Reconstruction of topologically correct and accurate cortical surfaces from infant MR images is of great importance in neuroimaging mapping of early brain development. However,due to rapid growth and ongoing myelination,infant MR images exhibit extremely low tissue contrast and dynamic appearance patterns,thus leading to much more topological errors (holes and handles) in the cortical surfaces derived from tissue segmentation results,in comparison to adult MR images which typically have good tissue contrast. Existing methods for topological correction either rely on the minimal correction criteria,or ad hoc rules based on image intensity priori,thus often resulting in erroneous correction and large anatomical errors in reconstructed infant cortical surfaces. To address these issues,we propose to correct topological errors by learning information from the anatomical references,i.e.,manually corrected images. Specifically,in our method,we first locate candidate voxels of topologically defected regions by using a topology-preserving level set method. Then,by leveraging rich information of the corresponding patches from reference images,we build regionspecific dictionaries from the anatomical references and infer the correct labels of candidate voxels using sparse representation. Notably,we further integrate these two steps into an iterative framework to enable gradual correction of large topological errors,which are frequently occurred in infant images and cannot be completely corrected using one-shot sparse representation. Extensive experiments on infant cortical surfaces demonstrate that our method not only effectively corrects the topological defects,but also leads to better anatomical consistency,compared to the state-of-the-art methods.