Latent fingerprints, or simply latents, have been considered as cardinal evidence for identifying and convicting criminals. The amount of information available for identification from latents is often limited due to their poor quality, unclear ridge structure and occlusion with complex background or even other latent prints. We propose a latent fingerprint enhancement algorithm, which expects manually marked region of interest (ROI) and singular points. The core of the proposed algorithm is a robust orientation field estimation algorithm for latents. Short-time Fourier transform is used to obtain multiple orientation elements in each image block. This is followed by a hypothesize-and-test paradigm based on randomized RANSAC, which generates a set of hypothesized orientation fields. Experimental results on NIST SD27 latent fingerprint database show that the matching performance of a commercial matcher is significantly improved by utilizing the enhanced latent fingerprints produced by the proposed algorithm.