This change improves the compression speed for DXT encoding.
Explanation:
In order to evaluate an endpoint solution, it is necessary to compute the sum of the squared distances from the source pixels to their nearest block colors, defined by the evaluated endpoint solution. Considering that we are looking for a solution with a minimal sum, the computation can be stopped as soon as the current sum is higher or equal than the previously found best sum. An interesting observation here is that the performance improvement, achieved by such early out approach, depends on the order in which the source pixels are processed. It makes sense to process the pixels with the highest introduced errors first, as this significantly increases the chances to exit the computation earlier.
On the one hand, equal source pixels are grouped together, so the computed distance from each unique source pixel is multiplied by its weight. For this reason it makes sense to first process the pixels with the highest weights, as their errors have the highest multipliers. On the other hand, the pixels which project onto the middle part of the endpoint interval, have higher chances of being close to one of the block colors. For this reason it makes sense to first process the pixels, which projections are the most distant from the middle of the endpoint interval, as those pixels will normally introduce the highest errors. In order to combine those two aspects, it is proposed to sort the pixels according to the multiplication of the weight and the distance from the projected pixel to the center of the endpoint interval.
Of course, reordering the pixels on each iteration would be very expensive and is not considered. However, there is a high chance that most endpoint intervals will be aligned in a similar way as the principle axis, as well as have their centers close to the mean color. As soon as the principle axis is computed, it can be used for approximation of all the future endpoint intervals. So the projection and reordering of the source pixels is performed only once.
Two approaches have been considered. In the first approach, the pixels have been sorted by the multiplication of the weight and the absolute distance in decreasing order. In the second approach, the pixels have been sorted by the multiplication of the weight and the signed distance, and then interleaved starting from the opposite sides of the ordered sequence. When tested on the Kodak image set, the interleaving approach shows better results.
Additional optimization: perceptual and uniform versions of the evaluation function are now implemented separately, which slightly improves the performance.
DXT Testing:
The modified algorithm has been tested on the Kodak test set using 64-bit build with default settings (running on Windows 10, i7-4790, 3.6GHz). All the decompressed test images are identical to the images being compressed and decompressed using original version of Crunch (revision ea9b8d8).
[Compressing Kodak set without mipmaps using DXT1 encoding]
Original: 1582222 bytes / 28.845 sec
Modified: 1468204 bytes / 10.071 sec
Improvement: 7.21% (compression ratio) / 65.09% (compression time)
[Compressing Kodak set with mipmaps using DXT1 encoding]
Original: 2065243 bytes / 36.929 sec
Modified: 1914805 bytes / 13.248 sec
Improvement: 7.28% (compression ratio) / 64.13% (compression time)
ETC Testing:
The modified algorithm has been tested on the Kodak test set using 64-bit build with default settings (running on Windows 10, i7-4790, 3.6GHz). The ETC1 quantization parameters have been selected in such a way, so that ETC1 compression gives approximately the same average Luma PSNR as the corresponding DXT1 compression (which is equal to 34.044 dB for the Kodak test set compressed without mipmaps using DXT1 encoding and default quality settings).
[Compressing Kodak set without mipmaps using ETC1 encoding]
Total size: 1607858 bytes
Total time: 17.126 sec
Average bitrate: 1.363 bpp
Average Luma PSNR: 34.050 dB
This change improves the compression speed for DXT encoding.
Explanation:
When performing per-component endpoint optimization, it is not necessary to go through all the source pixels on every iteration in order to calculate the total weighted squared error for a specific trial endpoint. The computation can be optimized in the following way:
sum(w(i) * (x - p(i)) * (x - p(i))) = sum(w(i) * x * x) - sum(w(i) * 2 * x * p(i)) + sum(w(i) * p(i) * p(i)) = sum(w(i)) * x * x - sum(2 * w(i) * p(i)) * x + sum(w(i) * p(i) * p(i))
The values of sum(w(i)), sum(2 * w(i) * p(i)), sum(w(i) * p(i) * p(i)) can be precalculated for each of 4 selectors, and only have to be updated when the solution improves. This way the error computation on each iteration can be performed using 12 multiplications instead of 2 * N (where N is the number of pixels in the processed cluster).
DXT Testing:
The modified algorithm has been tested on the Kodak test set using 64-bit build with default settings (running on Windows 10, i7-4790, 3.6GHz). All the decompressed test images are identical to the images being compressed and decompressed using original version of Crunch (revision ea9b8d8).
[Compressing Kodak set without mipmaps using DXT1 encoding]
Original: 1582222 bytes / 28.811 sec
Modified: 1468204 bytes / 10.520 sec
Improvement: 7.21% (compression ratio) / 63.49% (compression time)
[Compressing Kodak set with mipmaps using DXT1 encoding]
Original: 2065243 bytes / 36.936 sec
Modified: 1914805 bytes / 13.902 sec
Improvement: 7.28% (compression ratio) / 62.36% (compression time)
ETC Testing:
The modified algorithm has been tested on the Kodak test set using 64-bit build with default settings (running on Windows 10, i7-4790, 3.6GHz). The ETC1 quantization parameters have been selected in such a way, so that ETC1 compression gives approximately the same average Luma PSNR as the corresponding DXT1 compression (which is equal to 34.044 dB for the Kodak test set compressed without mipmaps using DXT1 encoding and default quality settings).
[Compressing Kodak set without mipmaps using ETC1 encoding]
Total size: 1607858 bytes
Total time: 17.121 sec
Average bitrate: 1.363 bpp
Average Luma PSNR: 34.050 dB
This change improves the compression speed for DXT encoding.
Explanation:
The main ideas used for the DXT endpoints computation optimization:
- Instead of using map in tree clusterizer, the source vectors can be stored in an array and sorted before the quantization. This might increase the amount of used memory, but is much more efficient in terms of memory reallocation.
- Endpoint caching can be used throughout the color endpoint computation, and not just within the optimize_endpoints function. The only place where endpoint caching can not be used is the final step of the try_combinatorial_encoding function, where alternate rounding is used.
- When computing endpoint codebooks, endpoint optimizer and endpoint refiner can be reused, which eliminates unnecessary memory reallocations.
DXT Testing:
The modified algorithm has been tested on the Kodak test set using 64-bit build with default settings (running on Windows 10, i7-4790, 3.6GHz). All the decompressed test images are identical to the images being compressed and decompressed using original version of Crunch (revision ea9b8d8).
[Compressing Kodak set without mipmaps using DXT1 encoding]
Original: 1582222 bytes / 28.879 sec
Modified: 1468204 bytes / 11.099 sec
Improvement: 7.21% (compression ratio) / 61.57% (compression time)
[Compressing Kodak set with mipmaps using DXT1 encoding]
Original: 2065243 bytes / 36.919 sec
Modified: 1914805 bytes / 14.621 sec
Improvement: 7.28% (compression ratio) / 60.40% (compression time)
ETC Testing:
The modified algorithm has been tested on the Kodak test set using 64-bit build with default settings (running on Windows 10, i7-4790, 3.6GHz). The ETC1 quantization parameters have been selected in such a way, so that ETC1 compression gives approximately the same average Luma PSNR as the corresponding DXT1 compression (which is equal to 34.044 dB for the Kodak test set compressed without mipmaps using DXT1 encoding and default quality settings).
[Compressing Kodak set without mipmaps using ETC1 encoding]
Total size: 1607858 bytes
Total time: 17.108 sec
Average bitrate: 1.363 bpp
Average Luma PSNR: 34.050 dB
DXT Testing:
The modified algorithm has been tested on the Kodak test set using 64-bit build with default settings (running on Windows 10, i7-4790, 3.6GHz). All the decompressed test images are identical to the images being compressed and decompressed using original version of Crunch (revision ea9b8d8).
[Compressing Kodak set without mipmaps using DXT1 encoding]
Original: 1582222 bytes / 28.866 sec
Modified: 1468204 bytes / 11.858 sec
Improvement: 7.21% (compression ratio) / 58.92% (compression time)
[Compressing Kodak set with mipmaps using DXT1 encoding]
Original: 2065243 bytes / 36.878 sec
Modified: 1914805 bytes / 15.625 sec
Improvement: 7.28% (compression ratio) / 57.63% (compression time)
ETC Testing:
The modified algorithm has been tested on the Kodak test set using 64-bit build with default settings (running on Windows 10, i7-4790, 3.6GHz). The ETC1 quantization parameters have been selected in such a way, so that ETC1 compression gives approximately the same average Luma PSNR as the corresponding DXT1 compression (which is equal to 34.044 dB for the Kodak test set compressed without mipmaps using DXT1 encoding and default quality settings).
[Compressing Kodak set without mipmaps using ETC1 encoding]
Total size: 1607858 bytes
Total time: 17.181 sec
Average bitrate: 1.363 bpp
Average Luma PSNR: 34.050 dB
This change significantly improves the compression speed for DXT encoding.
Explanation:
The main ideas used for the DXT color endpoints computation optimization:
- When the DXT endpoint computation function is called from the qunatization algorithm, almost all of its input parameters (except the color metrics) are hardcoded in the quantization code. This allows to optimize the endpoint evaluation function (which is the bottleneck of the endpoint computation algorithm) for this specific set of parameters.
- In the original version of the evaluation function, selectors are computed each time when a new endpoint is evaluated. While in fact, this is not necessary, because some selector values are never used, so they can be computed lazily, based on the previously determined optimal endpoint values. This approach significantly reduces the amount of computations.
Other improvements:
- The original version of Crunch has a minor bug: the counter for the cached endpoint values does not get initialized. This results in nondeterministic DXT conversion of large textures, as the counter overflow can occur at a random moment. The issue is now fixed in the current branch.
DXT Testing:
The modified algorithm has been tested on the Kodak test set using 64-bit build with default settings (running on Windows 10, i7-4790, 3.6GHz). All the decompressed test images are identical to the images being compressed and decompressed using original version of Crunch (revision ea9b8d8).
[Compressing Kodak set without mipmaps using DXT1 encoding]
Original: 1582222 bytes / 28.893 sec
Modified: 1468204 bytes / 11.882 sec
Improvement: 7.21% (compression ratio) / 58.88% (compression time)
[Compressing Kodak set with mipmaps using DXT1 encoding]
Original: 2065243 bytes / 36.946 sec
Modified: 1914805 bytes / 15.628 sec
Improvement: 7.28% (compression ratio) / 57.70% (compression time)
ETC Testing:
The modified algorithm has been tested on the Kodak test set using 64-bit build with default settings (running on Windows 10, i7-4790, 3.6GHz). The ETC1 quantization parameters have been selected in such a way, so that ETC1 compression gives approximately the same average Luma PSNR as the corresponding DXT1 compression (which is equal to 34.044 dB for the Kodak test set compressed without mipmaps using DXT1 encoding and default quality settings).
[Compressing Kodak set without mipmaps using ETC1 encoding]
Total size: 1607858 bytes
Total time: 17.352 sec
Average bitrate: 1.363 bpp
Average Luma PSNR: 34.050 dB
This change simplifies further modification of the code.
Explanation:
This change is required for further optimization of the quantization code.
Testing:
The modified algorithm has been tested on the Kodak test set using 64-bit build with default settings (running on Windows 10, i7-4790, 3.6GHz). All the decompressed test images are identical to the images being compressed and decompressed using original version of Crunch.
[Compressing Kodak set without mipmaps]
Original: 1582222 bytes / 28.935 sec
Modified: 1494501 bytes / 24.528 sec
Improvement: 5.54% (compression ratio) / 15.23% (compression time)
[Compressing Kodak set with mipmaps]
Original: 2065243 bytes / 36.982 sec
Modified: 1945365 bytes / 32.308 sec
Improvement: 5.80% (compression ratio) / 12.64% (compression time)
Alexander Suvorov
Rich Geldreich
richgel99@gmail.com