A Coded Aperture as a Key for Information Hiding Designed by Physics-in-the-Loop Optimization

This paper proposes a novel application of coded apertures (CAs) for visual information hiding. CA is one of the representative computational photography techniques, in which a patterned mask is attached to a camera as an alternative to a conventional circular aperture. With image processing in the post-processing phase, various functions such as omnifocal image capturing and depth estimation can be performed. In general, a watermark embedded as high-frequency components is difficult to extract if captured outside the focal length, and defocus blur occurs. Installation of a CA into the camera is a simple solution to mitigate the difficulty, and several attempts are conducted to make a better design for stable extraction. On the contrary, our motivation is to design a specific CA as well as an information hiding scheme; the secret information can only be decoded if an image with hidden information is captured with the key aperture at a certain distance outside the focus range. The proposed technique designs the key aperture patterns and information hiding scheme through evolutionary multi-objective optimization so as to minimize the decryption error of a hidden image when using the key aperture while minimizing the accuracy when using other apertures. During the optimization process, solution candidates, i.e., key aperture patterns and information hiding schemes, are evaluated on actual devices to account for disturbances that cannot be considered in optical simulations. Experimental results have shown that decoding can be performed with the designed key aperture and similar ones, that decrypted image quality deteriorates as the similarity between the key and the aperture used for decryption decreases, and that the proposed information hiding technique works on actual devices.