Skeletal representations of shape in human vision: Evidence for a pruned medial axis model

Abstract

A representation of shape that is low dimensional and stable across minor disruptions is critical for object recognition. Computer vision research suggests that such a representation can be supported by the medial axis-a computational model for extracting a shape's internal skeleton. However, few studies have shown evidence of medial axis processing in humans, and even fewer have examined how the medial axis is extracted in the presence of disruptive contours. Here, we tested whether human skeletal representations of shape reflect the medial axis transform (MAT), a computation sensitive to all available contours, or a pruned medial axis, which ignores contours that may be considered "noise." Across three experiments, participants (N = 2062) were shown complete, perturbed, or illusory two-dimensional shapes on a tablet computer and were asked to tap the shapes anywhere once. When directly compared with another viable model of shape perception (based on principal axes), participants' collective responses were better fit by the medial axis, and a direct test of boundary avoidance suggested that this result was not likely because of a task-specific cognitive strategy (Experiment 1). Moreover, participants' responses reflected a pruned computation in shapes with small or large internal or external perturbations (Experiment 2) and under conditions of illusory contours (Experiment 3). These findings extend previous work by suggesting that humans extract a relatively stable medial axis of shapes. A relatively stable skeletal representation, reflected by a pruned model, may be well equipped to support real-world shape perception and object recognition.

Figure 1

Cropped photograph of the tablet and stimulus display. In Experiments 1 and 2, each shape was presented as a white silhouette on a black background, as illustrated here. In Experiment 3, illusory shapes were presented using four black crescents on a white background (see Experiment 3). The location of the shape onscreen was randomized.

Figure 2

The different shapes used in Experiment 1: (a) rectangle, (b) T, (c) square, and (d) arc. Gray circles represent individual responses. Participants' responses for each shape are presented separately against the medial (left column, red dashed lines) and principal axes (middle column, red dashed lines), as well as the best-performing boundary-avoidance model (right column, red grid). Shapes are presented against a black background to mirror their presentation to participants on the tablet. Shapes are not drawn to scale.

Figure 3

Smooth curves from the density ridge algorithm with increasing variance parameters. Each row displays a single shape from Experiment 1. Each column displays the smooth curves from each variance parameter (variance parameters displayed along the bottom). Shapes are presented against a black background to mirror their presentation to participants on the tablet. Shapes are not drawn to scale.

Figure 4

The four conditions from Experiment 2: rectangle with (a) small and (b) large external perturbations, and rectangle with (c) small and (d) large internal perturbations. Gray circles represent individual responses. Participants' responses are presented against a medial axis with lenient pruning (left column, red dashed lines), a medial axis with stringent pruning (middle column, red dashed lines), and the MAT structure (right column, red dashed lines). Shapes are presented against a black background to mirror their presentation to participants on the tablet. Shapes are not drawn to scale.

Figure 5

Smooth curves from the density ridge algorithm with increasing variance parameters. Each row displays a single shape from Experiment 2. Each column displays the smooth curves from each variance parameter (variance parameters displayed along the bottom). Shapes are presented against a black background to mirror their presentation to participants on the tablet. Shapes are not drawn to scale.

Figure 6

Conditions from Experiment 3: Kanizsa (a) rectangle and (b) square. Gray circles represent individual responses. Participants' responses are presented against pruned medial axes in these conditions (left column, red dashed lines) and the MAT computation (right column, red dashed lines). As described in the main text, stimuli in this experiment were presented against a white background on the tablet computer. Shapes are not drawn to scale.

Figure 7

Smooth curves from the density ridge algorithm with increasing variance parameters. Each row displays a single shape from Experiment 3. Each column displays the smooth curves from each variance parameter (variance parameters displayed along the bottom). As described in the main text, stimuli in this experiment were presented against a white background on the tablet computer. Shapes are not drawn to scale.