Most automatic fingerprint identification systems identify a person using minutiae. However, minutiae depend almost entirely on the quality of the fingerprint images that are captured. Therefore, it is important that the matching step uses only reliable minutiae. The quality estimation algorithm deduces the availability of the extracted minutiae and allows for a matching step that will use only reliable minutiae. We propose a model-based quality estimation of fingerprint images. We assume that the ideal structure of a fingerprint image takes the shape of a sinusoidal wave consisting of ridges and valleys. To determine the quality of a fingerprint image, the similarity between the sinusoidal wave and the input fingerprint image is measured. The proposed method uses the 1-dimensional (1D) probability density function (PDF) obtained by projecting the 2-dimensional (2D) gradient vectors of the ridges and valleys in the orthogonal direction to the local ridge orientation. Quality measurement is then caculated as the similarity between the ID probability density functions of the sinusoidal wave and the input fingerprint image. In our experiments, we compared the proposed method and other conventional methods using FVC-2002 DB I, III procedures. The performance of verification and the separability between good and bad regions were tested.