How does the brain infer the structure of the external world from sensory inputs, while remaining insensitive to transformations such as translation and rotation? In vision, the image projected on the retina is not only subject to a static transformation: it continuously undergoes a dynamic transformation, due to motion of the eye and head. On the scale of foveal vision, the amplitude of this motion during fixation (known as fixational drift) is large. Thus, naively,  the eye’s motion should smear the image and hinder the brain’s ability to infer high resolution structure. I will discuss this puzzle in the context of the vernier hyperacuity task, in which a subject reports on the relative position of two slightly misaligned vertical bars. The range of eye motion during the performance of the task, is two orders of magnitude larger than the discernible bar separation of trained human subjects. I will first discuss how the brain might achieve hyperacuity despite eye motion. I will then focus on a counterintuitive effect known as the “contrast paradox”: increasing the contrast of both bars improves performance. However, increasing the contrast of only one bar degrades performance - even though naively more information about the position of the higher-contrast bar is arriving at the retina. I will argue that the contrast paradox may be tightly related to the task facing the brain, of inferring high resolution detail amid much larger random motion.