1. A line segment detector including a first line-segment detecting part comprising: a vertical line detecting part that detects whether or not an input image has a vertical line; a horizontal line detecting part that detects whether or not the input image has a horizontal line; a left-to-right downward slanting line detecting part that detects whether or not the input image has a left-to-right downward slanting line; a left-to-right upward slanting line detecting part that detects whether or not the input image has a left-to-right upward slanting line; and a line-segment detecting/synthesizing section implemented by a processor that calculates OR operation of output values from the vertical line detecting part, the horizontal line detecting part, the left-to-right downward slanting line detecting part, and the left-to-right upward slanting line detecting part, the line segment detector further comprising: a re-determining unit that re-determines whether or not the detection result output from the line-segment detecting/synthesizing section is a line segment, wherein the re-determining unit comprises a second line-segment detecting part that sets a window to the detection result near the target pixel, counts the number of pixels whose detection result is determined as the line segment in the set window, determines, when the counted value is not smaller than a predetermined threshold value, that the pixel is the line segment, further determines, when the counted value is smaller than the predetermined threshold value, that the pixel is not the line segment, and outputs a new detection result.