1. A histogram stretching apparatus for improving contrast of an image by stretching a histogram of an input image within a range of a preset maximum expansion level to a preset minimum expansion level, the histogram stretching apparatus comprising: a histogram calculation unit calculating a histogram displaying a frequency according to an image level of each pixel included in an input image; a histogram analysis unit obtaining an accumulative distribution of the frequency according to the image level from the calculated histogram, determining a maximum value, a minimum value and a median value of an accumulative distribution of an area on which the histogram stretching is to be performed, and determining a minimum value, a maximum value and a median value of an image level area corresponding to the maximum value, the minimum value and the median value of the accumulative distribution; a linear-function application unit mapping the maximum value and the minimum value of the image level area determined at the histogram analysis unit to a linear function that changes linearly between the maximum expansion level and the minimum expansion level to calculate a modified maximum expansion level and a modified minimum expansion level; a gamma-curve application unit selecting a gamma curve with reference to the median value of the image level and mapping the minimum value and the maximum value of the image level to the selected gamma curve to calculate a modified maximum value and a modified minimum value of an image level; and a histogram stretching unit modifying an image level of each pixel of the input image by using the modified maximum expansion level, the modified minimum expansion level, the modified maximum value of the image level, and the modified minimum value of the image level.