1. An image processing device, comprising: a data receiving unit configured to receive a plurality of sets of digital input signals for a plurality of pixels that constitute a desired image; a brightness determining unit configured to determine brightness of each pixel based on the set of digital input signals for each pixel; a subject area setting unit configured to set a subject area that is formed from several pixels that include a subject pixel to be processed and that are arranged adjacent to one another, the subject pixel being located at a center of the subject area; a pixel extracting unit configured to extract, from the subject area, a first fixed number of pixels while a remaining second fixed number of pixels is not extracted in the subject area, each of the first fixed number and the second fixed number being greater than one, a total number of the first and second fixed numbers being equal to the total number of the several pixels within the subject area, brightness of the extracted pixels being smaller than or equal to that of the non-extracted pixels, the pixel extracting unit extracting the first fixed number of pixels based on a relationship in brightness between the pixels located in the subject area, and the pixel extracting unit extracting the first fixed number of pixels by comparing the brightness of all the pixels in the subject area and by selecting, based on the comparing result, n pixels having brightness from the lowest brightness to the n-th lowest brightness, where n is equal to the first fixed number; a connected-and-aligned-state judging unit configured to judge whether or not the extracted first fixed number of pixels are in a connected-and-aligned state, the connected-and-aligned-state judging unit determines that the extracted first fixed number of pixels are in the connected-and-aligned state when the extracted first fixed number of pixels are connected with one another, are aligned in one direction, and include the subject pixel, the connected-and-aligned-state judging unit determining that the extracted first fixed number of pixels are not in the connected-and-aligned-state when the extracted first fixed number of pixels are not connected with one another, are not aligned in one direction or do not include the subject pixel; a fine-line part determining unit configured to determine that the subject pixel is in a fine-line part when the extracted first fixed number of pixels is determined as being in the connected-and-aligned state, wherein the plurality of pixels are arranged both horizontally and vertically in the desired image, wherein the subject area setting unit sets, as the subject area, a 3-row×3-column matrix area, in which nine adjacent pixels are arranged in three rows and in three columns, the subject pixel being located in the center of the 3-row×3-column matrix area, each row extending horizontally and each column extending vertically, wherein the pixel extracting unit extracts, from the subject area, three pixels, while the remaining six pixels be not extracted, brightness of the three extracted pixels being smaller than or equal to brightness of the non-extracted six pixels, and wherein the connected-and-aligned-state judging unit determines that the three extracted pixels are in the connected-and-aligned state when the three extracted pixels include the subject pixel and are connected with one another and are aligned in either one of a vertical direction, a horizontal direction, and a diagonal direction; and an identification number assigning unit configured to assign nine different identification numbers to the respective pixels within the 3-row×3-column matrix area, with a median value in the nine identification numbers being assigned to the subject pixel, the total values of the identification numbers assigned to first, second, third, and fourth groups of three pixels being equal to a predetermined total value, each group having three pixels including the subject pixel, each group of three pixels being aligned in one direction with the subject pixel being located at the center of the three pixels, the first group of three pixels extending horizontally, the second group of three pixels extending vertically, and the third and fourth groups of three pixels extending diagonally, wherein the connected-and-aligned-state judging unit determines that the extracted three pixels are in the connected-and-aligned state when the total of the identification numbers assigned to the extracted three pixels is equal to the predetermined total value.