Watermarking data in DCT coefficient has a significant challenge that the extracted data is different from the original data embedded (reference: "Digital Watermarking and Steganography: Fundamentals and Techniques", section 7, Frank Y. Shih). This is caused by IDCT and DCT that are applied after embedding:
- IDCT: converts DCT coefficient to image block
- DCT: converts image block to DCT coefficient before extraction
Traditional approaches embed data to the least significant bits (LSB) of DCT coefficient and round real numbers after IDCT. This small change directly in DCT coefficient causes inconsistency of data after IDCT and DCT. The aforementioned literature solves the problem using a genetic algorithm, and the algorithm in this repository has been implemented based on that.
In a case that data embedding shouldn't change at all such as hashes, a user may set the target fitness score to max. However, performance, in that case, is not great with this algorithm. It requires more generations and sometimes runs infinitely. Check the small performance evaluation below.
Here are details about the performance evaluation for our algorithm.
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Image block: 8x8
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Embedded message: 36 bits
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Target fitness score: 100% (36 bits)
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Number of Runs: 1000
Above result shows that 47% of the runs require less than 200 generations, and 35% of the runs exceeds 1000 generations. This is significant because latency increases as the number of runs required increases, and 1000 generation takes 4 seconds in average. Even the 0 to 50 generations takes 0.1 second in average which is still critical to watermark a whole image.
e.g., 1280x800 image has 16,000 image blocks (8x8).
16,000 * 0.1 sec == 1600 sec. == 26.6 min.
However, if a user targets 80% or 90% fitness score, the performance can be imporved significantly.
We changed the target fitness score to 90% (32.4 bits) and could get all 1000 runs with less than 50 generations. Also, the latency for each run takes 0.015 second.
e.g., 1280x800 image has 16,000 image blocks (8x8).
16,000 * 0.015 sec == 240 sec. == 4 min.
Run the main file (ga.py) by running below command:
$ python3 ga.pyDetails about each generation while generating the best fitness score will be printed to standard output.
In the algorithm, there are multiple parameters that a user can change to advance as needed:
- NUM_INDIVIDUALS: A number of individuals = population (default: 5)
- CRITICAL_VALUE: Critical value to set target fitness score (default: 10)
- EMB_SHIFT: How many bits to shift to embed data for each coefficient point. For example, shifting 2 means skipping two least significant bits from the right and embed data from third LSB. (default: 2)
- ENABLE_TWO_POINT: Whether to enable two point technique (default: True)
- ADV_1ST_POP: Whether to enable advanced population initialization (Default: True)
To understand the parameters, please refer to genetic algorithm and the literature mentioned.