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The current capabilities of modern pixel-detector technology has provided the possibility to design a new generation of radiation monitors. Timepix detectors are semiconductor pixel detectors based on a hybrid configuration. As such, the read-out chip can be used with different types and thicknesses of sensors. For space radiation dosimetry applications, Timepix devices with 300 and 500 microns thick silicon sensors have been used by a collaboration between NASA and University of Houston to explore their performance. For that purpose, an extensive evaluation of the response of Timepix for such applications has been performed. Timepix-based devices were tested in many different environments both at ground-based accelerator facilities such as HIMAC (Heavy Ion Medical Accelerator in Chiba, Japan), and at NSRL (NASA Space Radiation Laboratory at Brookhaven National Laboratory in Upton, NY), as well as in space on board of the International Space Station (ISS). These tests have included a wide range of the particle types and energies, from protons through iron nuclei. The results have been compared both with other devices and theoretical values. This effort has demonstrated that Timepix-based detectors are exceptionally capable at providing accurate dosimetry measurements in this application as verified by the confirming correspondence with the other accepted techniques.