Hi PEER,

Due to my lack of understanding, your questions seem kind of vague to me.

Are you referring to "integral-image", the Image Intensity Integral?
https://computersciencesource.wordpress.com/2010/09/03/computer-vision-the-integral-image/

Which (blocks of) pixels do you want to add up?.... in relation to your curve?

https://en.wikipedia.org/wiki/Summed-area_table

As the name suggests, the value at any point (x, y) in the summed-area table is the sum of all the pixels above and to the left of (x, y), inclusive:[3][4]
wikipedia has an algorithm.

- Brian

https://www.sciencedirect.com/topics/computer-science/intensity-value

Are the images black and white, greyscale, or color?