1. An image processing apparatus comprising: a processor including: a pre-processing unit configured to perform pre-processing on an input image; a contrast improvement unit configured to perform a contrast improvement process on the pre-processed image by comparing an object pixel of the pre-processed image with pixels that belong to surrounding areas of the object pixel; an image combination unit configured to combine an enhanced image obtained by the contrast improvement unit and the input image; a post-processing unit configured to perform post-processing on an image after combination; and an image output unit configured to output the post-processed image, wherein the contrast improvement unit comprises: a comparison pixel setting unit configured to set comparison pixels from among pixels in an area surrounding the object pixel to be used in the comparison; a correction data calculation unit configured to find a contrast improvement amount of the object pixel; a conversion standard value calculation unit configured to find a conversion standard value for converting the contrast improvement amount to a value of pixels in the enhanced image; and a pixel value conversion unit configured to convert the contrast improvement amount to the value of pixels in the enhanced image based on the conversion standard value, and wherein the correction data calculation unit comprises: a surrounding average unit configured to find a weighted average for density of the comparison pixels; an edge data detection unit configured to detect edge data of the object pixel; a correction coefficient calculation unit configured to calculate a correction coefficient for the edge data based on the edge data obtained by the edge data detection unit; a comparison amount correction unit configured to correct the weighted average obtained by the surrounding average unit using the correction coefficient; and an improvement amount calculation unit configured to find the contrast improvement amount from the corrected weighted average and density of the object pixel.