Engagement in dementia is typically measured using behavior observational scales (BOS) that are tedious and involve intensive manual labor to annotate, and are therefore not easily scalable. We propose AVEID, a low cost and easy-to-use video-based engagement measurement tool to determine the engagement level of a person with dementia (PwD) during digital interaction. We show that the objective behavioral measures computed via AVEID correlate well with subjective expert impressions for the popular MPES and OME BOS, confirming its viability and effectiveness. Moreover, AVEID measures can be obtained for a variety of engagement designs, thereby facilitating large-scale studies with PwD populations.