The emergence of large vision models (LVMs) is following in the footsteps of the recent prosperity of Large Language Models (LLMs) in following years. However, there's a noticeable gap in structured research applying LVMs to human-robot interaction (HRI), despite extensive evidence supporting the efficacy of vision models in enhancing interactions between humans and robots. Recognizing the vast and anticipated potential, we introduce an initial design space that incorporates domain-specific LVMs, chosen for their superior performance over normal models. We delve into three primary dimensions: HRI contexts, vision-based tasks, and specific domains. The empirical evaluation was implemented among 15 experts across five evaluated metrics, showcasing the primary efficacy in relevant decision-making scenarios. We explore the process of ideation and potential application scenarios, envisioning this design space as a foundational guideline for future HRI system design, emphasizing accurate domain alignment and model selection.