Magnetic platelets with a vortex configuration are attracting considerable attention. The discovery that excitation with small in-plane magnetic fields or spin polarised currents can switch the polarisation of the vortex core did not only open the possibility of using such systems in magnetic memories, but also initiated the fundamental investigation of the core switching mechanism itself. Micromagnetic models predict that the switching is mediated by a vortex-antivortex pair, nucleated in a dynamically induced vortex core deformation. In the same theoretical framework, a critical core velocity is predicted, above which switching occurs. Although these models are extensively studied and generally accepted, experimental support has been lacking until now. In this work, we have used high-resolution time-resolved X-ray microscopy to study the detailed dynamics in vortex structures. We could reveal the dynamic vortex core deformation preceding the core switching. Also, the threshold velocity could be measured, giving quantitative comparison with micromagnetic models.