Blind and low vision (BLV) users often rely on alt text to understand what a digital image is showing. However, recent research has investigated how touch-based image exploration on touchscreens can supplement alt text. Touchscreen-based image exploration systems allow BLV users to deeply understand images while granting a strong sense of agency. Yet, prior work has found that these systems require a lot of effort to use, and little work has been done to explore these systems' bottlenecks on a deeper level and propose solutions to these issues. To address this, we present ImageAssist, a set of three tools that assist BLV users through the process of exploring images by touch -- scaffolding the exploration process. We perform a series of studies with BLV users to design and evaluate ImageAssist, and our findings reveal several implications for image exploration tools for BLV users.