When the New Horizons spacecraft reached the Pluto system in 2015, the illuminated disks of Pluto and Charon revealed the complexities of these Kuiper Belt Objects' geologic histories (Stern et al., 2015). Pluto is a world with a surprising range of surface ages and processes (Moore et al., 2016), while Charon has experienced a large amount of tectonic deformation (Beyer et al., 2017). Understanding why this difference in surface expression has resulted from the evolution of the Pluto system is one way to understand Kuiper Belt objects in general. We use topography derived from the body edge (i.e. limb profiles) in images of Pluto and Charon to study if there is an observable difference in the topographic variance of the two worlds. While the current understanding of Pluto and Charon is based primarily on studies following the New Horizons spacecraft mission, we will use ideas and techniques used in studies of other icy bodies. Although there are likely geologic differences between the two types of worlds (icy dwarf planets and icy satellites) due to how they form (Bierson & Nimmo, 2020), their water ice crusts are likely to have similar rheologies. As a result, we will make use of previous studies that focus on understanding icy satellites with limb profiles (e.g. F. Nimmo et al., 2011). We analyze the shapes of Pluto and Charon to understand the internal, thermal, and surface history of the two worlds. F. Nimmo et al. (2017) started this analysis of Pluto and Charon, focusing on the global shape