Vast databases of billions of contact-based fingerprints have been developed to protect national borders and support e-governance programs. Emerging contactless fingerprint sensors offer better hygiene, security and accuracy. However the adoption/success of such contactless fingerprint technologies largely depends on advanced capability to match contactless 2D fingerprints with legacy contact-based fingerprint databases. This paper investigates such problem and develops a new approach to accurately match such fingerprint images. Robust thin-plate spline (RTPS) is developed to more accurately model elastic fingerprint deformations using splines. In order to correct such deformations on the contact-based fingerprints, RTPS based generalized fingerprint deformation correction model (DCM) is proposed. The usage of DCM results in accurate alignment of key minutiae features observed on the contactless and contactbased fingerprints. Further improvement in such cross-matching performance is investigated by incorporating minutiae related ridges. We also develop a new database of 1800 contactless 2D fingerprints and the corresponding contact-based fingerprints acquired from 300 clients which is made publicly accessible for further research. The experimental results presented in this paper, using two publicly available databases, validate our approach and achieve outperforming results for matching contactless 2D and contact-based fingerprint images.