Fingerprints are useful for biometric purposes because of their well known properties of distinctiveness and persistence over time. However, owing to skin conditions or incorrect finger pressure, original fingerprint images always contain noise. Especially, some of them contain useless components, which are often mistaken for the terminations that are an essential minutia of a fingerprint. Mathematical Morphology (MM) is a powerful tool in image processing. In this paper, we propose a linear time algorithm to eliminate impulsive noise and useless components, which employs generalized and ordinary morphological operators based on Euclidean distance transform. There are two contributions. The first is the simple and efficient MM method to eliminate impulsive noise, which can be restricted to a minimum number of pixels. We know the performance of MM is heavily dependent on structuring elements (SEs), but finding an optimal SE is a difficult and nontrivial task. So the second contribution is providing an automatic approach without any experiential parameter for choosing appropriate SEs to eliminate useless components. We have developed a novel algorithm for the binarization of fingerprint images [1]. The information of distance transform values can be obtained directly from the binarization phase. The results show that using this method on fingerprint images with impulsive noise and useless components is faster than existing denoising methods and achieves better quality than earlier methods.