One of the classical topics in neural networks is winner-take-all (WTA), which has been widely used in unsupervised (competitive) learning, cortical processing, and attentional control. Owing to global connectivity, WTA networks, however, do not encode spatial relations in the input, and thus cannot support sensory and perceptual processing where spatial relations are important. We propose a new architecture that maintains spatial relations between input features. This selection network builds on Locally Excitatory Globally Inhibitory Oscillator Networks (LEGION) dynamics and slow inhibition. In an input scene with many objects (patterns), the network selects the largest object. This system can be easily adjusted to select several largest objects, which then alternate in time. We analyze the speed of selection, and further show that a two-stage selection network gains efficiency by combining selection with parallel removal of noisy regions. The network is applied to select the most salient object in gray-level images. As a special case, the selection network without local excitation gives rise to a new form of oscillatory WTA.