The disclosure describes an image encoding apparatus, method, and medium and an image decoding apparatus, method, and medium to encode and decode an original image. The disclosure also describes a display driving circuit and a method and medium using the same. The image encoding apparatus may include an encoding mode determiner that determines a first encoding mode and a second encoding mode to be encoding modes of a first pixel and a second pixel that are adjacent to each other and are included in a line, a first encoder that encodes the first pixel whose encoding mode is determined to be the first encoding mode to generate a first bitstream, and a second encoder that encodes a difference of the second pixel whose encoding mode is determined to be the second encoding mode from its reference pixel to generate a second bitstream.