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Work at the intersection of vision science and deep learning is starting to explore the efficacy of deep convolutional networks (DCNs) and recurrent networks in solving perceptual grouping problems that underlie primate visual recognition and segmentation. Here, we extend this line of work to investigate the compactness and generalizability of DCN solutions to learning low-level perceptual grouping routines involving contour integration. We introduce V1Net, a bio-inspired recurrent unit that incorporates lateral connections ubiquitous in cortical circuitry. Feedforward convolutional layers in DCNs can be substituted with V1Net modules to enhance their contextual visual processing support for perceptual grouping. We compare the learning efficiency and accuracy of V1Net-DCNs to that of 14 carefully selected feedforward and recurrent neural architectures (including state-of-the-art DCNs) on MarkedLong -- a synthetic forced-choice contour integration dataset of 800,000 images we introduce here -- and the previously published Pathfinder contour integration benchmarks. We gauged solution generalizability by measuring the transfer learning performance of our candidate models trained on MarkedLong that were fine-tuned to learn PathFinder. Our results demonstrate that a compact 3-layer V1Net-DCN matches or outperforms the test accuracy and sample efficiency of all tested comparison models which contain between 5x and 1000x more trainable parameters; we also note that V1Net-DCN learns the most compact generalizable solution to MarkedLong. A visualization of the temporal dynamics of a V1Net-DCN elucidates its usage of interpretable grouping computations to solve MarkedLong. The compact and rich representations of V1Net-DCN also make it a promising candidate to build on-device machine vision algorithms as well as help better understand biological cortical circuitry.