Psychol Res (1992) 54:267-277
PsychoNgicalResearch
PsychologischeForschung © Springer-Verlag 1992
A good-continuation model of some occlusion phenomena Diederik Wouterlood and Frans Boselie Nijmegen Institute for Cognition and Information (NICI), University of Nijmegen, PO Box 9104, 6500 HE Nijmegen, The Netherlands Received August 16, 1991/AcceptedJune 27, 1992
Summary. Occlusion phenomena raise two questions: (1) When will an occluding and a partly occluded object be seen, as opposed to several nonoverlapping objects? (2) What is seen behind the occluding object? Available theories give no satisfactory description of occlusion data. In our view, this situation is at least partially due to the fact that patterns used in occlusion studies are always regular, whereas it is almost unknown which regularities are actually perceived in occlusion patterns. We have therefore collected a complete set of data for a restricted domain of patterns with minimal regularity. Starting from these data, we have developed a model of the perceptual organization of this class of patterns and tested it in a second experiment. The model is a specification of the Gestalt law of good continuation. It assumes that there is a tendency to describe a pattern by the smallest possible number of contour elements and with the smallest possible changes of direction within and between necessary contour elements. The results fit in well with the predictions of the model. It is further demonstrated that the model also describes the preferred interpretations of many regular patterns, published in other studies.
Introduction When looking around, one usually sees objects that are partly occluded by other objects in front of them. One often has a definite impression of the shape of the whole object in the background, though part of it is covered. This phenomenon has been given several names: interposition (Chapanis & McCleary, 1953), phenomenal overlapping (Dinnerstein & Wertheimer, 1957), amodal completion (Michotte, Thines, & Crabb6, 1964), occlusion (Gibson, 1979), and figural completion (Buffart, Leeuwenberg, & Restle, 1981). Although interest in the phenomenon of
Correspondence to: E Boselie
occlusion is of very long standing, only recently have a number of experimental studies on this subject been reported in the literature (Boselie, 1988; Boselie & Wouterlood, 1989; Buffart, Leeuwenberg, & Restle, 1981; 1983; Chapanis & McCleary, 1953; Dinnerstein & Wertheimer, 1957; Gerbino, 1978; Gerbino & Salmaso, 1987; Massironi, 1988; Moravec & Beck, 1986; Sekuler & Palmer, 1992; Shipley & Kellmarl, 1992). Research has focused on two questions: (1) When will an occluding and a partly occluded object be seen, as opposed to several nonoverlapping objects? (2) Exactly what will be seen behind the occluding object? Although many theories of occlusion phenomena have been advanced (see the Discussion section of Experiment 1), Boselie (1988) and Boselie and Wouterlood (1989) showed that available theories give no satisfactory explanation of the data. Specifically, Boselie (1988) showed that a global minimum principle operates only within the constraints of locally minimal descriptions. Boselie and Wouterlood (1989) further demonstrated (a) that locally complex interpretations of junctions of contour elements are easily made (but not in order to attain globally minimal interpretations), and (b) that preferred interpretations cannot be predicted from the locally simplest interpretations of separate junctions of contour elements. Inspection of the patterns commonly used in occlusion studies suggests a factor that may be responsible for this disappointing state of affairs. In all the studies under consideration, the stimuli were very regular. Most patterns contained one or more axes of reflection symmetry or n-fold rotation symmetry, or parallel contour elements or combinations of all these kinds of regularities. It is not unlikely that the perceptual organization of a pattern is codetermined by the detection of regularities in it. It is, however, almost unknown which regularities are actually perceived in occlusion patterns. Considering this, it is quite understandable that predictions concerning the amodal completion of patterns fail because essential knowledge is missing. It seems therefore adequate to restrict research for the moment to patterns from which regularities have been removed. So we shall proceed as follows: (a) data are col-
268
Regions
Junction
Name
Characteristics
T
Cross-bar and shaft;
c
T
big
shaft delineates one
Tee
region
(2) junctions (y, t, and a junctions) in which the shaft o f the junction delineates two regions. Each pattern of necessity always contains exactly two three-line junctions, a variable number of two-line junctions, and a c o m m o n border (i. e., the contour element separating the two adjacent regions).
E x p e r i m e n t 1: Exploration A ff~s
y
big
Chevron and shaft; shaft delineates one
Method
Arrow
region
Materials. Line drawings of irregular patterns (approx. 6 x 6 cm) were used as stimuli. Lines were l-ram thick and drawn in black ink on white paper. Both regions of a pattern were of about equal size. The orientation of each pattern was determined randomly and kept constant for all subjects. The number of corners of a region ranged between 3 and 11. As was mentioned above, common borders were always straight, Two factors were systematically varied in the drawings: (1) Junction combination: all possible combinations (15) of two three-line junctions were used; (2) Closure/No-closure; with respect to every combination (a total of nine combinations) that involves at least one T or A junction, two types of pattern were distinguished: (a) Closure: smooth continuation of one or two three-line junction line segments of one region results in the closure of that region within the boundaries of the other region (see Figure 2 A and 2 B); (b) No-closure: smooth continuation does not result in closure (as in Figures 2C and 2D). Closure/No-closure cannot be manipulated unambiguously in most combinations that consist of two junctions in which the shaft delineates.two regions, so the distinction was not made there. Thus (9 x 2) + 6 different types of pattern were used. For each type of pattern two different drawings were generated, resulting in a set of 48 stimuli. The examples given in Figure 2 are representative of the stimulus material used.
y
fork
T
Chevron and shah; shaft delineates tw___o regions
t small tee
Cross-bar and shaft; shaft delineates tw.__.~o
a small
Chevron and shaft; shaft delineates lw0
arrow
regions
regions
Fig. 1. Types of three-line junctions, their names and characteristics. In order to make the junction at issue conspicuous, junction types are depicted as simply as possible (i. e., with equal length of sides and equal angles), and the rest of the contour of the regions has been curved. A region delineated by a cross-bar or by a chevron is labeled C, a region delineated by a shaft is labeled S
lected for a set o f patterns with minimal regularity; (b) a model of the perceptual organization o f this kind o f patterns is formulated on the basis of those data; (c) the model is tested in a second experiment. To ensure compatibility with the kind of display studied in the literature, the class of patterns is restricted to drawings made up of two h o m o g e n e o u s adjacent regions, with straight boundaries and a straight c o m m o n border. The number of lines coterminating in one point is two or three. Regions are delineated by lines completely enclosing a region, or regions are filled in. Regularities are minimized: there are no overall symmetries, no parallel or collinear contour elements, and equal line lengths and equal angle sizes are avoided. Only those patterns are of interest here that are readily interpreted as several planar surfaces in one or two frontal planes. Given these restrictions, only five types of three-line junctions (i. e., points at which three line segments meet) can turn up (see Figure 1). They can be further subdivided into two groups: (1)junctions (T and A junctions) in which the shaft o f the junction delineates one region, and
Subjects and procedure. Twenty-five Nijmegen University undergraduates, tested individually, were asked to look carefully at each stimulus and tell the experimenter what they saw: a stimulus made up of surfaces, with one surface partly occluding another, or a stimulus made up of two nonoverlapping surfaces. When an occlusion interpretation was reported, the subject was asked to indicate the exact outline of the surface behind the occluding one. The stimulus set was presented in a booklet, four stimuli per page. In each booklet the pages were in a different random order. The subject looked at the page that lay before him/her on a table at a normal viewing distance. There was no time limit.
Resul~ Both Junction combination and Closure/No-closure had a clear effect on the preferred interpretations, as is shown by the percentages in Table 1 for combinations involving at least one T or A junction. A n analysis o f variance on the basis o f the percentages of " N o overlap" interpretations revealed a significant effect both of Junction combination, F(8,18) = 2.55, p
PsychoNgicalResearch
PsychologischeForschung © Springer-Verlag 1992
A good-continuation model of some occlusion phenomena Diederik Wouterlood and Frans Boselie Nijmegen Institute for Cognition and Information (NICI), University of Nijmegen, PO Box 9104, 6500 HE Nijmegen, The Netherlands Received August 16, 1991/AcceptedJune 27, 1992
Summary. Occlusion phenomena raise two questions: (1) When will an occluding and a partly occluded object be seen, as opposed to several nonoverlapping objects? (2) What is seen behind the occluding object? Available theories give no satisfactory description of occlusion data. In our view, this situation is at least partially due to the fact that patterns used in occlusion studies are always regular, whereas it is almost unknown which regularities are actually perceived in occlusion patterns. We have therefore collected a complete set of data for a restricted domain of patterns with minimal regularity. Starting from these data, we have developed a model of the perceptual organization of this class of patterns and tested it in a second experiment. The model is a specification of the Gestalt law of good continuation. It assumes that there is a tendency to describe a pattern by the smallest possible number of contour elements and with the smallest possible changes of direction within and between necessary contour elements. The results fit in well with the predictions of the model. It is further demonstrated that the model also describes the preferred interpretations of many regular patterns, published in other studies.
Introduction When looking around, one usually sees objects that are partly occluded by other objects in front of them. One often has a definite impression of the shape of the whole object in the background, though part of it is covered. This phenomenon has been given several names: interposition (Chapanis & McCleary, 1953), phenomenal overlapping (Dinnerstein & Wertheimer, 1957), amodal completion (Michotte, Thines, & Crabb6, 1964), occlusion (Gibson, 1979), and figural completion (Buffart, Leeuwenberg, & Restle, 1981). Although interest in the phenomenon of
Correspondence to: E Boselie
occlusion is of very long standing, only recently have a number of experimental studies on this subject been reported in the literature (Boselie, 1988; Boselie & Wouterlood, 1989; Buffart, Leeuwenberg, & Restle, 1981; 1983; Chapanis & McCleary, 1953; Dinnerstein & Wertheimer, 1957; Gerbino, 1978; Gerbino & Salmaso, 1987; Massironi, 1988; Moravec & Beck, 1986; Sekuler & Palmer, 1992; Shipley & Kellmarl, 1992). Research has focused on two questions: (1) When will an occluding and a partly occluded object be seen, as opposed to several nonoverlapping objects? (2) Exactly what will be seen behind the occluding object? Although many theories of occlusion phenomena have been advanced (see the Discussion section of Experiment 1), Boselie (1988) and Boselie and Wouterlood (1989) showed that available theories give no satisfactory explanation of the data. Specifically, Boselie (1988) showed that a global minimum principle operates only within the constraints of locally minimal descriptions. Boselie and Wouterlood (1989) further demonstrated (a) that locally complex interpretations of junctions of contour elements are easily made (but not in order to attain globally minimal interpretations), and (b) that preferred interpretations cannot be predicted from the locally simplest interpretations of separate junctions of contour elements. Inspection of the patterns commonly used in occlusion studies suggests a factor that may be responsible for this disappointing state of affairs. In all the studies under consideration, the stimuli were very regular. Most patterns contained one or more axes of reflection symmetry or n-fold rotation symmetry, or parallel contour elements or combinations of all these kinds of regularities. It is not unlikely that the perceptual organization of a pattern is codetermined by the detection of regularities in it. It is, however, almost unknown which regularities are actually perceived in occlusion patterns. Considering this, it is quite understandable that predictions concerning the amodal completion of patterns fail because essential knowledge is missing. It seems therefore adequate to restrict research for the moment to patterns from which regularities have been removed. So we shall proceed as follows: (a) data are col-
268
Regions
Junction
Name
Characteristics
T
Cross-bar and shaft;
c
T
big
shaft delineates one
Tee
region
(2) junctions (y, t, and a junctions) in which the shaft o f the junction delineates two regions. Each pattern of necessity always contains exactly two three-line junctions, a variable number of two-line junctions, and a c o m m o n border (i. e., the contour element separating the two adjacent regions).
E x p e r i m e n t 1: Exploration A ff~s
y
big
Chevron and shaft; shaft delineates one
Method
Arrow
region
Materials. Line drawings of irregular patterns (approx. 6 x 6 cm) were used as stimuli. Lines were l-ram thick and drawn in black ink on white paper. Both regions of a pattern were of about equal size. The orientation of each pattern was determined randomly and kept constant for all subjects. The number of corners of a region ranged between 3 and 11. As was mentioned above, common borders were always straight, Two factors were systematically varied in the drawings: (1) Junction combination: all possible combinations (15) of two three-line junctions were used; (2) Closure/No-closure; with respect to every combination (a total of nine combinations) that involves at least one T or A junction, two types of pattern were distinguished: (a) Closure: smooth continuation of one or two three-line junction line segments of one region results in the closure of that region within the boundaries of the other region (see Figure 2 A and 2 B); (b) No-closure: smooth continuation does not result in closure (as in Figures 2C and 2D). Closure/No-closure cannot be manipulated unambiguously in most combinations that consist of two junctions in which the shaft delineates.two regions, so the distinction was not made there. Thus (9 x 2) + 6 different types of pattern were used. For each type of pattern two different drawings were generated, resulting in a set of 48 stimuli. The examples given in Figure 2 are representative of the stimulus material used.
y
fork
T
Chevron and shah; shaft delineates tw___o regions
t small tee
Cross-bar and shaft; shaft delineates tw.__.~o
a small
Chevron and shaft; shaft delineates lw0
arrow
regions
regions
Fig. 1. Types of three-line junctions, their names and characteristics. In order to make the junction at issue conspicuous, junction types are depicted as simply as possible (i. e., with equal length of sides and equal angles), and the rest of the contour of the regions has been curved. A region delineated by a cross-bar or by a chevron is labeled C, a region delineated by a shaft is labeled S
lected for a set o f patterns with minimal regularity; (b) a model of the perceptual organization o f this kind o f patterns is formulated on the basis of those data; (c) the model is tested in a second experiment. To ensure compatibility with the kind of display studied in the literature, the class of patterns is restricted to drawings made up of two h o m o g e n e o u s adjacent regions, with straight boundaries and a straight c o m m o n border. The number of lines coterminating in one point is two or three. Regions are delineated by lines completely enclosing a region, or regions are filled in. Regularities are minimized: there are no overall symmetries, no parallel or collinear contour elements, and equal line lengths and equal angle sizes are avoided. Only those patterns are of interest here that are readily interpreted as several planar surfaces in one or two frontal planes. Given these restrictions, only five types of three-line junctions (i. e., points at which three line segments meet) can turn up (see Figure 1). They can be further subdivided into two groups: (1)junctions (T and A junctions) in which the shaft o f the junction delineates one region, and
Subjects and procedure. Twenty-five Nijmegen University undergraduates, tested individually, were asked to look carefully at each stimulus and tell the experimenter what they saw: a stimulus made up of surfaces, with one surface partly occluding another, or a stimulus made up of two nonoverlapping surfaces. When an occlusion interpretation was reported, the subject was asked to indicate the exact outline of the surface behind the occluding one. The stimulus set was presented in a booklet, four stimuli per page. In each booklet the pages were in a different random order. The subject looked at the page that lay before him/her on a table at a normal viewing distance. There was no time limit.
Resul~ Both Junction combination and Closure/No-closure had a clear effect on the preferred interpretations, as is shown by the percentages in Table 1 for combinations involving at least one T or A junction. A n analysis o f variance on the basis o f the percentages of " N o overlap" interpretations revealed a significant effect both of Junction combination, F(8,18) = 2.55, p
