A TOPOLOGY FOR DISCRETE SPACES AND ITS APPLICATION IN SCRATCH DETECTION FOR SURFACE INSPECTIONS

In conventional digital image processing, topological properties have been studied only for selected types of neighborhoods such as a 4- or 8-pixels connection. This paper analyzes properties of a finite topolo gical space by defining it as a topological space with no restriction on the shape of a neighborhood. This leads to the identification of to pological properties which are independent of the shape of a neighborh ood and can be applied to image processing using neighborhoods other t han a 4- or 8-connection. Since a finite topological space can treat o nly a single neighborhood this cannot be applied to image processing w hich uses multiple neighborhoods simultaneously A finite topological s pace has been extended to a formal topological space having multiple n eighborhoods, and its properties are analyzed in this paper. This theo ry is then applied to image processing. It has been difficult to detec t scratches on a surface with patterns, such as a hard disk or a hairl ine-finished metal, by using a conventional digital topology because t he scratches often consist of many small blocks and their images are s tained by noise. The properties obtained through the formal topology h ave successfully been applied to these problems, and its effectiveness has been confirmed.