1. A derivation method of a nail apparatus melanoma discrimination threshold, comprising: representing a color image of longitudinal melanonychia as three-dimensional vectors each having RGB parameter values of each pixel and finding an angle between each of the three-dimensional vectors and a reference vector; finding a probability of occurrence according to a frequency distribution of the found angles; and according to the probability of occurrence, finding a threshold for a parameter to discriminate whether the longitudinal melanonychia is malignant or benign.