The purpose of this study is to compare Euclidean and Mahalanobis geometry as a means of identifying a person using their iris. Iris is the only biometric that is truly unique and is extremely difficult to perform, making it the single most important consideration in the improvement of system security. To obtain the desired results, namely preprocessing and feature extraction, various methods will be used in image processing. Methods like the Gaussian filter, the operator sobel, and thresholding will be used in the pengolahan. Utilize the United Moment Invariant method to extend the circle (UMI). For projects that use the method of comparing the strengths of FAR and GAR, a smaller FAR was obtained for the eulidean to mahalanobis ratio. Additionally, value distance mahalanobis is smaller compared to FAR for GAR penetration. Keywords: Gaussian Filter, Iris, Sobel Operator, United Moment Invariat