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A new type of computer art image called secret-fragment-visible mosaic image is proposed, which is created automatically by composing small fragments of a given image to become a target image in a mosaic form, achieving an effect of embedding the given image visibly but secretly in the resulting mosaic image. This effect of information hiding is useful for covert communication or secure keeping of secret images. To create a mosaic image of this type from a given secret color image, the 3-D color space is transformed into a new 1-D colorscale, based on which a new image similarity measure is proposed for selecting from a database a target image that is the most similar to the given secret image. A fast greedy search algorithm is proposed to find a similar tile image in the secret image to fit into each block in the target image. The information of the tile image fitting sequence is embedded into randomly-selected pixels in the created mosaic image by a lossless LSB replacement scheme using a secret key; without the key, the secret image cannot be recovered. The proposed method, originally designed for dealing with color images, is also extended to create grayscale mosaic images which are useful for hiding text-type grayscale document images. An additional measure to enhance the embedded data security is also proposed. Good experimental results show the feasibility of the proposed method.