A depth-fused three dimensional (DFD) display composed of two two-dimensional (2-D) images displayed at different depths enables an observer to perceive a three dimensional image without the assistance of extra equipment. The original data for the display are a 2-D image and a depth map of objects. The two 2-D images are formed by dividing the luminance of a 2-D image of objects between the two 2-D images according to the depth data of the objects. This paper presents the effect of compressing the depth map on a DFD image. The results of subjective evaluations of still pictures using JPEG revealed that compression noises appearing on the decoded image appeared as position errors in depth on the DFD image; however, less data are possible for the depth map data than for a conventional 2-D image. This means that compressing the depth map is advantageous when transmitting a DFD image.