We propose a Tone Mapping Operator, denoted HMD-TMO, dedicated to the visualization of 360 • High Dynamic Range images on Head Mounted Displays. The few existing studies about this topic have shown that the existing Tone Mapping Operators for classic 2D images are not adapted to 360 • High Dynamic Range images. Consequently, several dedicated operators have been proposed. Instead of operating on the entire 360 • image, they only consider the part of the image currently viewed by the user. Tone mapping a part of the 360 • image is less challenging as it does not preserve the global luminance dynamic of the scene. To cope with this problem, we propose a novel tone mapping operator which takes advantage of both a view-dependant tone mapping that enhances the contrast, and a Tone Mapping Operator applied to the entire 360 • image that preserves global coherency. Furthermore, we present a subjective study to model lightness perception in a Head Mounted Display.