5.13.3 High Resolution Filtering

The accumulation buffer can be used to convolve a high resolution filter with a relatively small image under magnification. That is what we need to make the different octaves; the octave representing the lowest frequency band will be created from a very small input image under large magnification. Suppose we want to create a 512x512 output image by convolving a 64x64 filter with a 4x4 input image. Our filter takes a 2x2 array of samples from the input image at a time, but is discretized into 64x64 values in order to generate an output image of the desired size. The input image is shown on the left in Figure 17 with each texel numbered. The output image is shown on the left in Figure  18. Note that each texel of the input image will make a contribution to a 64x64 region of the output image. Consider these regions for texels 5, 7, 13, and 15 of the input image; they are adjacent to each other and have no overlap, as shown by the dotted lines on the left in Figure  18. Hence, these four texels can be evaluated in the same pass without interfering with each other. Making use of this fact, we redistribute the texels of the input image into four 2x2 textures as shown in the right of Figure 17. We also create a 64x64 texture that contains the filter function; this texture will be used to modulate the contribution of the input texel over a 64x64 region of the color buffer. The steps to evaluate the texels in Texture D are:

1. Using the filter texture, draw four filter functions into the alpha planes with the appropriate x and y offset, as shown on the right in Figure  18
2. Enable alpha blending and set the source blend factor to GL_DST_ALPHA and the destination blend factor to GL_ZERO.
3. Set the texture magnification filter to GL_NEAREST.
4. Draw a rectangle to the dotted region with Texture D, noting the offset of 64 pixels in both x and y.
5. Accumulate the result into the accumulation buffer.

Repeat the above procedure for Textures A, B, and C with the appropriate x and y offsets, and return the contents of the accumulation buffer to the color buffer.

A wider filter requires more passes of the above procedure, and also requires that the original texture be divided into more small textures. For example, if we had chosen a filter that covers a 4x4 array of input samples instead of 2x2, we would have to make 16 passes instead of 4, and we would have to distribute the texels into 16 1x1 textures. Increasing the size of either the output image or the input image, however, has no effect on the number of passes.