Having found that participants' responses were most consistent with the medial axes of different 2-D shapes, we next tested which formulation of the medial axis was best characterized by participants' responses under conditions of perturbation. More specifically, we tested whether participants' responses were better described by the MAT formulation or a medial axis that incorporates pruning (Shaked & Bruckstein,
1998). The MAT predicts a medial axis that accommodates every available contour of a shape, such that perturbations, regardless of size, lead to the growth of new axial branches. By contrast, a pruned computation predicts that the degree of medial axis accommodation will be proportional to the degree of change induced by the perturbation, thereby allowing for greater stability across contexts (Kimia, Tannenbaum, & Zucker,
1995; Shaked & Bruckstein,
1998). Importantly, the goal of the current experiment was not only to provide an answer to the general question of whether shape skeletons in human vision are better described by models that incorporate pruning but also to characterize the degree of pruning by the perceptual system. Although some models of pruning remove only those branches that describe the perturbation, leaving the remaining skeletal structure intact (e.g., Giblin & Kimia,
2003; H. Liu, Wu, Zhang, & Hsu,
2013), other models are more stringent such that they also remove branches that describe other aspects of the local geometry such as the corners of the shape (e.g., Ebert, Brunet, & Navazo,
2002; Feldman & Singh,
2006; Telea, Sminchisescu, & Dickinson,
2004). Because of the diversity of algorithms in the literature, our pruning models were created to exemplify two general classes of models (cf. Attali et al.,
2009; Wieser, Seidl, & Zeppelzauer,
2017). More specifically, we tested a lenient pruning model that included branches describing the local geometry and a stringent model without these branches. Both types of pruning are consistent with a hierarchical organization of the medial axis. However, whereas parent branches (from which other branches grow) and those describing larger portions of the shape (e.g., branches to the corners) are less likely to be pruned by a lenient model, both types of branches are pruned by a stringent model. The lenient pruning model was defined by first computing the skeletal structure according to the MAT and then removing the new branches elicited by the perturbation (those lowest in the hierarchy). For the stringent pruning model, we further removed branches describing the local geometry (i.e., the outer corners).