This paper presents a watermarking method in the spatial domain with HVS-imperceptibility for High Dynamic Range (HDR) images. The proposed method combines the content readability afforded by invisible watermarking with the visual ownership identification afforded by visible watermarking. The HVS-imperceptibility is guaranteed thanks to a Luma Variation Tolerance (LVT) curve, which is associated with the transfer function (TF) used for HDR encoding and provides the information needed to embed an imperceptible watermark in the spatial domain. The LVT curve is based on the inaccuracies between the non-linear digital representation of the linear luminance acquired by an HDR sensor and the brightness perceived by the Human Visual System (HVS) from the linear luminance displayed on an HDR screen. The embedded watermarks remain imperceptible to the HVS as long as the TF is not altered or the normal calibration and colorimetry conditions of the HDR screen remain unchanged. Extensive qualitative and quantitative evaluations on several HDR images encoded by two widely-used TFs confirm the strong HVSimperceptibility capabilities of the method, as well as the robustness of the embedded watermarks to tone mapping, lossy compression, and common signal processing operations. INDEX TERMS HDR, invisible watermarking, visible watermarking, LVT curve, HVS-imperceptibility.