1. An object positioning system that recognizes a position of an object having a flat face on the basis of its outline in a captured image of the object and that positions the object at a predetermined place, the object positioning system comprising: an image capturing unit that captures an image of the object from a direction perpendicular to the flat face of the object; an illuminating unit that illuminates the flat face of the object from a direction parallel to an optical axis of the image capturing unit; an image processing unit that performs calculation to find an outline of the object in the image captured by the image capturing unit; and an object arranging unit that moves the object, wherein the image processing unit includes: a recognition-line setting unit that sets a plurality of recognition lines that are to be across the outline of the object in the image captured by the image capturing unit; a brightness-detecting unit that detects brightness of image on each of the recognition lines; a possible dark-transition-boundary detecting unit that detects, on each of the recognition lines, a possible boundary point of dark-transition where a bright-to-dark transition in brightness occurs from outside toward inside of the object; a possible bright-transition-boundary detecting unit that detects, on each of the recognition lines, a possible boundary point of bright-transition where a dark-to-bright transition in brightness occurs from outside toward inside of the object; an edge detecting unit that detects, on each of the recognition lines, an edge point on the basis of the possible dark-transition-boundary point and the possible bright-transition-boundary point; and an outline-determining unit that determines an outline of the object so that the outline minimizes the sum of deviations between the outline and the respective edge points detected on the recognition lines.