This change improves the compression ratio.
Explanation:
In the original version of Crunch all the blocks are grouped into chunks of 2x2 blocks. Each chunk can have one of 8 different types. The type of the chunk determines which blocks inside the chunk share the same endpoints (for example, all the blocks inside the chunk share the same endpoints, or blocks in the right column share the same endpoints, or all the blocks have different endpoints, etc.). Encoding of endpoints equality is usually cheaper than encoding of duplicate endpoint indices. The used 8 chunk types do not cover all the possibilities, but they can be efficiently encoded using 0.75 bits per block (uncompressed).
The modified algorithm no longer uses the concept of chunks in the output file format and is based on an alternative approach. Endpoints for each block can be either copied from the left nearest block (reference to the left), copied from the upper nearest block (reference to the top), or decoded from the stream (reference to itself). Note that this is a superset of the original encoding, so all the images previously encoded with the original algorithm can be losslessly transcoded into the new format, but not vice versa. Even though the new endpoint equality encoding is more expensive (about 1.58 bits per block, uncompressed), it provides more flexibility for endpoint matching inside the former "chunks", and more importantly, it allows to inherit endpoints from outside the former "chunks" (which is not possible when using the original chunk encoding). The blocks are no longer grouped together and are encoded in the same order as they appear on the image.
Note:
This modification alters the output file format and makes it incompatible with the previous revisions.
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 / 28.903 sec
Modified: 1548791 bytes / 28.818 sec
Improvement: 2.11% (compression ratio) / 0.29% (compression time)
[Compressing Kodak set with mipmaps]
Original: 2065243 bytes / 36.978 sec
Modified: 2017245 bytes / 36.846 sec
Improvement: 2.32% (compression ratio) / 0.36% (compression time)
Explanation:
After switching to ordering histograms, the linear lists of endpoint and selector indices are no longer used in Zeng function, and therefore can be removed.
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 / 28.872 sec
Modified: 1561622 bytes / 28.434 sec
Improvement: 1.30% (compression ratio) / 1.52% (compression time)
[Compressing Kodak set with mipmaps]
Original: 2065243 bytes / 36.910 sec
Modified: 2033151 bytes / 36.369 sec
Improvement: 1.55% (compression ratio) / 1.47% (compression time)
This change improves compression ratio.
Explanation:
In the original algorithm the relative position of the block, used for prediction of the selector index for the currently decoded block, depends on the position of the current block in the chunk. It can be a horizontal neighbour or a diagonal neighbour. Using left nearest neighbour for selector index prediction for each block (except the blocks at the image borders) minimizes the average distance to the prediction block and therefore usually improves the selector index prediction. Similarly to the endpoint index processing, the selector ordering histogram in now generated based on the selector index prediction order.
Note:
This modification alters the output file format and makes it incompatible with the previous revisions.
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 / 28.869 sec
Modified: 1561622 bytes / 28.522 sec
Improvement: 1.30% (compression ratio) / 1.20% (compression time)
[Compressing Kodak set with mipmaps]
Original: 2065243 bytes / 37.038 sec
Modified: 2033151 bytes / 36.407 sec
Improvement: 1.55% (compression ratio) / 1.70% (compression time)
This change improves compression ratio.
Explanation:
The original histogram has been generated based on the linear order of encoded endpoint indexes. In the modified version of the algorithm, endpoint indexes are predicted using the nearest left block on the image, which is not necessarily the preceding block in the encoded sequence. Using the same block ordering both for prediction and Zeng optimization normally improves the compression ratio.
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 / 28.905 sec
Modified: 1566133 bytes / 28.457 sec
Improvement: 1.02% (compression ratio) / 1.55% (compression time)
[Compressing Kodak set with mipmaps]
Original: 2065243 bytes / 37.021 sec
Modified: 2040086 bytes / 36.300 sec
Improvement: 1.22% (compression ratio) / 1.95% (compression time)
This change makes the compression scheme more flexible.
Explanation:
In the original scheme, indexes are encoded in linear order, which means that each index uses the previously encoded index for prediction. However, more sophisticated schemes might require arbitrary references into the stream of already encoded indexes. For this reason, Zeng function has been modified to accept the ordering histogram as an input, instead of the linear array of indexes. Note that Zeng function itself does not rely on the indexes being encoded in linear order.
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 / 28.867 sec
Modified: 1570534 bytes / 28.524 sec
Improvement: 0.74% (compression ratio) / 1.19% (compression time)
[Compressing Kodak set with mipmaps]
Original: 2065243 bytes / 37.001 sec
Modified: 2051509 bytes / 36.388 sec
Improvement: 0.67% (compression ratio) / 1.66% (compression time)
This change improves compression ratio.
Explanation:
In the original algorithm the relative position of the block, used for prediction of the endpoint index for the currently decoded block, depends on the chunk encoding type. It can be a horizontal neighbour, a vertical neighbour, a diagonal neighbour, or in some rare cases even a block at relative position (-2, 0) or (-3, 0). Using left nearest neighbour for endpoint index prediction for each block (except the blocks at the image borders) minimizes the average distance to the prediction block and therefore usually improves the endpoint index prediction.
Note:
This modification alters the output file format and makes it incompatible with the previous revisions.
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 / 28.838 sec
Modified: 1570534 bytes / 28.629 sec
Improvement: 0.74% (compression ratio) / 0.72% (compression time)
[Compressing Kodak set with mipmaps]
Original: 2065243 bytes / 36.977 sec
Modified: 2051509 bytes / 36.568 sec
Improvement: 0.67% (compression ratio) / 1.11% (compression time)
This change slightly improves compression ratio and compression time.
Explanation:
The efficiency of the Crunch encoding scheme depends on the similarity between the neighbour chunks. For this reason in original version of Crunch the order of chunks is reversed after each scanline, so that there is no jump from one side of the image to another at the image borders. The problem here is that inside of each chunk, the blocks are normally ordered in a usual up-to-down-left-to-right manner, regardless of the chunk scanning order. While on the forward scan we normally need to perform diagonal jumps (+1, +1) in order to get to the next chunk, on the reverse scan we normally need to perform much larger (-3, +1) jumps, which usually defeats the advantage of not having discontinuity at the image borders.
Note:
This modification alters the output format and makes it incompatible with the previous revisions.
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 / 28.882 sec
Modified: 1579618 bytes / 28.743 sec
Improvement: 0.16% (compression ratio) / 0.48% (compression time)
[Compressing Kodak set with mipmaps]
Original: 2065243 bytes / 36.920 sec
Modified: 2061499 bytes / 36.833 sec
Improvement: 0.18% (compression ratio) / 0.24% (compression time)
Alexander Suvorov
richgel99@gmail.com