Study on Entropy and Emerging Complexity in the Visual Composition of Streetscapes in Tokyo and Kyoto Cities Mansourı Ahmed1, Matsumoto Naoji1, Andre Borges Cavalcante2, Kacha Epe Mansourı Lemya1 1 2
Nagoya Institute of Technology, Japan Nagoya University, Japan
Abstract The aim of this research is to explore complexity, as seen by subjects, in the visual composition of streetscapes in Tokyo and Kyoto cities. Then, to find out the origin of this complexity according to different levels of perception. 37 streetscape pictures were taken in Tokyo and Kyoto cities in RAW format using a Nikon D300S digital camera. 10 Japanese students were asked to categorize and to rank these streetscapes according to their degrees of complexity. The physical analysis was conducted according to two levels of perception. (1) First, Low-level vision that deals with textures and small scales. (2) High-level vision, which is a more perceptual level. The results of the physical analysis showed: (A) a direct proportionality between entropy and the degree of complexity of each streetscape. (B) An inverse proportionality between the degree of complexity and the difference of size between classes that compose each streetscape.
Introduction This study is about perception and complexity within streetscape as a system. Exploring the geometric logic and the intrinsic origins of this complexity in streetscape composition is the aim of this paper. The reviewed literature influenced the orientation of this research by concepts from studies done in Japan about disorder in the street view (Matsumoto 2002), and concepts from architectural design theories (Gero 2007). This research work tried to explore and analyze complexity within the visual composition of streetscapes, considered as two dimensional arrays, according to two kinds of data. These data were human as well as physical. The research was structured according to two main phases. The first Phase dealt with human data, using psychometric methods. 10 subjects were asked to categorize and to rank 37 streetscape pictures according to their degrees of complexity. Principal components analysis (PCA) helped in identifying 3 components from the classification done by the subjects. Ranking method was used to identify the common ranking of the data according to a 3-point scale of complexity. The second phase dealt with streetscape arrays as physical data. This phase included first the estimation of entropy based on the probabilities of pixel intensities, using the nearest neighbor method. Second, the analysis of the probabilities of the perceived classes using Shannon’s model of entropy estimation.
Data collection Because of research feasibility in terms of means and time limits, this research could not cover a large number of cities in Japan. In order to avoid over-simplification of the concepts related to this research, the authors based the data collection on the idea of
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Proceedings, IAPS International Network Symposium 2011
Keywords: Streetscape, visual composition, complexity, entropy, emergence, articulation
PhD, Ahmed Mansouri Foreign researcher, Nagoya Institute of Technology, Gokiso-Cho Showa-Ku Nagoya-City, 466-8555 Japan. /81527355510 /81527355569 /ahm71manso
[email protected] m
selecting 2 cities in Japan as study areas. Tokyo and Kyoto were chosen as cities rich in modern and traditional built environments. The data collection was done in August 2010 and the streetscape pictures were taken in RAW format using a Nikon D300S digital camera and Nikkor AF-S DX 35mm f/1.8G lens. The process of sample collection was based on the idea of taking two visual arrays of the same streetscape, from the same shooting location, one in daytime and another in nighttime (figure 1). All the pictures were taken between 14:00-18:00 in daytime and between 20:00-03:00 in nighttime. The selection of shooting times and locations respected the common features between the visual arrays in matters of activity (vehicles, people), street size, lighting, etc., in order to avoid any fallacious judgment by the subjects. A total number of 80 visual arrays were collected from different sites within these 2 cities. After a random screening, the authors selected 37 pictures as follows: 10 daytime pictures from Tokyo, 10 daytime photos from Kyoto, 7 nighttime pictures from Tokyo and finally 10 nighttime pictures from Kyoto. The authors canceled 3 nighttime pictures taken in Tokyo because of their poor quality. These 37 pictures represent the object of the experimental phase in this study. Figure 1 Data Collection method
Streetscapes Classification and ranking according to their degrees of complexity In this study, the authors applied Principal components analysis (PCA) and ranking method in order to classify the collected streetscapes according to their degrees of complexity. 10 Japanese students in Architecture at Nagoya Institute of Technology were asked to categorize and to rank the data in Jpeg format (taken basically in RAW format) according to a 3-point scale. That is to say: simple (1) – ordinary (2) – complex (3). Principal components analysis helped in identifying 3 components as a result of the data classification (figure 2). Cluster analysis helped in clustering the data according to their principal components loading (figure 3). Complexity seems to characterize daytime streetscapes in both cities. Because of the necessity of the streetscapes ranking in the physical Figure 2 Principal components loading
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analysis of the collected streetscapes, ranking method was applied in order to psychometrically measure the rank of each streetscape according to the 3-point scale. The ranking showed that Green crowded Boulevards in Tokyo city reflected the highest degree of complexity. The complex category was dominated by daytime streetscapes from both cities. No streetscape from the presented pictures was considered as simple.
Entropy estimation based on the probability of pixel intensities This phase of physical analysis was concerned with the low level of vision and the probability of pixel intensities. Entropy was the main concept in this analysis and it is estimated according to the nearest neighbor method, which is based on the concept of the nearest neighbor search (NNS), also known as proximity search, similarity search or closest point search. It is an optimization approach in order to find closest points in metric spaces (figure 4).
Mathematical interpretation of the nearest neighbor method The nearest neighbor search consists on the closest point to a query q within a metric space M that includes a set S of points in a metric. M is often considered as d-dimensional Euclidean space and distance is measured by Euclidean distance or Manhattan distance. Entropy can be estimated from the distribution of the nearest neighbor distances of a dataset.
Figure 3 Data clustering (component 1 & 2)
Results After estimating entropy (entropy was given in bits/pixel), the authors compared the results with the complexity ranking of the streetscapes. The results showed a direct proportionality between the degree of complexity of the selected streetscapes and their estimated degrees of entropy. The highest average entropy was the one of daytime streetscapes: Entropy H(I) = 0.71 bits/pixel . Figure 4 Pixel intensity
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Crowded Green Boulevards in Tokyo city represented the most complex category, with an Entropy H(I) = 0.686 bits/pixel. Entropy H(I) in the most complex nighttime streetscapes was 0.551 bits/pixel.
Analysis of articulation based on the probability of perceived classes The approach In this second phase of physical analysis, entropy was considered as an expression of the articulated classes or components within a streetscape. As suggested by Kaplan (1988), the authors selected 5 classes within each streetscape; that is to say: building, ground, vegetation, sky, and actors. The authors suggested a class called “actors” in order to include any element that may attract the attention of the subjects, for example: light, openings, human, vehicles, furniture, shadow, etc. This phase of analysis tried to explore articulation as a process of connection between the classes that compose a streetscape. According to information theory, there exist many interpretations of articulation. This study considers articulation as the way the parts of a system are joined, depending on what is happening at the beginning and end of each part, as well as between the parts.
Figure 5 Example of a streetscape in Tokyo segmented into 5 classes
Figure 6 Streetscapes ranking and image segmentation
The segmentation of classes within each visual array In order to identify the 5 suggested classes within each streetscape, as human beings see them, the authors tried to apply a Hybrid approach. This approach used K-means
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(1)
clustering in order to identify the possible classes within a streetscape. The results showed that k-means clustering is quite uninformative with regard to the aim of this study. Perfect algorithms for image segmentation were very complicated. They represent machine-based methods that do not reflect the real human nature of determining the classes within a visual array. The second step of the image segmentation was a heuristic approach (figure 5). The authors asked 10 Japanese students in Architecture, who had good skills in Adobe Photoshop, to segment each picture of the 37 streetscapes into 5 classes. The authors explained the meaning and features of each class, and then let them freely cluster the classes by themselves as they saw fit (figure 6).
Entropy estimation based on the probability of perceived classes The aim of this stage of the research is to study the way of articulation of the different classes within each streetscape in terms of size. The study of the articulation among classes in terms of size represents a preliminary approach for the study of the concept of emergence in streetscape composition. There exist 2 kinds of emergence, as a concept, in this field of study. The first one is related to perception as proposed by Gestalt theory. The second one is related to the way the parts of the streetscape articulate with each other. The concept behind the strategy of this research phase is based on the probability of perceived classes within each streetscape. The entropy of each streetscape visual array is based on the size of its perceived classes and estimated according to Shannon’s model. The probability of occurrence of a class Pi is:
Pi =
Ci α
Pi: Probability of the ith class α: Size of the picture Ci: Size of the ith class Entropy is estimated according to the following equation, and counted in bits/pixel:
H (I ) = −∑ Pi log 2 (Pi ) i
i = 1,2,3,..., n The results of the entropy estimation according to Shannon’s model showed that the average entropy increases when the classes get close or similar in terms of size. This means that complexity within a streetscape, expressed by its degree of entropy as a system, increases when the difference between classes in terms of size decreases.
Conclusion The common concepts that could be issued from this study is the direct proportionality between the degree of complexity within a streetscape and its intrinsic entropy. However, there exist an inverse proportionality between the degree of complexity of a streetscape and the difference between its composing classes, in terms of size. The logic by which the composing classes are articulated seems to influence the degree of complexity of the resulting scene or streetscape. Futures researches will aim to study the nature and characteristics of the classes composing a streetscape in general.
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Notes (1) K-means clustering is a method of cluster analysis that aims to identify clusters or groups of data points within a multidimensional space. The k-means algorithm clusters n points into k clusters, where k is provided as an input parameter. Each point is assigned to clusters based upon its proximity to the mean.
References Ashihara, Y 1983, “The aesthetic townscape”, trans. L E Riggs, the MIT press, Cambridge. Bishop, M C 2006, “Pattern recognition and machine learning”, Springer, New York. Costa J A & Hero, A O 2004, “Geodesic entropic graphs for dimension and entropy estimation in manifold learning”, IEEE Trans. on Signal Processing, Vol. 52, no. 8, pp. 2210–2221. Ding, L & Gero, J S 2001, “The emergence of the representation of style in design”, Environment and Planning B: Planning and Design, 28(5), pp. 707-731. Holland, J H 1998, “Emergence, from chaos to order”, Helix Books, Addison-Wesley Publishing Company, Massachusetts. Mansouri, A, Matsumoto, N 2010, “Study of emergence and analogy in night streetscape composition in Algeria and Japan”, MERA Journal, Vol. 13, no. 2, p. 19. Mansouri, A, Matsumoto, N, Aoki, I, Sugiyama, Y 2011, “Study on the cognitive patterns of complexity in the visual composition of streetscapes in Algeria and Japan”, Journal of Architecture,Planning and Environmental Engineering, Vol. 76, no. 659, pp. 101-107. Matsumoto, N, Teranishi, N & Senda, M 1991, “Studies on factors of disorder and regularity in the street view: Studies on disorder and regularity in the central business district -Part 1-“, Journal of architecture, planning and environmental engineering, No. 429, pp. 73-82.
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