1. An apparatus to detect homogeneous region of an input image, the apparatus comprising: a global region standard deviation calculation part to calculate a global region standard deviation of a whole region of the input image; a local region standard deviation calculation part to divide the input image into a predetermined number of local regions and to calculate a local region standard deviation of each local region; and a homogeneous region determination part to separate a homogeneous region from a non-homogeneous region in the input image using an adaptive threshold calculated based on an entropy constant of the input image and the global region standard deviation, wherein the homogeneous region determination part comprises: an adaptive threshold calculation part to calculate the adaptive threshold based on the global region standard deviation and the entropy constant of the input image; and a comparison part to compare the calculated adaptive threshold with the local region standard deviation of each local region and to determine one of the local regions to be the homogeneous region when the adaptive threshold is greater than the respective local region standard deviation, wherein the adaptive threshold calculation part calculates the adaptive threshold assuming that a local region entropy calculated based on the adaptive threshold, the global region standard deviation and the local region standard deviation is the same as the entropy constant.