1. A decoding device for decoding coded image data based on an estimation of a prediction mode of a target region to be intra-frame predicted, which estimation is made based on one or more prediction modes of one or more neighbor regions which are neighboring to the target region, said decoding device, comprising: estimated prediction mode deriving means for deriving an estimated prediction mode by estimating the prediction mode of the target region based on said one or more prediction modes of said one or more neighbor regions, said one or more prediction modes of said one or more neighbor regions being included in a sum of sets of prediction modes which are applicable to respective regions to be intra-frame predicted, the sum being identical to one of the sets of prediction modes.