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In an attempt to follow biological information representation and organization principles, the field of neuromorphic engineering is usually approached bottom-up, from the biophysical models to large-scale integration in silico. While ideal as experimentation platforms for cognitive computing and neuroscience, bottom-up neuromorphic processors have yet to demonstrate an efficiency advantage compared to specialized neural network accelerators for real-world problems. Top-down approaches aim at answering this difficulty by (i) starting from the applicative problem and (ii) investigating how to make the associated algorithms hardware-efficient and biologically-plausible. In order to leverage the data sparsity of spike-based neuromorphic retinas for adaptive edge computing and vision applications, we follow a top-down approach and propose SPOON, a 28-nm event-driven CNN (eCNN). It embeds online learning with only 16.8-% power and 11.8-% area overheads with the biologically-plausible direct random target projection (DRTP) algorithm. With an energy per classification of 313nJ at 0.6V and a 0.32-mm$^2$ area for accuracies of 95.3% (on-chip training) and 97.5% (off-chip training) on MNIST, we demonstrate that SPOON reaches the efficiency of conventional machine learning accelerators while embedding on-chip learning and being compatible with event-based sensors, a point that we further emphasize with N-MNIST benchmarking.