Tuesday, September 12, 2017


Below is the full online article examining in some capacity how the attractiveness of various differing arrangement of rocks in a garden can be actually measured.  Goodness! Pretty heady stuff. 



In this study, we examined pattern goodness in natural scenes using stone arrangements in a Japanese rock garden. The results showed that the stone arrangement simulating the rock garden at the Ryoan-ji Temple and arrangements with a single stone deleted from that simulation were evaluated highly. These arrangements had a self-similar spatial structure, namely, covert regularity, or had simple structures in medial axis transformation. These arrangements also produced impressions of greater width and depth than other arrangements. In contrast, sector arrangements, which gave the most regular impression, were evaluated the lowest for goodness. This suggests that the pattern goodness of natural scenes or the artistic evaluation does not always correspond to overt regularity, often considered to determine pattern goodness. The most important finding is that two types of sector arrangement and two types of random arrangement were classified in their respective groups by integrated multiple impressions, although they did not have similar perceptual appearances. An intuitive judgment based on integrated impressions may allow us to notice the hidden order in spatial structures and obtain substantial understanding of the structure.
In Gestalt theory, goodness is central to understanding the way in which the visual system organizes and stores percepts (Palmer, 1991). Summarizing Wertheimer's idea, Koffka (1935) said that psychological organization will always be as “good” as the prevailing conditions allow. In fact, we perceive a pattern or shape having perceptual goodness rather than understanding the structure or shape and afterward judging its goodness.
However, goodness is an idea that is not easily defined. Perceptual goodness is related to concepts such as simplicity, regularity, stability, order, harmony, and homogeneity (Kanizsa, 1979Koffka, 1935Palmer, 1991). Gestaltists have shown such relations by presenting visual examples, which are often more effective than explanations using words. However, if we define goodness in a scientific manner, we must redefine these related concepts.
After the Gestaltists, many have attempted to define goodness in operational terms or in quantitative ways, for example, using geometrical properties like the number of lines, the degrees of corners, and position (Hochberg & Brooks, 1960Wilson & Chatterjee, 2005), the amount of information (Attneave & Arnoult, 1956), redundancy (Garner & Clement, 1963), the amount of structural information (Leeuwenberg, 1969) and transformation structure (Hamada & Ishihara, 1988Imai, 1977Imai, Ito, & Ito, 1976). The experimental data generally fit with these theories as long as limited stimuli are used, such as experimentally controlled, simple, and meaningless geometric shapes and patterns.
However, definitions of goodness based on such spatial properties of shapes or patterns cannot explain the different goodness among patterns with similar spatial structures or individual differences in the same patterns (Matsuda, 1978). In fact, pattern goodness changes just by rotation of a pattern (Mitsui, Shiina, & Odaka, 2008). Pattern goodness can be reversed also based on whether the whole pattern is shown or each part is shown successively (Kodama & Miura, 2009).
To overcome this problem, instead of definitions using stimulus properties, the perceptual or cognitive processes of observers have been discussed, for example, perceptual organization (Kodama & Miura, 2009, 2011), mental workload or attention (Klein, 1982Miura, 2007Miura & Kawabe, 2004Pomerantz, 1991), length of verbalization (Glanzer & Clark, 1962), the association value (Garner, 1974), meaningfulness for observers (Markovic, 2002Wada, Oyama, & Yamada, 2000), and personal traits (Chipman & Mendelson, 1979Nakaya & Fujimoto, 1984Yamashita & Furusawa, 1993).
However, these concepts are often not independent of the stimulus properties. Rather, they are an aspect of two sides of the definition because the patterns or objects that can be processed using minimum energy have mostly simple or regular configurations or shapes.
It is more fitting to think of the concept of goodness as consisting of multiple aspects. Gyoba, Seto, and Ichikawa (1985) pointed out that there are two kinds of goodness or two aspects of goodness judgment. One is goodness related to geometrical regularity that is basically determined by symmetry. The other is goodness as an integrated impression, shown by the evaluation factor, which is often extracted using factor analysis. The former corresponds to the perceptual attributes of stimuli, and the latter corresponds to the synthesized evaluations made by observers. Kanizsa (1979) said that “there can be several criteria for describing this property (=goodness) and the selection of one criterion instead of another may lead to different results.”
In addition, goodness is dependent on the context. Nakajima and Ichikawa (2008) showed that aesthetic impression, a kind of goodness, changed if they used dot stimuli that had concrete meaning (e.g. a button) and were placed on natural images (e.g. textiles). Inoue and Miura (2000) showed that a pattern evaluated highly was a little more irregular, such as when natural images of brick walls were compared to geometric black and white brick patterns. For natural scenes or objects, the standards of goodness seem to change compared to those for geometric patterns or shapes.
Breakthrough research on goodness in natural scenes or art works was conducted by Taylor, Micolich, and Jonas (2000) and van Tonder, Lyons, and Ejima (2002). Taylor et al. (2000) analyzed abstract paintings drawn by Jackson Pollock using fractal analysis and found that invisible fractal structure contributed to good impressions of the artistry. It is noteworthy that covert order was critical in the impressions of artworks. However, the study by van Tonder et al. (2002) gives more direct suggestions about pattern goodness in natural images.
van Tonder et al. (2002) and van Tonder and Lyons (2005) applied medial axis transformation to the stone arrangement of the famous Japanese rock garden at the Ryoan-ji Temple and uncovered a multiscale self-similar structure like a dichotomously branched tree, which can often be found in natural scenes. They also found that the trunk of the tree-like structure passed close to the main viewing area, reportedly the best place to appreciate the whole garden. They suggested that “the hidden order” (a term used by Japanese architect Yoshinobu Ashihara (1986) seems to give us impressions of calmness and sophistication when appreciating the dry garden, although we cannot see the self-correlation structure of the stone arrangement directly. With regard to observers' mental activity, this self-correlation structure seems to facilitate the perceptual organization of the spatial structure, reduce the mental workload involved in seeing it, and offer a relaxing and comfortable impression. That is, goodness can be defined again from both the spatial properties of a stimulus and observers' mental mechanisms.
The discussion by van Tonder et al. (2002) and van Tonder and Lyons (2005), however, was theoretically based on computational analysis showing the covert spatial structure of various stone arrangements. The observers' impressions were not directly examined. Moreover, according to their theory, based on medial axis transformation, the observers' evaluations are independent of their viewing point. However, in real scenes, the impression of a garden changes according to the viewing point.
In this study, we examined pattern goodness in natural scenes using the simulated stone arrangements of a Japanese rock garden that were used in the research of van Tonder et al. (2002) and van Tonder and Lyons (2005). We discuss the following points. First, do hidden spatial structures affect the evaluation of pattern goodness? Second, are arrangements that include hidden order, for example, a self-correlating spatial structure, evaluated highly? Third, do evaluations from the viewing point from which observers usually appreciate the garden support the theoretical analysis of van Tonder et al. (2002) and van Tonder and Lyons (2005)? Fourth, is the evaluation of pattern goodness related to the impression of depth (space extension in front and back) and width (space extension to the right and left) of the garden? Reportedly, there are several perspective devices in the stone arrangement of the rock garden of Ryoan-ji that cause the small garden to appear deeper. This extended spatial impression resulting from the devised stone arrangement may contribute to a good impression of the garden.



Stimuli.  Using the software, LightWave 3D, we rendered a 2-D computer graphic (30 cm × 150 cm), imitating the rock garden at Ryoan-ji. We created eight variations of the stone arrangement according to the research of van Tonder and Lyons (2005) and van Tonder et al. (2002): A, the original arrangement surveyed by Oyama (1970), the researcher of dry gardens; B and C, arrangements with a single stone deleted; D, an arrangement with a single stone added; E and F, arrangements with stones at random; and G and H, arrangements with stones in sectors. It is speculated that the stones of Ryoan-ji were arranged in sectors so that gazes to each stone gather from the best place to appreciate the garden. The stone arrangements in all stimuli were created according to those of van Tonder et al. (2002) so that the obtained results can be compared with the simulation of the arrangement. We also added another original arrangement measured by Nishizawa (2006), which was more recently surveyed and is said to be closer to the actual stone arrangement of Ryoan-ji. These two measurements, however, basically produce the same spatial structure using medial axis transformation, although the spatial impression, in particular, the impression of spatial extent, is different. Thus, we used a total of nine arrangements as stimuli.
All the arrangements were computer-generated images, assuming the observer was sitting on the veranda (Figure 1). The camera (at the eye-level of the observers) was set 1.8 m off the ground and turned to where a back wall touches the ground. The location of the camera (at the viewing point of the observers) was set where the main stem of the tree-like structure, based on medial axis transformation, passed. van Tonder and Lyons (2005) stated that this point is the location of maximal Shannon information. Thus, we set the camera at the ideal place to appreciate the garden. To see the whole stone arrangement of the garden, the camera was turned 10 deg toward the center (Figure 2). All of the medial-axis structures corresponding to each arrangement are shown in Figure 1.
Figure 1.

Figure 1. 

The stimuli of stone arrangements (right) and their spatial structures obtained using medial axis transformation by van Tonder et al. (2002) (left).
Figure 2.

Figure 2. 

Position and angle of a camera for drawing the garden stimuli. Left: The camera position shown in a white circle from an overhead view. Right top: The camera angle from an overhead view. Right bottom: The camera angle from a side view.
Each stimulus was projected on a 120 cm × 160 cm screen and was viewed from 300 cm. We used the large screen instead of a monitor-size display to facilitate an impression more similar to the real setting, although the retinal images in this viewing condition were not larger than when actually viewing the garden.
Procedure.  To reduce visual distractions, the experiment was conducted in a dark room. Using the semantic differential method, each participant reported their impressions of the gardens using 12 adjective pairs (see Table 1) on a 7-point scale, at their own pace. The order of the presentations of the stimuli and the adjective pairs was randomized among the observers. Before the experiment, the observers viewed all stimuli, presented for 3 s each.
Table 1.  Results of the factor analysis: the factors related to appreciating gardens 
Adjective scaleEvaluationQuietRegularityCommunality
  1. Note. The numbers in bold indicate the adjectives pairs with the highest factor loadings.
Liked – disliked.895−.043.106.815
Good – bad.890−.024.148.813
Beautiful – unbeautiful.838−.101.182.746
Interesting – uninteresting.674.265−.095.534
Wide – narrow.446−.413−.205.699
Deep – shallow.274−.036−.164.280
Desolate – bustling.007.836−.004.613
Modest – brave.216.752−.028.411
Quiet – noisy−.207.487−.018.103
Regular – irregular.081−.040.799.465
Organized – disorganized.025.052.600.647
Simple – complex−.064−.466.494.363
Variance explained (%)26.0416.4711.56 
Accumulated variance explained (%) 42.5254.08 
Observers.  Thirty Japanese students (21 female and 9 male, mean age = 23.3 years) without special knowledge about Japanese rock gardens participated in this experiment.


Stone arrangements with similar impressions.  Based on the data, we conducted cluster analysis using Ward's method to determine the arrangements producing similar impressions. The results, shown in Figure 3, indicated that there were three types of arrangements that resulted in similar impressions, namely, original and deletion arrangements (A, A′, B, C), sector arrangements (G, H), and random and addition arrangements (D, E, F).
Figure 3.

Figure 3. 

The results of cluster analysis: the stone arrangements with a similar impression.
Factors related to evaluating stone arrangements.  We conducted factor analysis using unweighted least squares with Varimax rotation to determine the factors related to appreciating rock gardens. We extracted three factors based on both screen plot and Eigenvalues greater than 1. The results are shown in Table 1. The first factor comprised “liked,”“good,”“beautiful,” and “interesting.” Thus, we considered it the evaluation factor. The second factor comprised “desolate,”“modest,” and “quiet,” termed the quiet factor. The third factor comprised “regular,”“organized,” and “simple.” We considered it to be the regularity factor.
Relation between stone arrangements and impressions.  Based on the results of cluster analysis and factor analysis, we conducted a one-way analysis of variance (ANOVA) for the three groups of arrangements. Significant mean effects were found in all factor conditions: Evaluation: F(2, 358) = 33.637, p < .001; Quiet: F(2, 178) = 65.983, p < .001, and Regularity: F(2, 178) = 83.976, p < .001. Post hoc multiple comparisons using Ryan's method showed significant differences between every pair of groups for all factors (p < .05), as shown in Figure 4.
Figure 4.

Figure 4. 

The results of the analysis of variance: the relation between the stone arrangements and the factors.
In the original and deletion arrangements, the averaged rating scores of the evaluation (goodness) and quiet factors were the highest. In the random and addition arrangements, the averaged rating scores of the quiet and regularity factors were the lowest. In the sector arrangements, the averaged rating score of the evaluation factor was the lowest, and that of the regularity factor was the highest.
Relation between goodness and impression of spatial extent.  Based on the rating scores for the adjective pair wide-narrow, we conducted a one-way ANOVA for the nine arrangements. A significant difference in means was found in impressions of width, F(8, 232) = 11.672, p < .001. Post hoc multiple comparisons using Ryan's method showed significant differences (p < .001) between A′-D, A′-E, A′-F, A′-G, A′-H, A–E, A-G, B-D, B-E, B-G, C-D, C-E, C-G, C-H, F-G; significant differences (p < .005) between B-H, G-H; and a significant tendency (p < .01) between B-F. Regarding the impressions of depth shown from the deep-shallow judgment, a significant tendency in the mean effects was found, F(8, 232) = 2.764, p < .01. Post hoc multiple comparisons using Ryan's method showed significant differences between A-G (p < .001).
The correlations of the mean evaluation value between goodness and width impression, and goodness and depth impression were 0.673 and 0.787, respectively, although these correlation coefficients were not significant.
All arrangements obtaining higher scores on the wide-narrow scale belonged to the original and deletion groups, as shown in Figure 5a. The highest score was obtained for the original arrangement using the measurement of Nishizawa (2006), and the lowest score was obtained for one of the sector arrangements. Regarding depth impression, the highest score on the deep-shallow scale was obtained for the original arrangement using the measurement of Oyama (1970), and the lowest score was again obtained for one of the sector arrangements (Figure 5b).
Figure 5.

Figure 5. 

Scatter plot of the mean rating scores (a) between the goodness and the width impressions, and (b) between the goodness and the depth impressions. Circles: Original and deletion arrangements. Squares: Random and addition arrangements. Triangles: Sector arrangements.


In this study, we examined pattern goodness using rock garden stimuli that were more realistic than the dot patterns typically used in studies of pattern goodness. The results show that a hidden spatial structure affected the evaluation of pattern goodness. The arrangement including a self-similar spatial structure (the original arrangement) was evaluated highly. Thus, the hypothesis by van Tonder et al. (2002) and van Tonder and Lyons (2005), based on medial axis transformation, was supported. Moreover, the goodness of the spatial arrangement was related to the impression of the spatial extent. The highly evaluated arrangements tended to be judged as wider and deeper.
The most noteworthy result in this study was that the spatial structures of stone arrangements could be correctly distinguished by intuitive and comprehensive impressions (Figure 3), although they could not be distinguished by perceptual appearance. That is, although the observers may not have noticed that the stones in G and H were arranged in sectors, they classified them in the same group. The two random arrangements were also distinguished from other arrangements. Intuitive judgment or insight seems to allow us to grasp spatial structures without awareness. Ashihara (1986) showed that certain covert proportions in depth and height (e.g. the depth of a street or the height of a building) give us particular spatial impressions. Similarly, certain covert spatial structures of the stone arrangements give us particular impressions, and these impressions are useful in distinguishing arrangements. We always pay attention not to spatial structure, but to the objects in it. However, not the objects in space (the figure), but the spatial structure itself (the ground) seems to be important for spatial impressions. Intuitive impressions can judge the covert spatial structure, without the distraction of attentive objects.
Arnhaim (1969) suggested that a judgment is already implicit in the seeing. In this experiment, it might be appropriate to say that a more accurate judgment is not in the seeing but in the feeling. However, as mentioned by Kanizsa (1979), expecting too much of unconscious judgment may be risky because it can cause us to make certain types of mistakes, for example, as shown by Shimojyo and Ichikawa (1989).
The second noteworthy result is that goodness does not always correspond to an impression of regularity, the total impression evaluated by the adjectives “regular,”“organized,” and “simple” in this experiment. In the case of the sector arrangements (Figure 4), the evaluation factor was the highest, although these arrangements were the lowest in pattern goodness. Goodness is often said to relate to geometrical regularities such as repetition and symmetry, or geometrical regularities are causes of goodness. Moreover, goodness is considered to relate to regularity not only in geometrical regularity but also in the comprehensive regularity shown in impressions. The rating score for the evaluation factor often corresponds to that of the regularity factor (Imai et al. 1976Matsuda, 1978Miura, 2007Miura & Inoue, 2000Oyama, Yamada, & Iwasawa, 1998), although each factor obtained using factor analysis is theoretically independent of the others. However, Nakajima and Ichikawa (2008) and Inoue and Miura (2000), both using natural images, showed that the peak of the evaluation scores deviated from the peak of the regularity scores. In addition, artistry judgment can be independent of regularity. Goodness judgment in this experiment might be related to the artistry aspect of the rock garden. Whether the results in this experiment were dependent on the stimuli of natural images or artistry judgment remains a question.
However, the original and deletion arrangements were evaluated highly, while the arrangements including complex structures using medial axis transformation were not preferred (Figures 1,4). That is, the self-correlative spatial structures or simpler and well-organized structures were highly evaluated in the goodness judgment. The hidden order or implicit regularity of spatial structures is considered to relate to the goodness judgment. Van Tonder and Lyons (2005) pointed out that natural patterns are often self-similar, but the shapes themselves are irregular and asymmetrical. An asymmetrical configuration, including hidden order, appears to be required for goodness of rock gardens. Too much regularity or vague symmetry seems not to be preferable.
Regarding the impression of spatial extent, the scores on the wide-narrow and deep-shallow scales suggest that gardens evaluated highly are rated high on both dimensions. It is reported that various means were used in designing the rock garden at Ryoan-ji that contribute to the narrow garden appearing wider. The height of the stones, the walls, and the trees gradually becomes lower from the front to the back (Miyamoto, 1998), while the height of the ground becomes higher from the front to the back. Such linear perspectives contribute to the impressions of depth in this garden. Biederman, Hilton, and Hummel (1991) pointed out that “goodness may be epiphenomenal, reflecting the operation of perceptual mechanisms designed to infer a three-dimensional world from parts segmented from a two-dimensional image and to provide descriptions of objects that can be recognized from a novel viewpoint or that are partially occluded.” The sector arrangement of G, evaluated the lowest, had a flat configuration in 3-D space, and all stones were visible. Subjective involvement in perception brings about positive impressions (Miura, 2007).
As for the impression of wideness, empty space (“Yohaku”) is considered to be a critical factor. However, the results of this experiment did not clearly show this. More controlled experiments should be conducted. Onaka and Matsuda (2006) pointed out that the panoramic impression and the perceived lateral distances differ in their qualities. We also posit that the extension of space in an impression is different from a perceptual extension such as the filled/unfilled illusion.
Last, we refer to the next step of this experiment. In this experiment, we showed all stones of a garden in one computer-generated picture. However, actually, we cannot see all the stones in the rock garden of Ryoan-ji at a glance while sitting on the veranda. We must turn our heads or walk through the veranda if we want to see all the stones in the garden. We use not only vision but also somatic sensation to appreciate this garden. Therefore, time, memory, and somatic sensation should be considered in goodness judgments of garden stimuli. Regarding the rock garden of Ryoan-ji, Nakaji (1999), a Japanese philosopher, said that “moving the viewing position just by several millimeters will give you other rich and beautiful spectacles that you didn't see before. At that time, you will understand that you will be surrounded and filled by unlimited spectacles in a natural scene. At the same time, you will also find that you can take in only one viewing point and one spectacle at a time.” The influence of motor sensation and time course on pattern goodness as well as goodness judgment from various viewing points is our next research problem.



  1. I found your September posts to be especially interesting John, not least the scholarly investigation of 'goodness.' thanks.

  2. I might add that I've shared it on the Stonexus Magazine FB page.