1. A computer-implemented character image extracting method comprising: an extracting step for obtaining a linked component composed of a plurality of mutually linking pixels from a character string region composed of a plurality of characters and extracting section elements from the character string region, the section elements each being surrounded by a circumscribing figure circumscribing the linked component; a first altering step for altering the section elements extracted in the extracting step into new section elements, by determining which respective section elements among the section elements extracted in the extracting step have at least mutually overlapping circumscribing figures, and combining the determined respective section elements to form a new section element, while setting remaining section elements thereof as other new section elements without being combined; a first selecting step for selecting, from among the section elements altered in the first altering step, section elements having a size greater than a predetermined reference size; a second altering step for altering the section elements selected in the first selecting step into new section elements by combining the section elements of the section elements selected by the first selecting step that are smaller in dimension in a character alignment direction than a predetermined first reference dimension and that are adjacent to each other in the character alignment direction to form a new section element, while setting remaining section elements thereof as other new section elements without being combined; and a second selecting step for selecting, of the section elements altered by the second altering step, section elements that are greater in dimension in a character alignment direction than a predetermined second reference dimension.