User-friendly sharing of images: Progressive approach based on modulus operations

Image sharing is a popular technology to secure important images against damage. The technology decomposes and transforms an important image to produce several other images called shadows or shares. To decode, the shared important image can be reconstructed by combining the collected shadows, as long as the number of collected shadows reaches a specified threshold value. A few sharing methods produce user-friendly (i.e., visually recognizable) shadows-in other words, each shadow looks like a replica of reduced visual quality of a given image, rather than completely meaningless random noise. This facilitates visual management of shadows. (For example, if there are 100 important images and each creates 2 to 17 shadows of its own, then it is easy to visually recognize that a stored shadow is from, say, a House image, rather than from the other 99 images.) In addition to visually recognizable shadows, progressive decoding is also a convenient feature: It provides the decoding meeting a convenient manner to view a moderately sensitive image. Recently, Fang combined both conveniences of visually recognizable shadows and progressive decoding [W. P. Fang, Pattern Recogn., 41, 1410-1414 (2008)]. But that method was memory expensive because its shadows were too big. In order to save memory space, we propose a novel method based on modulus operations. It still keeps both conveniences, but shadows are two to four times smaller than Fang's, and the visual quality of each shadow can be controlled by using a simple expression.