Abstract: A data communication system is so adapted that even if E-mail received by a mobile telephone has an image file attached thereto, the image represented by the image file can be displayed. An E-mail file is received by a mobile telephone and text represented by text data contained in the file is displayed on the display screen of the mobile telephone. When a received E-mail file has an image file attachment, the portable telephone interrogates a digital still camera as to whether the camera is capable of displaying the image contained in this image file. When the camera is capable of displaying the image, the image file is transmitted to the camera. The image represented by the image file is then displayed on the display screen of the camera.

Abstract: A transformation curve for compressing the color image signal within the color reproduction range of the color image output system is generated according to the number of picture elements whose colors are inside the color reproduction range of the color image output system out of the picture elements included in the predetermined region. The color of each picture element is transformed on the basis of the transformation curve thus generated, and a color image signal made up of signal components representing the colors of the picture elements thus transformed is output to the color image output system as the processed image signal.