1. An apparatus for estimating depth to convert a two-dimensional (2-D) monocular video into a stereoscopic video, the apparatus comprising: a feature information extraction unit to extract at least one feature information from a single input image, the feature information being independent of any pre-established depth values of the input image; and a depth establishment unit to establish a depth of a portion of the input image based on the at least one feature information with regard to the portion of the input image, the portion being less than the entire image, wherein the feature information extraction unit calculates a weight so as to depend on similarities of feature information between the at least one pixel of the input image and adjacent pixels within the input image based on the at least one feature information, wherein the depth establishment unit includes a depth map initialization unit, the depth map initialization unit configured to establish an initial depth of the portion of the input image based on a position of the portion of the input image within the input image, such that portions of the input image having different positions are established to have different initial depths, determine the depth of the object located in the upper portion of the input image to be deeper than the depth of the object located in the lower portion of the input image, wherein the depth establishment unit further includes a depth update unit to filter depths stored in the depth map by repeatedly performing updating operations based on the weight, wherein the depth establishment unit comprises, a depth map initialization unit configured to establish an initial depth of at least one pixel of the input image, and to store the established initial depth in a depth map, and a depth update unit configured to calculate the depth of the portion of the input image by performing filtering based on the initial depth, and to update the depth map based on the calculated depth, wherein the apparatus further comprises, a down-scaling unit configured to down-scale the input image to a predetermined resolution, a second depth map initialization unit configured to establish a second initial depth of at least one pixel of the down-scaled input image, and to store the second initial depth in a second depth map, a second feature information extraction unit configured to extract at least one second feature information from the down-scaled input image, and a second depth update unit configured to calculate a second depth of the down-scaled input image by performing filtering based on the at least one second feature information and the second initial depth, and to update the second depth map using the second depth, and an up-scaling unit configured to upscale the updated second depth map based on a resolution of the input image, and wherein the depth map initialization unit is configured to establish the initial depth based on a depth stored in the up-scaled second depth map.