Boundary Extension: A Special Case of Rectilinear Borders?
Karen Daniels& Helene Intraub
Department of Psychology, University of Delaware
Experiment 1
Introduction


Viewers remember having seen beyond the edges of a given view (boundary
extension, BE; Intraub & Richardson, 1989).
BE may facilitate view integration by providing a surrounding spatial context
and perhaps by priming upcoming layout (Intraub, 2OO2; Gottesman & Intraub,
2003).

But is the research on BE ecologically valid?
Problem
• In all BE experiments only views with rectangular boundaries (photographs,
drawings), have been tested; this also includes recent research on memory for
3D views (through “windows”; Intraub, 2004).
• However, the visual field itself (a biological determined boundary) has a
tapering elliptical border (see Fig. 1) so the view diminishes in increments, not
abruptly as in the case of manmade, rectilinear borders.
• Also, view-boundaries in the natural world, unlike photographs and drawings,
tend to be irregular (as when looking through foliage or the opening of a cave;
see Fig 1). Irregular boundaries may provide “landmarks”, unavailable in
rectangular views, that would help the viewer remember boundary placement.
Experiment 2
Participants: 124 undergraduates (N=31 per
aperture-shape condition) -- run in small groups.
Stimuli & Participants: Rectangular and oval border conditions: (700 X 526
pixels at the midpoints for both). Participants were individually run (N=42 per
condition). Visual angle was approx. 16˚ x 12˚.
Stimuli: 15 close-up views with rectangular, oval,
odd-linear, or odd-curved borders (Fig. 2). All nonrectangular views fit within the rectangular region
(upper left); outermost points were therefore the
same for all views. Visual angle ranged from
approx. 6° X 4° to 3° X 2° depending on seating.
Procedure:
Figure 2
Procedure:
• Pictures were presented sequentially, 10 s each with a 2 s visual noise mask
between stimuli using Microsoft PowerPoint.
• Instructions: Remember the objects, background, and layout of the pictures in
as much detail as possible.
• Test: The same 15 views were shown again. Participants rated each as ‘same’,
‘closer-up’ or ‘farther away’ than the stimulus-view using the following scale:
• Pictures were presented for 10 s each with a 3 s visual noise mask between
stimuli. Multilayer graphics allowed presentation of pictures with the black
boundaries (rectangular or oval) superimposed on top so that viewers could
adjust aperture size during the test.
• Test: Same 15 views were repeated. If the view was not recognized as “same”,
participants could expand or contract the aperture to reconstruct the view they
remembered (“+” and “-” keys). Their settings were recorded in pixels.
Results and Discussion
Results and Discussion
• BE occurred for both shapes (Fig. 4 - error bars
show the 95% confidence intervals).
Opening Through Foliage
• Does BE occur for any view of a scene, regardless of the shape of the
aperture that defines its boundaries, or is it primarily limited to unusual cases
(i.e., crisp rectilinear boundaries), that rarely, if ever, occur in nature?
Two Hypotheses
1) Natural aperture shapes (e.g. tapering or irregular) will eliminate BE.
Rectilinear boundaries are unique in eliciting extrapolation beyond the
boundaries of a view.
2) BE reflects processes that help provide a coherent representation from a
succession of partial views of the world (e.g., Intraub, 2002), and therefore should
occur irrespective of aperture shape. If true, two alternative corollary
hypotheses arise:
- More naturally shaped boundaries will elicit less BE than rectilinear
boundaries (for reasons described earlier)
or
- Shape may not affect the amount of BE; spatial extrapolation may be
elicited by the outermost points of the view.
(Fig. 3 - error bars show the 95%
confidence intervals).
•Amount of BE did not differ across
shapes (F=(3,120)=.52, n.s.).
Fig. 3
• BE is not an artifact of rectilinear views. Viewers remembered seeing beyond
the edges of apertures with organic shapes (i.e., shapes that are more
representative of those occurring in nature).
• Furthermore, the amount of extrapolation was the same for all views, regardless
of aperture shape, suggesting that BE emanates from the outmost points of a
view.
• However, BE was evaluated using a qualitative measure that may have been
too coarse to pick up subtle differences in spatial memory across shapes.
• To address this, in Exp.2, a quantitative measure was used in which viewers
adjusted the size of the aperture to match what they remembered.
indicating that BE, and not a pleasing ratio of
picture size to screen size was the cause of
the bias.
• Again aperture shape had no effect on the
amount of extension, (t(44)=-.71, n.s.).
Fig. 5
• As in Exp. 2, this result was not due to a few extreme scores. Participants tended
to extend rather than to restrict the boundaries (sign test, z=-5.19, p<.01).
Summary
• BE occurred across participants: sign test
showed they were more likely to extend than
to restrict (z=-10.7, p<.01).
occurs for a variety of aperture-types; it is not elicited by the special
characteristics of rectilinear boundaries. New aperture shapes tested are
consistent with those occurring in nature: rounded, elliptical views (similar to the visual
field) as well as irregular views typical of the environment (rounded and angular).
amount of extension appears to be determined by the outermost points of
the view (at least across the range of apertures in the present study). With
outermost points held constant, the shape of the view did not affect the amount of
BE. Both qualitative (Exp 1) and quantitative (Exps 2 & 3) test methods yielded the
same results.
Fig. 4
• The sign test also shows that the results cannot be explained by a tendency to
expand and restrict borders equally often, but with different magnitudes (e.g.,
greater expansion than restriction). The error was clearly unidirectional.
•BE occurred for all aperture shapes
(Fig. 5 – error bars show 95% confidence intervals),
 The
• Results replicated those in Experiment 1 using a quantitative measure.
Monocular View (From Gibson, 1979)
• Participants tended to expand the apertures
 BE
• Again, amount of BE did not differ across
aperture shapes (t(82)=.34, n.s.).
Figure 1.
Results and Discussion
• Although the area of the visible region was different for the oval and rectangle,
the width and height were the same – so that the outermost points of the oval
were identical to those of the rectangle. The suggests that boundary extension
emanates from the outmost points of a view.
Alternative Explanation. However, perhaps the similarity obtained between
shapes is not due to BE at all, but instead to participants expanding the
borders to create a pleasing ratio of picture size to screen size.
In Exp 3, the length and width of the apertures were increased to equal the
mean length and width set by participants in Exp 2. If the results were due to
setting a pleasing ratio, then no BE should occur in Experiment 3.
 Finally,
Experiment 3 shows that aperture expansion obtained in Experiment 2, was
not due to viewers adjusting the aperture to create a more pleasing ratio of picture
size to screen size. Aperture size in Exp 3 was based on the mean remembered
size in Experiment 2, yet the same amount of BE occurred.
Conclusion
The world is always perceived a piece a time. The present research shows
that the representation of a scene includes an extrapolated region beyond the edges
that anticipates the continuity of layout, irrespective of the shape of the view. Even
more natural aperture shapes similar to our visual field incite this extrapolation.
Boundary extension may serve to place successive views within a larger spatial
context, perhaps even serving to prime upcoming layout during visual exploration
(Intraub, 2002).
References
Gibson, J.J. (1979). The Ecological Approach to Visual Perception (p. 119). Boston: Houghton Mifflin Co.
Gottesman, C.V. & Intraub, H. (2003). Constraints on spatial extrapolation in the mental representation of
scenes: View-boundaries vs. object-boundaries. Visual Cognition, 10(7), 875-893.
Intraub, H. & Richardson, M. (1989). Wide-angle memories of close-up scenes. JEP: LMC, 15(2), 179-187.
Experiment 3
Procedure: Same stimuli and procedure as Exp. 2. Midpoints were 723 X 544
pixels (the mean remembered midpoints from Exp. 2). N=23 per condition -individually run. Visual angle was approx. 17° X 13°.
Intraub, H. (2002). Anticipatory spatial representation of natural scenes: Momentum without movement? Visual
Cognition. Special Representational Momentum, 9 (1-2), 93-119.
Intraub, H. (2004). Anticipatory spatial representation of 3D regions explored by sighted observers and a deafand-blind-observer. Cognition, 94, 19-37.
Acknowledgments
The authors thank programmer, Scott Kay. Research was supported by NIMH Grant MH54688.