Identifying areas where the signal is prominent is an important task in image analysis, with particular applications in brain mapping. In this work, we develop False Discovery Controlled Regions (FDCRs) for excursion sets, the set of locations where the values are above or below a given level. We achieve this by treating the confidence procedure as a testing problem at the given level, allowing control of the False Discovery Rate (FDR). Methods are developed to control the FDR, separately for positive and negative excursions, as well as jointly over both. Furthermore, power is increased by incorporating a two-stage adaptive procedure. Simulation results in a variety of different settings show that the FDCRs successfully control the FDR under the nominal alpha level. We showcase our methods with an application to functional magnetic resonance imaging (fMRI) data from the Human Connectome Project illustrating the improvement in statistical power over existing approaches.

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