Figure 1. Edgels in a sample of natural images are first detected and localized to sub-pixel accuracy.

Figure 2. Example tracing.

Figure 3. Magnification of tracing showing linear interpolants between edgel pairs.

Figure 4. The angles induced by linear interpolation are shown here.

Prior studies of the ecological statistics of good continuation cues for contour grouping have ignored the sequencing of edgels along contours or have restricted attention to cues between neighbouring edgels. Here we examine the statistics of good continuation between pairs of edgels as a function of their separation along a curve. Edgels in a sample of natural images are first detected and localized to sub-pixel accuracy.

See Figure 1.

Edgels bounding prominent objects are then hand-traced in sequence, and the two angles induced by linear interpolation between edgel pairs are extracted.

See Figures 2 and 3.

The angles induced by linear interpolation are shown in Figure 4. Parallelism is strongest when the angles sum to zero and cocircularity is strongest when the difference between the angels is zero as shown in Figure 5.

See Figures 4 and 5.

We report a number of new results:

1. A principal component analysis reveals that parallelism and cocircularity form a roughly decorrelated basis for good continuation over all edgel separations.See Figure 6.
2. The inferential power of the good continuation cues is maximal for neighbouring edgels, falling steadily to roughly half peak for separations of 64 edgels.
3. While for neighbouring edgels the parallelism cue is stronger than the cocircularity cue, this reverses for edgels separated by 4 edgels or more, suggesting that estimation noise limits the utility of the cocircularity cue at small separations.
4. Statistical distributions for good continuation are found to be more kurtotic for man-made objects than for natural objects.See Figure 7.

Figure 5. Parallelism is strongest when the angles sum to zero and cocircularity is strongest when the difference between the angels is zero as shown here.

Figure 6. A principal component analysis reveals that parallelism and cocircularity form a roughly decorrelated basis for good continuation over all edgel separations.

Figure 7. Statistical distributions for good continuation are found to be more kurtotic for man-made objects than for natural objects.