Gradient Cuts: A Ground Bias in Figure-Ground Organization

with Stephen E. Palmer (UC Berkeley)

The goal of this project is to identify and empirically study gradient cuts (GCs) in shaded images that give rise to a ground bias in figure-ground organization.

The shaded side appears to be figural and closer in the left image (Figure-1A). Some modifications to the shaded part of an image (Figure-1B) make it appear farther from the viewer, (i.e., more ground-like).Why?

Figure-1A: Shaded side appears to be closer

Figure-1B: Shaded side appears to be farther than the flat side

Definitions (see Figure-2)

  • Equi-Luminant Contours (ELC): Lines in the image having the same luminance.
  • ELC Angle is defined as the angle between the equiluminant contours and the shared edge.
  • Depending on the orientation of a shared edge with respect to the equiluminant contours edges can be classified as
    • Extremal Edges: ELCs are parallel to the shared edge (ELC-angle=0)
    • Gradient Cuts: ELCs are not parallel to the shared edge (ELC-angle>>0)

Figure-2: Definitions

Experiment 1: Influence of Angle ELC 
The strength of GC as a ground cue was tested for many different ELC angles, when pitted against an extremal edge. Results show that the figural bias drops exponentially as the angle between the shared edge and equiluminance contours increases from zero. The data (Figure-3) is coded as the percentage of times the gradient cut side was seen as figural. In the examples shown on the x-axis, the gradient cut side is the on the left of the shared contour.

Figure-3: Data from Experiment 1

Experiment 2: Effects of Gradient Edge Alignment 
In addition to the size of ELC angle the alignment between light and dark striations of a shading gradient and the minima and maxima of the adjacent edge seems to affect figure-ground organization. In Figure 4, ELC angles are the same for all images (45 degrees everywhere except at inflections) but the alignment of the edge with the shading gradient is different, as indicated by the relative phase (delta-P) of the shading gradient and edge. 

Figure-4: Types of Gradient Edge Alignment

The results (see Figure-5) show that the strength of the bias depends strongly (ranges from 34% to 84%) on how the shading gradient and the edge are aligned. In particular, the shaded side appears as a closer figure when the phase difference is zero (red outlined images containing dark Y- junctions and light arrow juncti0ns) and as farther ground when phase difference was 180 degrees (green outlined images containing light Y-junctions and dark arrow-junctions). The images in which phase difference is 90 degrees (images with no colored outlines, containting light and dark T-junctions) are intermediate in figure-ground bias. 


Figure-5: Data from Experiment-2

Experiment 3: Effects of Junction-type: Arrows, Ys- and Ts- 
In Experiment 2, light arrows are always paired with dark-Ys and dark arrows with light-Ys. In this experiment we removed this confound by using asymmetrical triangular edges. The results (see Figure-6) show that the presence of dark-Y junctions bias a region to be appear figural and closer. 

Figure-6: Junction Types

The data demonstrate that type of alignment between egdes and shading gradients play a decisive role in determining relative depth across a contour and figure-ground organization.