By a method of detecting a branch point, the branch point in a random line pattern of neovascularization or the like is detected accurately and efficiently. After a binary image is obtained from an original image, noise filling is performed for removing a noise in a line element to provide a filled image. The filled image is thinned to provide in a thinned image including the line element having its width change to one pixel. Plural previously-registered branch patterns are collated with the thinned image, and consequently, the branch point at which the line element of the random line pattern branches off is detected.