We present a framework for acuity-driven visualization of super-high resolution image data on gigapixel displays. Tiled display walls offer a large workspace that can be navigated physically by the user. Based on head tracking information, the physical characteristics of the tiled display and the formulation of visual acuity, we guide an out-of-core gigapixel rendering scheme by delivering high levels of detail only in places where it is perceivable to the user. We apply this principle to gigapixel image rendering through adaptive level of detail selection. Additionally, we have developed an acuity-driven tessellation scheme for high-quality Focus-and-Context (F+C) lenses that significantly reduces visual artifacts while accurately capturing the underlying lens function. We demonstrate this framework on the Reality Deck, an immersive gigapixel display. We present the results of a user study designed to quantify the impact of our acuity-driven rendering optimizations in the visual exploration process. We discovered no evidence suggesting a difference in search task performance between our framework and naive rendering of gigapixel resolution data, while realizing significant benefits in terms of data transfer overhead. Additionally, we show that our acuity-driven tessellation scheme offers substantially increased frame rates when compared to naive pre-tessellation, while providing indistinguishable image quality.