Optimization of Size of Pixel Blocks for Orthogonal Transform in Optical Watermarking Technique

We previously proposed a novel technology with which the images of real objects with no copyright protection could contain invisible digital watermarking, using spatially modulated illumination. In this “optical watermarking” technology, we used orthogonal transforms, such as a discrete cosine transform (DCT) or a Walsh-Hadamard transform (WHT), to produce watermarked images, where 1-b binary information was embedded into each pixel block. In this paper, we propose an optimal condition for a technique of robust optical watermarking that varies the size of pixel blocks by using a trade-off in the efficiency of embedded watermarking. We conducted experiments where 4 × 4, 8 × 8, and 16 × 16 pixels were used in one block. A detection accuracy of 100% was obtained by using a block with 16 × 16 pixels when embedded watermarking was extremely weak, although the accuracy did not necessarily reach 100% by using blocks with 4 × 4 or 8 × 8 pixels under the same embedding conditions. We also examined the effectiveness of using a Haar discrete wavelet transform (Haar DWT) as an orthogonal transform under the same experimental condition, and the results showed that the accuracy of detection was slightly inferior to DCT and WHT under very weak embedding conditions. The results from experiments revealed the effectiveness of our new proposal.