Question

I realize both mipmaps and integral images have the problem that the resulting pixel value is not the integral of an arbitrary polygon in original texture space. Integrating over axisaligned rectangle in texture coordinates using integral images requires 4 texture lookups. Using mipmaps, opengl interpolates across the 4 adjacent pixel values in the mipmap so also 4 memory lookups. Using an integral image you need less memory (no extra preresized images, only an integral image instead of the original) and no level determination. Of course this can be implemented through shaders, but why was the (now being deprecated) fixed function pipeline ever designed with mipmap support and no integral image support?

Answer 1

Using an integral image you need less memory

I very much doubt that this statement is true

From what I understand the values of an integral image can get quite large, therefore requiring floating point representation which will use a lot more space than a typical 24bit mipmap (mipmaps only double the size of an image) and/or be less precise and create noise during interpolation. Also floating point images were not really used that often with the fixed function pipeline and GPUs may have been a lot slower with floating point images.

If you would use integers for the picture then the bit-depth required for the integral image would rise unreasonably high (bitdepth = extents+8 for a white image which means a 256×256 image would need a bit-depth of 264bit per color channel) with higher resolution images.