1. A method for detecting a closed-loop area on a document from bi-level image data read from the document, said bi-level image data made up of a set of two-dimensionally arranged black and white dots, said method comprising steps of: reading a dot matrix from bi-level image data sequentially for dots on a line in the image data in a first direction opposite to a reading direction, said dot matrix arranged in a first formation and comprising a target dot and two or more contiguous dots contiguous to the target dot; performing a first pattern matching to detect whether the dot matrix arranged in the first formation coincides with one of a plurality of first patterns, said first pattern matching being performed sequentially for the dots on the line in the first direction; setting a first flag for the target dot to a first value or a second value based on the result of said first pattern matching so that the first flag for each of the dots on the line is set; reading a dot matrix from the bi-level image data sequentially for the dots on the line in the reading direction opposite the first direction, said dot matrix arranged in a second formation and comprising a target dot and two or more contiguous dots contiguous to the target dot; performing a second pattern matching to detect whether said dot matrix arranged in the second formation coincides with one of a plurality of second patterns, said second pattern matching being performed sequentially for the dots on the line in the reading direction; setting a second flag for the target dot to the first value or the second value based on the result of said second pattern matching and based on the values of the first flags set in said first flag setting step, so that the second flag for each of the dots on the line is set; repeating the first flag setting step and the second flag setting step so that the second flags for all the dots of the bi-level image data are set; and detecting a dot as lying in the inside of the closed-loop area when the second flag is set to the first value, and detecting a dot lies on the outside of the closed-loop area when the second flag is set to the second value, wherein the second flag for the target dot is set in accordance with the value of the second flag previously set for one of the contiguous dots and in accordance with the image data for the target dot.