Background: Ion-beam radiography is a promising technique to verify the range of ion-beam radiotherapy treatments regularly. To detect and quantify the water-equivalent thickness (WET) of potential anatomical changes, ion-beam radiographs must provide a sufficient WET accuracy on the level of 1%. Purpose: In this work, we show an energy-painted helium-beam radiograph of an anthropomorphic head phantom acquired with thin silicon pixel detectors for the first time. Furthermore, we determine the WET accuracy of our helium-beam radiography system for the especially heterogeneous skull base region, which is highly relevant for the treatment of head and neck and skull base tumors. Methods: With a detection system based on pixelated semiconducting Timepix detectors, we track single ions upstream and downstream of the head phantom. Furthermore, we measure their energy deposition in a thin Timepix detector behind the anthropomorphic phantom. To ensure a high precision of the image, we acquired a radiograph by using helium beams with five initial energies between 146.84 and 188.07 MeV/u following the energy painting algorithm. With a Siemens SOMATOM Confidence CT scanner, a single- and dual-energy CT were acquired with clinical protocols and translated to relative stopping power (RSP) values. After projecting these scans, the resulting WET maps were compared to the helium-beam radiograph. To evaluate the accuracy of all three modalities, a reference data set based on range-pullback measurements and a segmentation of a high-resolution CT scan was taken into account. Results: The mean absolute percentage error (MAPE) of all modalities was determined to be between 0.95% and 1.16%. Also, the root-mean-square percentage error (RMSPE) was similar for all modalities ranging from 1.19% to 1.46%. These deviations from the reference scan were found to mainly stem from an overestimation of air and sinus tissue and underestimation of cortical bone. Conclusions: The helium-beam radiograph was shown to achieve a WET accuracy competitive with that of clinically used imaging methods. If certain technical aspects are addressed, helium-beam radiography may emerge as an auspicious imaging modality for on-couch range verification of ion-beam radiotherapy treatments allowing for regular detection and quantification of anatomical changes.