1. An image-processing apparatus comprising: a hierarchical structure generating unit that identifies for each gradation value a connected component of pixels of not less than or not more than the gradation value neighboring and connected to each other in an input image, and generates hierarchical structure data of a hierarchical structure including the connected component; a region extracting unit that determines based on the hierarchical structure data whether the connected component satisfies a feature of character likelihood, and extracts the connected component satisfying the feature of character likelihood as a character-like region; a correcting unit that acquires based on a maximum gradation value and a minimum gradation value of pixels included in the character-like region a threshold of binarization used exclusively for the character-like region, and acquires based on the threshold of binarization a corrected region where the character-like region is binarized; and an image acquiring unit that acquires a background region where a gradation value of a pixel included in a region of the input image other than the corrected region is changed to a gradation value for a background, and acquires binary image data of a binary image composed of the corrected region and the background region.