Sources of Variability in Cartographers’ Deconstruction
of Fractals
by  © Visvalingam, M.
CISRG Discussion Paper Series No 17, University of Hull, 25 pp

For the sake of posterity, please cite from the published version:
Visvalingam, M (1999)
"Deconstruction of Fractals and its Implications for Cartographic Education", The Cartographic J 36 (1) 15 - 29.

3. From algorithmic to human deconstruction of the teragonss

Different deconstructors impose a different structure on even relatively simple lines. The rows in Figure 3 list the various algorithmic deconstructors and show the series of decogons output by each. To facilitate comparison, all the decogons in a given column have the same number of points. Only a couple of line filtering algorithms was investigated; Fourier and wavelet analyses, which were not included, are likely to produce other patterns. Wang’s (1996) bendsimplify algorithm only extracted the final square initiator shown in the fourth row from the bottom in Figure 3; it used 11 points for depicting a square (Visvalingam and Herbert, 1998). Although all these decogons are equally plausible, the purpose of the research was to ascertain whether cartographers would tend to agree on particular decogons or whether they would also output quite dissimilar decogons. It was hoped that the artificial exercise of having to generalise a meaningless geometric pattern would a) provide some insights into the cartographer’s cognitive processing of these lines, and b) inform further research into digital line segmentation, structuring and generalisation.

4. The exercises and method of data collection and analysis

Appendix 1 provides a listing of the exercises set. Exercise 1 requires the subject to select 12 out of the 32 points defining the teragon. Similarly, in Exercise 2, they were expected to select 20 to 40 points from the 250-point curve. The exercise is based on that designed by the psychologist Attneave (1954), which was also used by cartographers, such as Marino (1979), White (1983) and several others since then. In this particular set of experiments, sample numbers were specified to enable the participants to get a feel for the required scale of abstraction. It was hoped that having done so, they would then be able to express what they felt was the appropriate solution for that scale in the second part of each exercise.

The exercise was initially undertaken by participants at the British Cartographic Society’s Design Group meeting at the 1996 Annual Symposium in September at Reading. Unfortunately, the aspect ratio of the drawings was distorted by the fax machine. However, this seems to have affected only the output of one respondent. Although there were over 25 people at the meeting, only 8 cartographers returned the completed exercise. Two other veteran cartographers, who were not at the Symposium, also undertook this exercise in a less time-constrained fashion. Ten results are by no means representative of the cartographic community and were only treated as indicative. In Tables 1 & 2, the set returned by practising cartographers is referred to by the label C. The label S refers to 18 student returns; David Forrest from Glasgow University kindly persuaded Diploma level cartography students to attempt this exercise. Not all subjects included explanations for their choice of points.

These results were analysed and interpreted as follows. The first task was to study the figures and tentatively group them into categories. The categories were not pre-defined but were data-driven. The variants within each category were then sub-classed and related, using links in figures and the explanations where possible. Having structured the data, the author tried to deduce the implications of the results. In the meantime, the BCS Design Group members repeated the exercise some 18 months later at their meeting in April 1998 at Southampton. The author was not present. The author presented her interpretation to three of these participants at the September 1998 BCS Symposium. This prompted them to reveal aspects of their behaviour that they had not recorded at Reading in 1996. On reflection, they felt that some patterns seemed to be better than their original ones. This paper was presented to the BCS Design Group meeting at Glasgow University in November 1998. Visvalingam (1998) provided an interpretation of the original returns made by individuals in 1996 (Sections 5 to 8). Her paper provided the framework both for assessing the results from the repeat exercise at Southampton (see Section 9) and for guiding discussions at Glasgow (Section 10). The conclusions of this paper (Section 11) take account of these discussions.

5. Some initial reactions

Everyone at the meeting attempted the exercise. Some said that they were too embarrassed with the results to hand them in. Some of the comments made by cartographers at Reading are worth noting. Firstly, and most importantly, they felt that the exercise was far too artificial and that it did not relate to how cartographers worked on lines. Some said that they went dizzy parsing the line forwards and backwards, checking the number of points. In comparison to the length of source lines and the number of points to be selected in the exercises undertaken by Marino (1979) and White (1983), Exercise 1 was not at all onerous. Even so, this suggests that the results presented here (and possibly those presented by other authors) may be partial and that some types of cognitive processing of lines (in the non-returns) are perhaps not being detected.

Several cartographers asked the sort of questions they were trained to ask, namely - Why are we doing this? What type of geographic phenomenon does the data refer to? What scale of reduction does the subset represent? Some felt that without such information, the exercise was artificial, meaningless and a waste of time. Some of those, who returned their output, stated that they hoped that their solution was what I was looking for and said that they were looking forward to hearing what the solution should have been. Again, this reflects some uncertainty and discomfort with performing a deconstruction as opposed to a generalisation.

Other cartographers, who were users of mapping software, stated that they found it difficult to project a mental visualisation of target shapes since their normal working practice had made them reliant on the feedback provided by software, which produced curves based on points they input. Without such feedback in a paper exercise, they were unwilling to draw their own curves. These comments are noted here since they provide opportunities for further research into how software may be conditioning cartographic visualisation. This paper itself is more focused on the pattern of results in the returns.

Since most of the non-returns were discarded in the room, they were studied later. Although they were not included in the analysis, some anecdotal reference is made to some of the discarded output later. Scribbles, showing steps in exploring progressive abstraction, have influenced the summary of the results presented here.
 

6. Initial Observations and Comments on Exercise 1

The results from Reading are classified and presented in Figures 4 to 7. Some of the figures have been re-drawn by the author where the originals were either too untidy or where the scanned image was not clear. Table 1 shows the number of times a figure of a particular type was produced. In classifying the results, output with mixed patterns have been assigned where justifiable to the class which it most resembled since the aim of the exercise is to study the types of patterns rather than individual patterns per se. Not all subjects gave reasons for why they had chosen a particular pattern, so again the reasons suggested in this paper should be treated as anecdotal even if plausible.  All, except one person, attempted to retain the 4-fold rotational symmetry. In general, the figure was being perceived as a whole and the original partition planes were largely ignored. In 10 out 50 figures, subjects appeared to be attempting to use the four parts to explore different patterns. Figure 4a is a good example of such varied exploration. Figure 4b shows a leaning towards a convex rather than concave shape but there were an equal number of people drawing concave shapes. Figure 4c shows a drift towards wings. Figure 4d, shows the exploration of different wing shapes.

Nineteen (of the 56 figures) consisted of rectilinear patterns (Figure 5). The only figure to show a deliberate directional bias was Figure 5f - this orientational bias could be due to the distorted aspect ratio on the faxed figures on which they were originally drawn. Fourteen of the 19 figures corresponded to Figure 5a. Nearly all cartographers, who drew this pattern, produced it during the exploratory phase; only one cartographer produced this as the final rendition. The following reasons were presented in its favour:

1. It is a simpler, “less busy” pattern
2. It omits the smaller juts
3. It retains the biggest branches of the figure
4. It retains the original rectilinear features
5. The original figure resembles a road network

One person included a frame which just fitted the teragon and chose to focus on the background consisting of 4 disjoint parts which were easier to simplify as shown in Figure 5b (which is the complement of Figure 5a). The same cartographer felt that Figure 5c was the best simplification. There was some discomfort with the somewhat awkward offset cross in Figure 5a. Figures 5d and 5e seek to retain the rectangular pattern while showing the extent of the figure (perhaps for display at reduced scale or to make the offset cross look less awkward). The offset cross is clearly being interpreted as on offset junction in Figure 5f but this visualisation may have been induced by the distorted aspect ratio of the faxed figures

All except one person who started with the offset cross (Figure 5a), then chose the wing and petal shapes shown in Figure 6; 21 of the 56 figures were of this type. The subjects stated that they deliberately chose to discount the rectangular shape since the winged shapes were more useful for indicating the main and sub-branches in the structure. Cartographers were clearly aware that this structure could be shown using different shaped wings (e.g. exploration of them in Figure 4d as noted earlier). In their final renditions, the cartographers tended to produce straight edged wings, while the students tended to prefer curvy petal-shapes. But, 12 of the 21 figures used the midpoints on edges, instead of the corner points, in the straight edged and curvy shapes. The cartographers indicated a preference for figures which applied the give and take rule (as in Figure 6a, 6e and 6f). Five students produced the pattern in Figure 6g, which was more concerned with showing the overall shape and extent of the 4-petalled shape, perhaps for display at smaller scale.

The shapes In Figure 7 also appear to be more concerned with showing the overall extent of the figure. Here again, opinion was divided between the use of convex and concave forms. Of the 14 shapes in this class, 9 were broadly convex. However, the final preference was for concave figures. One of those who produced the concave form in Figure 7c said that she had attempted to balance the give and take and then adjust the shape as in Figure 7d. Note that Figure 7d could be viewed as a stylised version of the offset cross in Figure 5a, in which the minor branch was omitted. Note also, that many of the patterns in Figure 7 use near-redundant points in preference to information rich points located on curvatures in lines.  In the final analysis, 15 out of the 28 respondents chose wing and petal shapes for their final rendition. It is interesting that , like the line generalisation algorithms, several respondents decided to sacrifice the level 4 bilateral symmetry in order to preserve the first three levels of symmetry. Some students were also tending to ignore the level 2 symmetry.

7. Observations and Comments on Exercise 2

People had much more difficulty performing a point-based exercise with the second exercise given the line with 256 points. They tended to ignore the specified target range of points and focused on the desired shape instead. Again, the first of the pair, used for exploration, showed mixed patterns but there was an overwhelming convergence towards wing and petal shapes in this exercise. Five people, four of whom were students, abstracted the first generation teragon (Figure 8a) during the exploratory stage; ten considered rotating the shape (Figures 8b and c). Interestingly, Figure 8b is one of the decogons abstracted by the Douglas-Peucker algorithm (Visvalingam and Brown, 1999). One student produced a generalised winged pattern with just 12 points (Figure 8d), showing a re-use of a pattern already encountered in Exercise 1.

There were some variations in the petal shapes but they all have the same orientation as Figures 8b-d. Figure 8e, produced by the same student who produced Figure 6e, shows a tendency to re-use the same strategy. Note that this student's conscious segmentation of the figure involves a rotation of the partition planes and of the figure, which is implicit in many of the other figures. The emergent central square in Figure 8f, produced by 5 students, is noteworthy since it shows an attention to form; this figure was then generalised as shown in Figures 8g and 8h, which correspond to Figure 6g. They show that many students and cartographers preferred to include redundant points to pick out a petal shape and ignore the level 2 symmetry. Two people, one of whom had produced Figures 5a-c, explored the spatial coverage of the figure (Figures 8j and 8k) and then provided stylised abstractions with centrelines. The drawings, which had been discarded by two cartographers, were a cross between Figures 7d and 8j. One of them told the author that she tended to explore patterns using curves and that she found it difficult to fit curves to the level 2 teragon. Although the symbolic shapes are distinctly different, they too have segmented the figure as in Figures 8b-h. The subjects were tending to ignore the low-level rectilinear pattern (which made them think of pixels in remote sensed images) and were focusing more on the overall pattern which has a four winged shape.

8. Some Implications of the Observations

The results indicate that the art of line generalisation is not entirely intuitive and impenetrable. They suggest some of the types of assumptions and cognitive processes responsible for the variations in output in this case study; for example:

1. Despite reassurances to the contrary, there was an initial assumption that there must be a correct answer and that the exercises had been designed to reveal the level of knowledge and competence of respondents. There has been much more interest in the study now that the participants have grasped the difference between deconstruction and generalisation and see the study as probing the various cognitive processes involved in manual generalisation.
    

2. The majority of participants were tending to see the closed curves, with or without a bounding box, as an object - i.e. the figure as opposed to the background. Only one cartographer also analysed the figure in terms of spatial coverage, on the one hand, and typifying skeletons at the other. Although cartographic training covers figure-ground relationships and centrelining, the results suggest that most cartographers are selecting a preferred strategy for analysis at the outset. If further tests confirm this, cartographic training should perhaps emphasise different approaches to encourage lateral thinking.
    

3. Having 'seen' the pattern as figure, there is a tendency to ignore the original partition planes and orientation of the 4-fold symmetry. The spatial coverage of the figure, which was consciously explored in Figure 8i, induced a rotation of the pattern.
    

4. There was also a very strong urge among some cartographers and students to mentally map the seen figure onto known prototypical forms of objects; i.e. to objectify the figure. Nouns, such as roads, islands, lake, built-up area, woodland, wings, cross and swastica, were used in written and verbal descriptions; reference was also made to segmented remote sensed images and to roads. Such semantic labelling could have been induced by the normal practice of selecting a generalisation that was appropriate for a given object. The psychologist Rubin reported in 1915 that we have a tendency to see objects - not the retinal patterns. We see objects even in clouds and in ink blots. The Rorschach ink blot personality test is based on the assumption that perceptual and personality differences tend to affect what we see. Here previous experience is another factor.
    

5. The process of recognition appears to involve the mental projection of the prototypical object shape onto the figure, leading to a biased view of the latter, especially in Figure 8h.
    

6. Equally, the conscious rejection of the rectilinear outline (Figure 8a) in favour of the overall shape of the figure, especially in the case of the level 2 teragon, indicates a capacity to review the output and try another object or form.
    

7. Those who rejected the rectangular pattern in Figure 5a noted that it violated the give and take rule in cartography. They preferred some of the wing shapes in Figure 6 because they articulated this rule. Cartographers appear to be using this rule to track the loss of symmetry.
    

8. Curiously, it appears that the tendency to see a known object involves a disregard for certain types of symmetry and this is especially evident in Figure 8. Figure 6g and Figure 8 show a tendency to place much greater emphasis on the shape of the extruding parts rather than on the detail in the centre. This involves a disregard for the level 2 symmetry that is particularly noticeable in Figures 6g and 8h.
    

9. Some people were undertaking scale independent generalisation while others were thinking in terms of scale-dependent reduction (Figures 5d and 5e, 6g and Figure 7). Both approaches are valid. However, several of those who assumed a scale reduction not only exaggerated the area of the figure but also used many superfluous points in the extruding parts at the expense of the inner parts.
    

10. This lends weight to the psychological presumption that figures may be segmented at their inner concavities; for example, outlines of a person and of an aeroplane can be segmented into their component parts using this approach. Figures 6g and 8h, for instance, could be segmented at the apex of the central V-shape into four petals. However, the perception of open curves, such as coastlines, may not be biased in favour of identifying the extrusions and needs to be tested. Even here, the line would be segmented differently if the main aim was to show its extent.
     

11. The lack of preservation of the two-fold level 2 rotational symmetry may be due to innate distortions in perception and not necessarily due to the conscious use of recalled prototypical object forms. During the review process two professional cartographers, who thought they had returned Figure 6d, offered new information when shown Figure 4. They stressed that it took repeated meticulous checks and conscious effort to preserve the four-fold symmetry. To their surprise, in their initial attempt at abstracting the 4-fold symmetry they had only drawn similar, and not identical, shapes. On closing the curve, they realised that the first and last parts were not identical (as in Figures 4c, 4d, 6c and 6f. They had thought that they were drawing the same pattern. It was only at the stage of self-review that they had noticed the lack of identity, which prompted them to enforce the symmetry at the edit stage prior to handing in the figure. One person suggested that her output might have been different had she rotated the paper as she worked around the curve but was uncertain as to which specific wing-shape she would have chosen.
    
    There are two factors that may be biasing their perception, namely the orientation of the parts and the involuntary switch of figure and ground. Visvalingam (1996) and Visvalingam and Brown (1999) demonstrated that the triadic Koch curve had its counterpart in the Cesaro curve. It was quite obvious that the orientation of the geometrically identical shapes (e.g. when the paper was rotated) made them appear different. Figure 4d and, to a lesser extent, Figure 6b have orientation dependent shapes. It is interesting that, unlike professional cartographers, students do not appear to have engaged in self-review and edit.
    
    In addition to the orientation-induced perception, there may also be some difficulty in holding a consistent mental image of the figure-ground classification. It is well known that given an ambiguous figure, the brain does not settle for a single interpretation but tends to involuntarily switch between two visual interpretations as it does with the Rubin and Mach figures (Gregory, 1970, p16 and p38). Here, there are three factors that may be facilitating the switch - the linear symbolism, the repeating pattern and local focusing. The perception may have been more stable had the 'island' been shaded. In this context, it is noteworthy that several participants at the 1998 Annual Symposium of the British Cartographic Society at Keele said that they found the up-side down maps of Britain (USDMC, 1998) very disconcerting. It was obvious that there was a need to recreate a mental map of the place in much the same way that one has to consciously learn to use a new keyboard with a different layout.
    
    Even impossible pictures showing normal objects, such as those drawn by Hogarth and by Escher, have to be carefully analysed to detect logical inconsistencies since the eye does not immediately perceive these. When working on the line, people were tending to focus on local sections of the line. The output shape is inevitably dependent upon the shape and orientation of the segment of line being processed, which could also be inducing figure-ground reversals. Where the figure had not been consciously partitioned into identical segments, there would be a tendency to output only similar shapes. Trained cartographers rely on wholistic vision and systematic comparisons during the 'standing back' stage to adjust their tentative shapes, which may have been only similar, into symmetrically identical ones. The behaviour of learners may be suggesting that such evaluative techniques are acquired rather than innate; equally it may be reflecting the fact that professionals work much faster than students, who may not have had enough time for evaluation of their drawings.
     

12. The results also show that students have a distinct preference for curves while some cartographers are happy to render edges connecting points. The reliance on computer software for fitting curves has already been noted.
     

13. Individuals tended to stick with a strategy which proved to be successful in Exercise 1. They may have covertly explored other approaches for Exercise 1 and it is hoped that group discussions will provide more information.
     

14. Although several participants were suspicious that there was perhaps a right answer, which they were missing, the results confirm that there are several equally valid deconstructions of the given line. Not all of these patterns, including Figure 5a, can be derived using existing line deconstruction algorithms. Although the offset cross in Figure 5a was initially rejected by the cartographers at Reading, some two years later, some cartographers felt that it was the best abstraction. It looks as if the rectilinear pattern may have been biasing recognition after all. If the figure had been interpreted as a road, it would make sense to drop the smallest branch. Although there were two equally sized branches, the Gestalt law on continuance may be justifying the elimination of the orthogonal branch. This constitutes a form of bend simplification. However, neither the bendsimplify algorithm (Wang and Muller, 1998) nor its ArcInfo implementation can provide this abstraction (Visvalingam and Herbert, 1998). Also, given teragon 2, the bendsimplify algorithm outputs distorted figures that do not resemble any of the manual deconstructions. There is thus a continuing research opportunity for identifying additional line generalisation algorithms. As pointed out by Brassel and Weibel (1988), significant advances in the design of generalisation algorithms awaits algorithms for segmenting and structuring lines.

This experiment and the results have confirmed that artificial lines may be segmented and structured in a variety of ways as noted by Visvalingam and Brown (1998). Although the semantics associated with natural lines tend to bias consensus towards specific line structuring schemes, the output of different individuals is known to vary. This suggests that like the algorithms for line generalisation, the algorithms for structuring lines may not be universally applicable either and that there would be a requirement for context-dependent techniques. The results point to some of the issues which need to be taken into account in the design of algorithms and in cartographic training.

9.  Insights from a second attempt

Some 18 months after the initial attempt at Reading, members of the BCS Design Group re-did the exercises. Only nine members returned their work. With the exception of one person, a computer specialist, all the others were cartographers by profession.

With Exercise 1, five of the respondents chose wing patterns (Figure 6a-d). The wing shapes were still not necessarily identical in the 4 parts, showing the difficulty that people have in switching between holistic perception and local processing. Four of the five people in this group used mid points as in Figure 6d. One person switched to Figure 5a, stating that it was a better representation, which used existing points to maintain the shape of the figure. Two others opted for this figure initially but felt that it should be adjusted to that in Figure 5d to balance the give and take and preserve the area of the figure. Another person, who started off with Figure 7b changed to Figure 5e - both of which place emphasis on the extent of the figure.

When it came to Exercise 2, two individuals claimed that they could not visualise the degree of generalisation required at all but the shapes they produced showed the rotation of the figure as in Figure 8b. In all, 7 people rotated the figure. Four of them then smoothed their patterns with curves as in Figure 8g, saying that point filtering made the figure too angular. One of the figures in this set of 7 was particularly interesting since it consisted of a rotation of Figure 8a. None of the figures lost sight of the level 2 symmetry as Figure 8h did. Two other cartographers reproduced Figure 8a. One said that she was "trying to keep the shape, orientation and square character of the feature - area is OK too". Places where the line had been re-worked showed the conscious application of the give-and-take rule.

Visvalingam and Brown (1999) noted the effect of start and end points on algorithmic deconstruction. These results show that the manual application of even the give-and-take rule generates different results since it was being applied within different stretches of the line. One cartographer noted that it was difficult to see the overall shape since there was too much choice, and that it was easier to see the shape to aim for if the picture was viewed at a distance. But, it looks as if neither the attempt at holistic vision nor logical visual analysis led to consensus.

10.  Peer Discussion

There were 17 participants (excluding the author) at the Glasgow meeting; 7 of these were professional cartographers and the rest were students. After a presentation of the material in Secions 1 to 8 of this report, the questions in Table 3 were used to spur discussion. The participants were unsure as to whether they consciously manipulated the priorities of cartographic rules during their intuitive generalisation and abstained on Q14. Indeed, practising cartographers have questioned the value of rules and guidelines in design (Collinson, 1997). The extracts from individual responses indicate that several considerations were being consciously evaluated and balanced. Although, this experiment was not successful in extracting a statement of priorities, there is clear indication that many cartographers consciously apply the give-and-take rule during the evaluation phase, even if not during the construction phase (Q5 and individual responses). The output of students and their unwillingness to vote on some questions, such as Q5, indicate that the principle of using give-and-take is not in-born and intuitive but that it is acquired through training and/or experience. The students also abstained from Q9 and did not fully understand what figure/ground switch alluded to, suggesting that this is also learnt, but they did feel that it would be easier to maintain a stable view of the figure if it had been area-filled. Both cartographers and students showed that they tended to rely on proven strategies (Q13), and evidence indicates that give-and-take is regarded as a reliable technique.

There was unanimous agreement that there is tendency to see a closed curve as the figure (Q1) and to objectify it (Q3), even if not everyone felt that the gridded outline should be ignored (Q2). Here, teachers of cartography felt that while non-cartographers may be looking to make a shape, cartographers would (perhaps as a result of training?) distinguish between point, line and area objects rather than real world objects, such as woodlands and roads. At the same time, it was pointed out in response to Q11 that the approach adopted would depend upon whether the feature was man-made (angular buildings) or natural features (which would be represented by curves). The evidence to-date suggests that both cartographers and students are inclined to objectify and generalise but that the latter are more inclined to use abstractions in deconstruction (especially on the second attempt; see Q4).

There was strong support for the observation that there is a tendency to focus on extruding parts (Q6), although the evidence and the votes show that experienced cartographers and some students are aware of and watch out for this perceptual bias. There was disapproval of the use of redundant, and especially of new, points (Q7).

The impact of the orientation of the figure was confirmed (Q8). However, one cartographer wondered whether people would have made a conscious effort to maintain the elements of symmetry (for example, by rotating the figure) if this had been pointed out at the outset; but, see Section 8 (11).


 

11. Conclusion

In this collaborative research, undertaken by the BCS Design Group, participants were encouraged to deconstruct (produce meaningless forms) which best represented the patterns, represented by the two simulated lines. Line generalisation algorithms can generate a wide variety of patterns given the same lines. The initial aim of the research was to discover whether cartographers would produce more consistent deconstructions. The research was open-ended and exploratory and was not hypothesis driven. The results show how the manual deconstruction of lines can be even more variable. The observations may be no more than anecdotal since the sample size is limited. Nevertheless, they are interesting and provide ideas for further research. These observations suggest the following tentative conclusions (the text in parenthesis provides the type of information on which specific conjectures are based).

1.  Cartographic training appears to be fostering :

• A tendency to assume semantic meanings and engage in semantic labelling (written comments).
  This tendency to map occurs because the practice of generalisation is knowledge-based. This facilitates recognition and exploits the psychological tendency to re-use (mentally project) previously successful solutions when facing new problems.
   

• An awareness of the compromises arising from the application of different cartographic guidelines and the need to make choices, e.g. preservation of the orientation and rectilinearity versus the need to give and take; or, emphasis on structure versus shape and/or coverage (written comments).
   

• The awareness of distortions in subconscious perception, for example, figure-ground reversal - see below (review of output with individuals).
   

• Active self-monitoring, review and editing of output, including semantic re-labelling (review of output with individuals).

2.  Potential distortions arising from a perceptual tendency :

• To focus on extruding parts and to morph the shape to fit the mentally projected form (output).
   

• To see shapes differently on close scrutiny and on taking a holistic view when standing back (personal discussion). This could be due partly to orientation and partly to figure-ground reversals; the wholistic view takes the island to be the figure, but this classification need not be maintained during local processing.
   

• To emphasise the features that continue rather than change direction. This is well known but was not explicitly stated by respondents.
   

• To initially reject figures to which there is an adverse muscular reaction impressing itself as a negative feeling (personal communication). The offset cross was said to be disconcerting.

3.  Some potential inhibitions to creative cartographic visualisation:

• An assumption that there must be a preferred singular solution especially among students (general verbal articulation). This may have been induced by training.
   

• A psychological predisposition to see a closed curve as figure and not ground (output).
   

• A tendency to re-use solutions (forms). The re-used forms suggest that there is a tendency to re-use (mentally project) known patterns, not necessarily known objects. This may be indicating a re-use of successful strategies without attempting to explore other strategies to discover new possibilities.
   

• Over-reliance on software and work-related training (verbal articulation by non-respondents conditioned to fitting curves).

When these results were shown to participants some two years later, they were surprised a) at their initial subconscious behaviour and subsequent change of mind, and b) at the need to monitor subconscious perception-induced behaviour and consciously apply visual logic based on common sense and cartographic precepts. This shows the value of adopting a variety of techniques for knowledge elicitation, such as introspection and thinking aloud on paper, individual retrospection, peer review and dialogues on the psychological and 'cultural' origins of their overt behaviour. These individuals were also interested in the way some of the others had approached the exercises and amazed at just how much even this small set of results revealed about their own inner cognition. This experiment shows that the art of generalisation is not entirely intuitive and inscrutable.

The extracts from individual responses indicate that several considerations were being consciously evaluated and balanced. It suggests that different cognitive processes may be engaged during construction and evaluation. This is plausible since this is what happens during other creative tasks, such as writing and painting. It appears that ‘standing back’ is essential during the planning and evaluation stages but that this cannot be maintained during the enacting stage. Such holistic evaluation could be guided by a formal framework for checking. For unlike construction, which could be intuitive and right-brained, planning and evaluation are logical left-brain processes. Evaluation is, by definition, logical and context dependent. As an exercise in deconstruction, all output patterns may be regarded as equally valid. Although, this experiment was not successful in extracting a statement of priorities, some patterns were regarded as more appropriate than others. For example, there was a rejection of over-generalised figures (8c-d) and those which included redundant points (especially Figures 7a & b and & 8h). This is different from the more acceptable fitting of curves to a non-redundant set of points. The conscious elimination of symmetry (i.e. structure) in some of these figures also caused concern. It looks as if this source of variability in deconstruction is being discounted as not adhering to cartographic principles.

The need to retain the symmetric structure of the figure was emphasised to the extent that Figure 5a (bend elimination) was abandoned in favour of Figures 6a & 6d. As noted earlier, this shows a tension between preservation of structure and the shape of the main elements of that structure in the absence of contextual knowledge. Those who opted for bend elimination found it difficult to apply this in exercise 2. Equally, many found it difficult to assess the structure in Teragon 2. Figures such as 8i-k, like Figures 5b &c, show the sort of technique which could be adopted for exploring structures.

Many cartographers and students were able to abstract Figures 8a, 8b, 8f, and 8h without explicit analysis of the structure by relying instead on other techniques, involving extreme points or give-and-take rule during evaluation, even if not during construction. Figures 8a and 8b may be regarded as the basic decogons from which the other stylised versions may be derived by further filtering, fitting of curves and skewing the symmetry. Both these patterns have a similar shape but they differ in orientation. 8b and derivatives retain the extreme points on the extruding and intruding parts. Indeed, this forms the basis of the Douglas-Peucker algorithm which produces a rotated four point pattern in Figure 3. It also outputs a version corresponding to Figure 8b as one of 24 decogons for Teragon 2 (Visvalingam and Brown, 1998). Visvalingam and Whyatt (1990) noted how the retention of extreme points can distort shape. Figure 8b and that out by this algorithm do not balance give-and-take nor retain the angular corners and similarity of parts. Despite this, many cartographers clearly feel that this looks right. The readers may wish to comment on this paradox.

Figure 8a, like Figure 6a, was arrived at by the conscious application of give-and-take (see Section 9). However, the give-and-take idea, may be applied quite differently. For unlike wholistic, top-down structure based deconstruction, it can be applied locally to inconsistent partitioning of the line, resulting in unbalanced and clumsy shapes. Such inconsistencies may be regarded by some as falling within the realms of drafting, which is increasingly being replaced by software. However, the design of such algorithms is inhibited by a lack of knowledge of how people partition lines.

Algorithms developed within Artificial Intelligence, for segmenting curves at their concavities (Hoffman and Richards, 1984), tend to suggest different segmentations for figure and ground. Plazanet (1995) and Wang and Muller (1998) focused on Hoffman and Rchards’ convex and concave bends. While the basic analysis of a line into convex and concave sections may be correct, the complex Bendsimplification system seems to be flawed (Visvalingam and Herbert, 1998). It was hoped that people would see teragons more consistently and that this would inform the further development of algorithms. The evidence is that there is even greater variation in the cartographers’ deconstruction of fractals.

If we ignore the variations introduced by a) inattention to detail during drafting, and b) lack of adherence to cartographic principles, variations in deconstruction initially appear to depend upon perceived tensions between the preservation of structure versus shape. However, where the structure is not self evident, there appears to be a reliance on geometric heuristics, such as extreme points and coverage (which offer scope for mentally projecting pertinent objects, often exaggerating the figure) or give-and-take, which ignores the semantics of the line.

The need to discern structure, the geometric heuristics which can be used where this is difficult, the subjective tendency to focus on the extruding parts, the scope that this gives for segmenting lines at their concavities, and the inappropriateness in many cases of figure-ground based judgements, are already known. These experiments have also not provided any new insights into procedures for line segmentation. However, the results are interesting because they differentiate between in-born tendencies and some of the ideas which should be stressed through cartographic education to enable students to be both creative and critical.
 

ACKNOWLEDGEMENTS

I would like to thank all those who undertook the exercises on which this study was based. I am particularly grateful to Alan Collinson, Convenor of the BCS Design Group for his enthusiasm and support, and David Forrest of Glasgow University for getting his students to do this exercise. I would also like to extend my thanks to Chris Brown, a PhD student in the Cartographic Information Systems Research Group for providing the data for the two teragons, and Margaret Greenman for her comments on the draft of this paper.

REFERENCES

Attneave F(1954) “Some informational aspects of visual perception”, Psychological Review 61 (3) 183 - 193.

Buttenfield, B P and McMaster, R B (1991, eds.) Map Generalization: making rules for knowledge representation, Longman, UK

Collinson, A (1997) “Virtual Worlds”, The Cartographic J 34 (2) 117 - 124

Douglas, D H and Peucker, T K (1973)  “Algorithms for the reduction of the number of points required to represent a digitised line or its caricature”, The Canadian Cartographer 10 (2), 112 - 122

Gregory , R L  (1970) The Inteligent Eye, Weidenfield & Nicolson, London

Hoffman, D D and Richards, W A (1982) “Parts for Recognition”, Cognition  18, 65 - 96.

Mandelbrot, B (1983) The Fractal Geometry of Nature, W.H. Freeman, New York, 3rd edition.

Marino, J S (1979) “Identification of characteristic points along naturally occurring lines : an empirical study”, Canadian cartographer 16 (1) 70 - 80

McMaster, R B (1987) “Automated line generalisation”, cartographica 24 (2) 74 - 111

Plazanet, C (1995)”Measurement, characterization and classification for line generalization”, Proceedings of AutoCarto 12, Bethesda, Md., 59-68

USDMC - The Upside Down map Company Ltd (1998) Upside Down Maps, ISBN: 0 952930412

Visvalingam, M (1996) “Approximation, generalisation  and deconstruction of planar curves”, Cartographic Information Systems Research Group Discussion Paper 14, University of Hull, 12 pp

Visvalingam, M (1998) “Sources of variability in cartographers’ deconstruction of fractals”, Cartographic Information Systems Research Group Discussion Paper 17, University of Hull, 22 pp

Visvalingam, M and Brown, C I (1999) “The Deconstruction of Teragons into Decogons”, Computers & Graphics 23 (1), in press

Visvalingam, M and Herbert, S P (1998) “A Computer Science perspective on the Bendsimplify algorithm”, Cartographic Information Systems Research Group Discussion Paper 16, University of Hull

Visvalingam, M and Whyatt, J D (1990) “The Douglas-Peucker algorithm for line simplification : re-evaluation through visualisation”, Computer Graphics Forum 9 (3), 213 - 228

Visvalingam, M and Whyatt, J D (1993) “Line generalisation by repeated elimination of points”, The Cartographic Journal 30 (1), 46 - 51

Wang, Z (1996) “Manual versus automated line generalization”, In: Proceedings of GIS/LIS ‘96, Denver, Colorado, 94 - 106.

Wang, Z and Muller, J-C. (1998) “Line generalization based on an analysis of shape characteristics”.  Cartography and Geographical Information Systems, 25 (1) 3-15.

White, E R (1983) “Perceptual evaluation of line generalisaton algorithms”, Unpublished Masters Thesis, University of Oklahoma.