The statements in this section merely provide background information related to the present disclosure and may not constitute the prior art. 
Moving Picture Experts Group (MPEG) and Video Coding Experts Group (VCEG) have developed an improved and excellent video compression technology over existing MPEG-4 Part 2 and H.263 standards.  The new standard is named H.264/AVC (Advanced Video Coding) and was released simultaneously as MPEG-4 Part 10 AVC and ITU-T Recommendation H.264. 
In H.264/AVC (hereinafter referred to as ‘H.264’), in order to interpolate a reference frame used in the inter prediction, a reference frame interpolated with ¼ fractional pixel precision is generated using a 6-tap filter and an average value filter.  More specifically, the 6-tap filter is used so as to generate the ½ fractional pixel and the average value filter is used so as to generate the ¼ fractional pixel.  As described above, when the inter prediction is performed based on H.264, a motion is predicted and compensated with the ¼ fractional pixel precision by using the reference frame interpolated in the fractional pixel precision, so that it is possible to obtain the higher compression efficiency than the conventional method which uses only the reference frame having the integer pixel precision. 
Further, in H.264, not only fixed filter coefficients may be used for an interpolation of a reference image with the fractional pixel precision, but the coefficients of the interpolation filter may also be adaptively determined at each frame for the interpolation of a reference image.  To this end, H.264 encodes the image of each frame by using the conventional fixed filter coefficients, so as to find motion information and information (including the block type and the block shape) of each block mode.  In this event, if the block mode is an inter block mode, information required for obtaining the coefficients of the interpolation filter is accumulated and the encoded information is not included in the bit stream.  When the encoding for one frame is completed, coefficients of the interpolation filter are generated by using the accumulated information, a reference image is interpolated by using the generated coefficients, and an image is then encoded by using the interpolated reference image. 
However, since the filter coefficients obtained at every frame in the way described above are not optimum for all the inter block modes, they may cause degradation in the encoding efficiency.  Moreover, since the filter coefficients determined at every frame should be transmitted to an image decoding apparatus by an image encoding apparatus, they may increase the bit rate.