,y)$$. How shall I formulate? I am interested in formulating the problem only. The following figure provides illustration.

Note: The field is a blackbox function so we cant evaluate integral directly.

• Do you require subpixel accuracy ? – Yves Daoust May 7 at 13:33
• @YvesDaoust Not really because the final measure shall be more or less an estimate – GENIVI-LEARNER May 7 at 16:49
• Then average the pixels such that $(x-x_c)^2+(y-y_c)^2\le r^2$. – Yves Daoust May 7 at 16:52
• Allright. If I have to have subpixel accuracy, how shall I go about then instead? – GENIVI-LEARNER May 7 at 21:43
• You need to weigh the pixels on the outline with an estimate of the overlapped area. – Yves Daoust May 8 at 6:22