1. A three-dimensional (3D) image generation apparatus, comprising: a processor comprising: a filtering unit to filter a depth image using a first filter and a second filter; and a rendering unit to render a two-dimensional (2D) color image and the filtered depth image and to generate a 3D image using a processor, wherein the filtering unit smoothes, by using the first filter, a depth value of an object of the depth image, and substitutes, by using the second filter, the smoothed depth value for a depth value of a peripheral region of the object of the depth image to extend an outermost boundary of the object, wherein the peripheral region corresponds to surroundings of the object, and wherein a depth value of each pixel in the peripheral region is equal to the smoothed depth value.