Greyscale encoding is less interesting than RGB because there is less potential for compression. So far, one 8×8 RGB block is encoded with these steps:

- Get the min/max of each component:
// the input data for one 8×8 block: var R=Array(64), G=Array(64), B=Array(64); // scan: var minR=R[O], minG=G[O], minB=B[O], maxR=minR, maxG=minG, maxB=minB; for (var i=1; i<64; i++) { var t=R[i], u=G[i], v=B[i]; if (minR > t) minR = t; if (maxR < t) maxR = t; if (minG > u) minG = t; if (maxG < u) maxG = t; if (minB > v) minB = t; if (maxB < v) maxB = t; }

- Send
**min**/**max**|**R**/**G**/**B**/ right away, or store them somewhere else for further processing. Here it's the case of direct transmission:**min**is encoded right away as a byte,**max**is encoded with phase-out code because it is in the range [**min**..255]send_byte(minR); send_byte(minG); send_byte(minB); maxR -= minR, maxG -= minG; maxB -= minB; send_phaseout(maxR, 255-minR); send_phaseout(maxG, 255-minG); send_phaseout(maxB, 255-minB);

In a more elaborate version, the minX and maxX are collected in another 8×8 array for further processing and compaction. - This step is just for the formal definition but it will be merged with other steps: remove the
**min**X offset from the respective blocksfor (var i=0; i<64; i++) { R[i] -= minR, G[i] -= minG, B[i] -= minB; } // Prediction filter can be applied here too

Now, minX is out out of the way. We'll bother only about the amplitudes after this point. - Sort the component in order of max. amplitude

`var Cmax, Cmed, Cmin; var maxMax, maxMed, maxMin; Cmed = G; // speculative assignation maxMed = maxG; // (used by two cases) // possible cases: BGR, BRG, GBR, GRB, RBG, RGB if (maxR > maxG) { // possible cases: BRG, RBG, RGB Cmin = G; // speculative assignation maxMin = maxG; // (used by two cases) if (maxR > maxB) { // possible cases: RBG, RGB Cmax = R; maxMax = maxR; if (maxG > maxB) { // actual case: RGB Cmin = B; maxMin = maxB; } else { // actual case: RBG // (can goto to case GBR) Cmed = B; maxMed = maxB; } } else { // actual case: BRG Cmax = B; maxMax = maxB; Cmed = R; maxMed = maxR; } } else { // possible cases: BGR, GBR, GRB Cmin = R; // speculative assignation maxMin = maxR; // (used by two cases) if (maxG > maxB) { // possible cases: GRB, GBR Cmax = G; maxMax = maxG; if (maxR > maxB) { // actual case: GRB Cmin = B; maxMin = maxB; Cmed = R; maxMed = maxR; } else { // actual case: GBR Cmed = B; maxMed = maxB; } } else { // actual case: BGR Cmax = B; maxMax = maxB; } }`

*This block of code might look large and scary but it's optimised for fast execution: at most 5 assignations and 3 tests.*

(note that**Cmin**,**Cmed**and**Cmax**are just "pointers", or can be implemented as different types of circuits) - Implement the nested color transformations σα( σα(
**Cmax**,**Cmed**),**Cmin**)- σα(
**Cmax**,**Cmed**) generates- the sum
**S1=Cmax+Cmed**, with limit**L1=maxMax+maxMed**, - the reversed data
**A1**(depending on**Cmed**), with limit**L2≤maxMed**

**A1**and**L2**can be used (almost) immediately or they can be stored in two new arrays for further compaction with 3R. - the sum
- σα(
**S1**,**Cmin**) generates- the sum
**S2=S1+Cmin**, with limit**L3=L1+maxMin**, - the reversed data
**A2**(depending on**Cmin**), with limit**L4≤maxMin**

**A2**and**L4**can be used (almost) immediately or they can be stored in two new arrays for further compaction with 3R. - the sum

- σα(
- For the direct transmission, send the computed values in reverse order of the previous part (to allow decompression)

for (var i=0; i<64; i++) { // (Compute step 5 here) send_phaseout(S2, L3); // Sum send_phaseout(A2, L4); // Cmin send_phaseout(A1, L2); // Cmed }

Notice that certain values do not change within a block (L1, L3 and some parameters of σα), so they can be precomputed before the loop's body. The others require additional temporary storage (S1, A1, L2, A2, L4). - Steps 5 and 6 can also be computed in parallel with a similar version, which uses predictions from the previous neighbours.
- The sizes of the resulting 2 bistreams (with and without prediction) are compared and the largest block is discarded.
- If prediction is used, a single-bit flag must also be set in the prefix of the block. You can't decode the whole block if there is a mix of raw and predicted values.
- The prediction can be computed in step 3 for example.
- Linear prediction is computed modulo the given component's range, such that negative predictions wrap around (but still give a bit-accurate result when added again, modulo the range)

- Both versions (raw and predicted) can also be tentatively encoded with 3R. The order of encoding follows the order in step 6, which allows accurate reconstruction:
- First, the block of the sums
**S2**is processed, with total**MAX = L3<<6**, and individual**MAX=L3**(global for the whole tree, implicit from the data provided in step 2, which also allows to de-shuffle**Cmin**,**Cmed**and**Cmax**) - Then,
**Cmin**is encoded with the individual**A2**s. The individual**L4**are used for the limits, and the total sum is limited by the sum of all**L4**(that depends on**maxMin**and**S2**). - Finally,
**Cmed**is encoded with the individual**A1**s and**L2**s (which can be recovered from the previous steps 8.a and 8.b as well as**maxMed**)

**Cmax**can be recovered later by the subtraction of the previous data.

Of course, another flag must be set to indicate that 3R is used instead of direct encoding. - First, the block of the sums

OK, it looked pretty easy and simple in the beginning and now we're doing pretty complex stuff but in theory, none of these steps should (significantly) expand input data (except for a few control bytes). For both cases of prediction (with/without) the shortest result is chosen.

Another version/approach encodes **S2**, **A2** and **A1** in separate sub-blocks with phasing-out, while at the same time computing the tree sum of the corresponding 3R. This way, each of the block can be selected for the shortest version, in case 3R inflates. The 3R flag is then stored in the first bits of the sub-block.

The number of cases is further increased for the situation of delta-images, with the encoding of the difference with the previous frame. This is possible for pre-computed videos, where a fast computer can compute all 3 cases and choose the best result, while the overhead for the decoder is marginal (only one block to decode, with just a few parameters to change).

Note: for delta-blocks, the parameters **min**X might be dropped because differences are centered around 0. Samples then have to be "folded" to keep them positive.

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