Part-based approaches organize global shape in terms of segmented parts and their spatial relationships, and are robust under transformations such as articulating limbs that are common in biological objects. It is well documented that transformations that alter qualitative part structure of a shape are more noticeable than those that do not. However, previous work has not compared sensitivity to transformations that change quantitative parameters involving the spatial relationships between parts, without altering the shape's qualitative part structure. Shape transformations were applied to a protruding part attached to a larger base (two-axial-branch shape: Experiment 1) or to a simple elongated shape (single-axis shape, Experiment 2): length, width, curvature, orientation, and location change of the part. Using a 2IFC task, increment thresholds were derived, and in Experiments 1 and 2 were converted into common metrics to enable comparison across transformations. Higher sensitivity was found for transformations involving the intrinsic parameters of a single axial branch such as length, width, curvature, and lower sensitivity for those involving two axial branches such as orientation, location, providing evidence for the single-part superiority effect. In Experiment 3, the orientation of the shapes (two-part and single-part) varied randomly on each trial. Results showed no benefit in sensitivity provided by presence of the base in the two-part shape in Experiment 1. In Experiment 4, the influence of surface, as opposed to contour, geometry was investigated by manipulating figure and ground regions defined by a fixed contour using stereoscopic depth. A protrusion (a positive part) in the figure region corresponded to an indentation in the complementary region (a negative part). Two conditions were tested, orientation and location; for each, sensitivity to positive and negative part changes was compared. Sensitivity was better for positive compared to negative parts in the case of orientation, indicating differential processing for transformations that are biologically plausible; no difference was found for location. Even when sensitivities were compared using a common scale, different transformations elicited very different sensitivities, indicating that purely physical measures of shape similarity are inadequate for perceptual similarity. The results also indicate that shape sensitivity depends on both contour and surface geometry.