Signage systems are critical for communicating environmental information. Signage that is visible and properly located can assist individuals in making efficient navigation decisions during wayfinding. Drawing upon concepts from information theory, we propose a framework to quantify the wayfinding information available in a virtual environment. Towards this end, we calculate and visualize the uncertainty in the information available to agents for individual signs. In addition, we expand on the influence of new signs on overall information (e.g., joint entropy, conditional entropy, mutual Information). The proposed framework can serve as the backbone for an evaluation tool to help architects during different stages of the design process by analyzing the efficiency of the signage system.
Information theory is the branch of mathematics used to describe how uncertainty can be quantified, manipulated, and represented [Ghahramani, 2007]. According to Shannon and Weaver [Shannon and Weaver, 1949], a communication system can be characterized with respect to this uncertainty and the information being transmitted. Modeling the exchange of information within a system essentially involves representations of uncertainty and can facilitate an understanding of the behavior and properties of its individual elements. This approach has been applied to several different types of systems, including those from computer science, philosophy, physics, and cognitive science [Smyth and Goodman, 1992; Floridi, 2002; Still, 2009; Resnik, 1996]. For example, information may be transferred within and between internal and external representations of space [Craik and Masani, 1967] [Montello et al., 2004]. In the present work, we propose an information-theoretic approach to quantify the spatial information provided by individual or sets of signs for wayfinding in a virtual environment.
Navigation is a process by which internal spatial
representations are obtained. In turn, these representations act as the
basis of future navigation decisions. In unfamiliar
environments (i.e., before any initial representation), individuals
often have to rely on knowledge that is immediately available
in the environment [Golledge, 1999]. However, this relevant
information must be separated from irrelevant information
and noise. There are a variety of visual cues in the
environment that can help individuals find their way (e.g., signage,
maps, landmarks, and building structure) [Montello, 2005;
Arthur and Passini, 1992]. Signs may be particularly easy to
interpret (i.e., require less abstraction than a map), adapt (i.e.,
can accommodate changes to the environment), and
quantify (i.e., allow for the measurement of relevant information).
An efficient signage system can drastically reduce the
complexity of the built environment and improve the wayfinding.
In contrast, an inefficient signage system or lack of signage
can render a simple built space complex and stressful for
patrons. Indeed, signs are typically used to guide
unfamiliar patrons to specific locations within shopping centers and
airports [Becker-Asano et al., 2014]. An efficient signage
system can drastically reduce the navigational complexity of
such environments, but this reduction in complexity or
uncertainty (i.e., information) is not always evident to the
architect using existing measures
In this paper, we first review previous research on information theory, human wayfinding, and signage systems. Next, we introduce our framework for quantifying information and uncertainty for systems of signs in complex virtual environments and apply these measures to signs within a virtual airport. The results are discussed with respect to the development of a novel application to aid architects in the (re)design of real environments. 2
This section briefly describes both Shannon’s basic measures of information and summarizes research on navigation and 2.1
Information theory was developed in the 1940s and 1950s as a framework for studying the fundamental questions of the communication process, the efficiency of information representation, and the limits of reliable communication [Atick, 1992] [Shannon and Weaver, 1949]. In information theory, entropy represents the amount of uncertainty in a random variable as a probability distribution. The Shannon entropy of a discrete random variable X with alphabet and probability mass function p(x); x is defined as
H(X) =
X p(x)log2p(x) x The probability of x, p(x) [0:0; 1:0] and log2p(x) represents the information associated with a single occurrence of x. Entropy is always positive and represents the average number of bits required to describe the random variable. Entropy is a measure of information such that higher entropy represents more information.
There are several measures that combine information from two random variables [Cover and Thomas, 1991]. Joint entropy represents the information provided by either one random variable or a second random variable in a system. The joint entropy of a pair of random variables (X; Y ) with a joint probability distribution p(x; y) can be represented as H (X; Y ) = X X p(x; y)logp(x; y) x
y In addition, conditional entropy H(XjY ) is the entropy of one random variable given knowledge of a second random variable. The average amount of decrease in the randomness of X given by Y is the average information that Y provides regarding X. The conditional entropy of a pair of random variables (X; Y ) with a joint probability distribution p(x; y) can be represented as
H (XjY ) = X X p(x; y)log x y p(x) p(x; y) Mutual information quantifies the amount of information provided by both random variables. The mutual information I(X; Y ) between the random variables X and Y is given as I(X; Y ) = X X p(x; y)log( y"Y x"X p(x; y) p(x)p(y) )
In Section 3, we will describe how the aforementioned measures can be used to quantify the information provided by two (or more) signs in an environment. 2.2
In an unfamiliar environment, navigation largely depends
on picking up ecologically relevant information
The communication of wayfinding information from the
world to the individual observer can be facilitated by an
appropriate signage system or map [Arthur and Passini, 1990]
[Allen, 1999]. Previous research has demonstrated that
signage has distinct advantages over maps for navigating the
built environment [Holscher et al., 2007; O’Neill, 1991] also
found that textual signage led to a reduction in incorrect
turns and an overall increase in wayfinding efficiency
compared to graphic signage
Visual Catchment Area. One existing way of
quantifying the visibility of a sign is its visual catchment area
In this section, we apply the principles of information theory to quantify the information provided by signage in a virtual environment. While there are a number of physical and psychological factors that influence the effectiveness of signage systems (e.g., color and contrast, interpretability and and attentiveness), we will focus exclusively on signage visibility. Rather than considering sign visibility as a binary value [Xie et al., 2007], we model sign visibility as a continuous function, which depends on distance and direction from the observer. We model the entropy of a sign’s visible information P (l; s) as a measure of the navigation-relevant information that is available to an agent at location l from sign s. Let X(l; sa) be a random variable that represents a particular piece of information at a location l and sign sa. The probability of a particular value for the random variable X(l; sa) will depend on the distance of sign sa from the location l and the relative angle between location l and sign sa. The probability distribution is generated by sampling information X from sign sa at l 1000 times. Based on our experiments, we found 1000 samples to provide a reasonable trade-off between granularity of calculations, and compute time. Further investigation is needed to determine the sensitivity of our calculations based on this parameter.
The uncertainty function U (l; sa) represents the likelihood of viewing information from a sign sa at location l as
U (l; sa) = N ( ; ) N is a normal distribution with mean and standard deviation . In addition, is directly proportional to the distance and relative angle between sign sa and location l. Larger distances and relative angles between sign sa and location l result in higher values for (i.e., closer to 1), and represents the range of uncertainty values (which are held constant). Here, is dependent on the mean of the normalized distance dn (over 30 m) and normalized relative direction ran (over 180 degrees; see Equation 7). is the weight of the sum between distance and the relative direction: = (dn + ran)=2
The work done in [Filippidis et al., 2006], makes an assumption between the relationship of the relative direction between the observant and the sign with the probability of visibility (see Figure 2). We use this relationship in the calculation of (see Equation 7) and add our own assumption of probability of visibility with the distance between the observant and the sign (see Figure 3).
These two relationships form the basis of I(sa) (i.e., the actual information contained in sign sa) and can be combined b sin(o) = x2 + y
15 Distance (meters)
Information measures that describe signage systems can also be extended for the combination of two or more signs. Another random variable Y (l; sb) can be used to represent the amount of navigation-relevant information available to an agent at location l from a second sign sb. An uncertainty function U (l; sa;b) can represent the likelihood of viewing information from two signs (sa and sb) at location l: U (l; sa;b) = N (( a + b)=2; ) (9)
Finally, the joint probability distribution can be computed by sampling information X from sign sa and sign sb at l several times:
Pa;b(l; sa;b) = N oise(I(sa); U (li; sa;b)) (10) For all locations from which both signs are visible, we can calculate joint entropy, conditional entropy, and mutual information. The joint entropy of visible information from both signs sa and sb refers to the amount of information contained in either of the two random variables X and Y . For two mutually independent variables X and Y (i.e., when the two signs can be viewed from each other), joint entropy is the sum of the individual entropies H(X) and H(Y ) for each sign. When the two variables are not mutually independent, joint entropy H(X; Y ) can be calculated by using equation 2 in which the joint probability distribution Pa;b is defined by equation 10. In the case of signage, joint entropy indicates the extent to which an observer may navigate from one sign to another towards a goal location.
Conditional entropy is the reduction in uncertainty (i.e., information from the sign sa) due to the presence of another sign sb and vice versa. For example, an observer is located between signs sa and sb but closer to sb. Both signs are indicating the same destination along the same route. The probability of viewing the information from sign sa is low because the individual entropy of sa is high. At the same time, the probability of viewing information from sb is high because the individual entropy of sb is low. Because the two random variables are not mutually independent, conditional entropy for sa given sb is lower than the individual entropy of sa, and conditional entropy for sb given sa is lower than the individual entropy of sb. In other words, both signs become more visible in the presence of the other sign. In addition, the conditional entropy of sb given sa is lower than the conditional entropy of sa given sb. Because entropy is inversely related to the probability of viewing each sign, sb is more visible than sa from this location.
Mutual Information measures the correlation of the two random variables X (information from sign sa ) and Y (information from sign sb). It quantifies the amount of information known about sign A by knowing sign B and vice versa. Mutual information can be calculated as the difference between conditional entropy for any sign and its corresponding individual entropy. Higher mutual information represents higher redundancy, which may result in improvements in navigation performance. However, increases in redundancy may not be linearly related to improvements in navigation performance. The information measures presented here provide one method for estimating the expected increase in performance for each additional sign.
In Figure 9 MI can be computed by subtracting the entropy of sign A( in black) with the conditional entropy of sign A with sign B( shown in yellow). 4
In this section, we use a simplified building information model (BIM) of a virtual airport (Figure 4) in order to illustrate the information theoretic approach to signage systems. The model was created using Autodesk Revit [Revit, 2012] and then imported into Unity 3D [Unity3D, 2016] to perform simulations. In this example, the 3D model of the building includes two signs placed at different locations and pointing towards a common destination (represented by A and B in the Figure 4). The walkable region of the floor of the 3D built environment was divided into n square grid cells of 0.5 m x 0.5 m. This grid cell size approximates the space occupied by an average human.
Figures 5 (a) illustrate the probabilities of viewing wayfinding information provided by signs A from several locations (represented as density maps). These uncertainties are based on the distance and relative direction of the grid cell from each sign according to the functions in Figures 2 and 3 as well as Equations 6, 7 and 8. Agents at grid cells in a lighter shade of gray have a higher probability of viewing the information provided by the sign than agents at grid cells in darker shades of gray. Agents at grid cells at greater distances or larger relative directions from each sign have smaller probabilities of viewing the information compared to agents at grid cells at smaller distances or relative directions from that sign. Black grid cells do not provide any information to an agent. Figures 5 (b) and (c) represents the first person view of an agent from a location which has high information (shown in yellow star in 5 (a)) and an agent from a location which has low information ((shown in yellow circle in 5 (a)). The text on the signage is visible from a high information location since the distance between the agent and the signage along with the relative angle between them is acute. Which results in lower value of entropy and a higher probability of perceiving the information. Which is not the case from the location which is outside the VCA ((shown in yellow circle in 5 (a)). The relative angle between the agent and the sign is high which creates more noise and increases the entropy of visibility. We showcase the similar effect for the sign B in 6 (a), (b) and (c).
Figure 7 (a) illustrates the individual and joint probabilities of viewing the information provided by both signs A and B iitsbn .4906 y p o tr n e 5 0 9 . 6 3 0 9 . 6 from each grid cell. The probability of viewing information from both signs (i.e., mutual information) is higher than the probability of viewing the information provided by either sign in isolation for the common grid cells.
Figure 8 demonstrates the relationship between the information viewed from sign A, the distance of the observer from sign A, and the relative direction of the observer from sign A. An increase in entropy indicates higher uncertainty in viewing the information provided by sign A. Finally, Mutual information can also visualized in Figure 9 as the difference between individual and conditional entropies. Here, the green line represents the individual entropy of sign A, and the black line represents the conditional entropy of sign A given sign B. 5
The quantification of information provided by a system of signs can be beneficial to architects attempting to improve the navigation of building patrons. This approach may be particularly useful for buildings that are especially complex and require redesigns of signage. For this paper, we adapted Shannon’s entropy measures in order to study the information provided by two signs in a 3D virtual environment. We then visualized these entropy measures in an understandable way for practitioners, including architects and engineers. The benefit of using a gaming engine (Unity 3D) is that these visualization can be dynamically updated during navigation.
For simplicity, we have focused on the distance and
relative direction between the observer and one or two signs.
Future work will extend this framework to include additional
physical and psychological factors (e.g., color and contrast,
interpretability and attentiveness) and additional signs (i.e.,
more than two). The former addition will provide the
groundwork for a cognitively inspired, agent-based model of
navigation behavior. Additional signs will allow us to address some
of the difficulties associated with decomposing complex
systems in terms of information theory
We also plan to further inform this framework with at least two empirical studies with human participants in virtual reality. The first study will investigate the relationship between the visibility of a sign at different distances and relative directions at a finer granularity than previous work. The second study will test different signage systems with respect to their effect on the wayfinding behavior in complex virtual buildings. Together, these studies will provide the necessary groundwork for incorporating research on human perception and cognition into evidence-based design.