Grounding spatial deixis is essential for establishing shared spatial understanding in HRI. This paper presents the Spatial Deixis Model (SDM), a perceptual framework allowing a robot to infer the English spatial deixis here and there from pointing gestures and using a dynamic, embodied peri-personal space. We performed an empirical evaluation of the SDM with 12 participants in 5 scenarios with different contexts (e.g., varying distances and/or heights with respect to human and robot). Results show that the localization accuracy for the pointed-at objects across 174 trials is 92% and the overall agreement across all trials is 63.7%, demonstrating that SDM generally captures the dynamic notion of spatial deixis.