ETC1S texture format encoding and how it's transcoded to BC1

I developed the ETC1S encoding method back in late 2016, and we talked about it publicly in our CppCon '16 presentation. It's good to see that this encoding is working well in crunch too (better bitrate for near equal error). There are kodim statistics on Alexander's checkin notes:

https://github.com/Unity-Technologies/crunch/commit/660322d3a611782202202ac00109fbd1a10d7602

I described the format details and asked Alexander to support ETC1S so we could add universal support to crunch.

Anyhow, ETC1S is great because it enables simplified transcoding to BC1 using a couple small lookup tables (one for the 5 bit DXT1 components, and the other for 6). You can precompute the best DXT1 component low/high endpoints to use for each possibility of used ETC1S selectors (or low/high selector "ranges") and ways of remapping the ETC1S selectors to DXT1 selectors. The method I came up with supports a strong subset of these possible mapping (6 low/high selector ranges and 10 selector remappings).

So the basic idea to this transcoder design is that we'll figure out the near-optimal DXT1 low/high endpoints to use for a ETC1S block, then just translate the ETC1S selectors through a remapping table. We don't need to do any expensive R,G,B vector calculations here, just simple math on endpoint components and selectors. To find the best endpoints, we need the ETC1S base color (5,5,5), intensity table index (3 bits), and the used selector range (because ETC1/ETC1S heavily depends on endpoint extrapolation to reduce overall error, so for example sometimes the encoder will only use a single selector in the "middle" of the intensity range).

First, here are the most used selector ranges used by the transcoder:
{ 0, 3 },
{ 1, 3 },
{ 0, 2 },
{ 1, 2 },
{ 2, 3 },
{ 0, 1 },

And here are the selector remapping tables:
{ 0, 0, 1, 1 },
{ 0, 0, 1, 2 },
{ 0, 0, 1, 3 },
{ 0, 0, 2, 3 },
{ 0, 1, 1, 1 },
{ 0, 1, 2, 2 },
{ 0, 1, 2, 3 },
{ 0, 2, 3, 3 },
{ 1, 2, 2, 2 },
{ 1, 2, 3, 3 },

So what does this stuff mean? In the first table, the first entry is { 0, 3 }. This index is used for blocks that use all 4 selectors. The 2nd one is for blocks that only use selectors 1-3, etc. We could support all possible ways that the 4 selectors could be used, but you reach a point of diminishing returns.

The second table is used to translate ETC1S selectors to DXT1 selectors. Again, we could support all possible ways of remapping selectors, but only a few are needed in practice.

So to translate an ETC1S block to BC1/DXT1:

- Scan the ETC1S selectors (which range from 0-3) to identify their low/high range, and map this to the best entry in the first table. This is the selector range table index, from 0-5.
(For crunch/basis this is precomputed for each selector codebook entry, so we don't need to do it for each block.)

- Now we have a selector range (0-5), three ETC1S base color components (5-bits each) and an ETC1S intensity table index (3-bits). We have a set of 10 precomputed tables (for each supported way of remapping the selectors from ETC1S->DXT1) for each selector_range/basecolor/inten_table possibility (6*32*8*10=15360 total tables).

- Each table entry has a DXT1 low/high endpoint values (either 5 or 6 bits) and an error value. But this is only for a single component, so we need to scan the 10 entries (for each possible way of remapping the selectors from ETC1S->DXT1) for all components, sum up their total R+G+B error, and use the selector remapping method that minimizes the overall error. (We can only select 1 way to remap the selectors, because there's only a single selector for each pixel.) The best way of remapping the selectors for R may not be the best way for G or B, so we need to try all 10 ways we support, compute the error for each, and select the best one that minimizes the overall error.

In code:

// Get the best selector range table entry to use for the ETC1S block:

const uint selector_range_table = g_etc1_to_dxt1_selector_range_index[low_selector][high_selector];

// Now get pointers to the precomputed tables for each component:

//[32][8][RANGES][MAPPING]

const etc1_to_dxt1_56_solution *pTable_r = &g_etc1_to_dxt_5[(inten_table * 32 + base_color.r) * (NUM_ETC1_TO_DXT1_SELECTOR_RANGES * NUM_ETC1_TO_DXT1_SELECTOR_MAPPINGS) + selector_range_table * NUM_ETC1_TO_DXT1_SELECTOR_MAPPINGS];

const etc1_to_dxt1_56_solution *pTable_g = &g_etc1_to_dxt_6[(inten_table * 32 + base_color.g) * (NUM_ETC1_TO_DXT1_SELECTOR_RANGES * NUM_ETC1_TO_DXT1_SELECTOR_MAPPINGS) + selector_range_table * NUM_ETC1_TO_DXT1_SELECTOR_MAPPINGS];

const etc1_to_dxt1_56_solution *pTable_b = &g_etc1_to_dxt_5[(inten_table * 32 + base_color.b) * (NUM_ETC1_TO_DXT1_SELECTOR_RANGES * NUM_ETC1_TO_DXT1_SELECTOR_MAPPINGS) + selector_range_table * NUM_ETC1_TO_DXT1_SELECTOR_MAPPINGS];

// Scan to find the best remapping table (from 10) to use:

uint best_err = UINT_MAX;

uint best_mapping = 0;

CRND_ASSERT(NUM_ETC1_TO_DXT1_SELECTOR_MAPPINGS == 10);

#define DO_ITER(m) { uint total_err = pTable_r[m].m_err + pTable_g[m].m_err + pTable_b[m].m_err; if (total_err < best_err) { best_err = total_err; best_mapping = m; } }

DO_ITER(0); DO_ITER(1); DO_ITER(2); DO_ITER(3); DO_ITER(4);

DO_ITER(5); DO_ITER(6); DO_ITER(7); DO_ITER(8); DO_ITER(9);

#undef DO_ITER

// Now create the DXT1 endpoints

uint l = dxt1_block::pack_unscaled_color(pTable_r[best_mapping].m_lo, pTable_g[best_mapping].m_lo, pTable_b[best_mapping].m_lo);

uint h = dxt1_block::pack_unscaled_color(pTable_r[best_mapping].m_hi, pTable_g[best_mapping].m_hi, pTable_b[best_mapping].m_hi);

// pSelector_xlat is used to translate the ETC1S selectors to DXT1 selectors

const uint8 *pSelectors_xlat = &g_etc1_to_dxt1_selector_mappings1[best_mapping][0];

if (l < h)

{

std::swap(l, h);

pSelectors_xlat = &g_etc1_to_dxt1_selector_mappings2[best_mapping][0];

}

pDst_block->set_low_color(static_cast<uint16>(l));

pDst_block->set_high_color(static_cast<uint16>(h));

// Now use pSelectors_xlat[] to translate the selectors and we're done

If the block only uses a single selector, it's a fixed color block and you can use a separate set of precomputed tables (like stb_dxt uses) to convert it to the optimal DXT1 color.

So that's it. It's a fast and simple process to convert ETC1S->DXT1. The results look very good, and are within a fraction of a dB between ETC1S and BC1. You can also use this process to convert ETC1S->BC7, etc.

Once you understand this process, almost everything else falls into place for the universal format. ETC1S->BC1 and ETC1S->PVRTC are the key transcoders, and all other formats use these basic ideas.

There are surely other "base" formats we could choose. I choose ETC1S because I already had a strong encoder for this format and because it's transcodable to BC1.

You can see the actual code here, in function convert_etc1_to_dxt1().

It's possible to add BC7-style pbits to ETC1S (1 or 3) to improve quality. Transcoders can decide to use these pbits, or not.