Visualizing ETC1 block encoding error as a 4D function

Given a particular 4x4 pixel block, what does the error of all possible ETC1 5:5:5 base color+3-bit intensity encodings look like? The resulting 4D visualization could inspire better optimization algorithms.

To compute these images, I created an ETC1 block in differential mode (5:5:5 base color with a 3:3:3 delta), set the base color to R,G,B, the diff color to (0,0,0), and set both subblock intensity table values to the same index from 0-7. I then encoded the source pixels (by finding the optimal selectors for each pixel), decoded them, and computed the overall block error (as perceptually R,G,B weighted color distance).

These visualizations are linear, where the brightest value (255) is max error, black is 0 error. The blocks used to compute each visualization are here too:

Finding the "best" block color+intensity table index to use in a subblock is basically a 4D search through functions like above. Hill climbing optimization seems useful, except for those pesky local minimums. For fun, I've already tried random-restart hill climbing, and it works, but there's got to be a better way.

rg_etc1 starts at the block's average color and scans outwards along the RGB axes, trying to find better colors. It always tries all 8 intensity tables every time it tries a candidate color (which in retrospect seems wildly inefficient, but hey I wrote it over a weekend years ago). It also has several refinement steps. One of them factors in the selectors of the best color found so far, in an attempt to improve the current block color. rg_etc1 ran circles around Mali's reference encoder, from what I remember, which was my goal.