=Paper=
{{Paper
|id=None
|storemode=property
|title=A Quantitative Evaluation Approach for Cognitive Maps of Blind People
|pdfUrl=https://ceur-ws.org/Vol-888/SKALID2012_Miao.pdf
|volume=Vol-888
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==A Quantitative Evaluation Approach for Cognitive Maps of Blind People==
https://ceur-ws.org/Vol-888/SKALID2012_Miao.pdf
A Quantitative Evaluation Approach for Cognitive Maps
of Blind People
Mei Miao, Gerhard Weber
Technische Universität Dresden, Institut für Angewandte Informatik,
Nöthnitzer Straße 46, 01187 Dresden, Germany
{mei.miao, gerhard.weber} @tu-dresden.de
Abstract. In the field of Human-Computer Interaction, several projects aim to
develop new technological aids, which enable and provide people who are blind
the ability to navigate themselves around on their own. In order to evaluate
these technological aids, the created cognitive maps which are built by the help
of technological aids should be evaluated at first. A new approach has been de-
veloped for evaluating these reconstructed cognitive maps quantitatively. In this
paper, we describe how this approach has been developed. Nine criteria are
identified and weighted with help from the blind people. Using weighted
Euclidean distance enables the cognitive maps to be compared with each other.
Keywords: cognitive map, blind people, quantitative evaluation.
1 Introduction
Cognitive maps also referred to as mental maps, express the essential structure of
spatial information through learning processes [1]. One of a cognitive map’s functions
is to support navigation. Research into cognitive maps is particularly useful to urban
planners, mobility specialists, and navigation aid designers [2]. For most of the blind
people, it is usually impossible to travel independently. Therefore, in the field of Hu-
man Computer Interaction, several projects [3-5] aim to develop new technological
aids to provide blind people the ability so that they can navigate indoor/outdoor on
their own.
In order to evaluate such technological aids, the blind people are often asked to
create cognitive maps which are built by the help of technological aids. Two themes
will be mostly measured: route knowledge and configurational knowledge [6]. Route
knowledge means the knowledge of a route from point A to point B. Configurational
knowledge means the knowledge of where the roads and landmarks are located. For
blind people, there are two main ways to create cognitive maps with respect to route
knowledge and configurational knowledge. We can ask them to verbally describe it
[7] or to reconstruct it with help of things like Modelling kit, whiteboard, bar magnets
[7, 8]. Sketch mapping is the most common method for sighted people, but it is rarely
used for blind people, because most of blind people are unfamiliar with it.
For evaluating the technological aids, the reconstructed cognitive maps should be
evaluated. Figure 1 shows 3 maps: the original map (left, the street names are not
Proceedings SKALID 2012 37
Miao & Weber
displayed), cognitive map 1 reconstructed by subject A (middle), and cognitive map 2
reconstructed by subject B (right). How can we evaluate these maps with respect to
configurational knowledge?
original map created map 1 created map 2
Fig. 1. Examples of cognitive maps created by blind people
In this paper, a new approach will be presented to quantitatively evaluate cognitive
maps which are reconstructed by blind people.
2 Related Work
Until now, there has been comparatively less attention paid towards the evaluation
approach of cognitive maps for the blind than for the sighted people. [9, 10] describe
the methods of evaluating cognitive maps quantitatively. However, the considered
cognitive maps were drawn from sighted people. In the following, we just discuss the
evaluation of cognitive maps of blind people. With technological aids, blind people
build the cognitive maps just based on auditory and haptic cues, so their reconstructed
cognitive maps differ somewhat from those based on vision. For evaluating these
cognitive maps, there is no systematic approach available. In this context, the study in
[11] should be mentioned. In their study, the blind subjects were asked to model the
layout of labyrinths (see fig. 2) after having explored them.
Fig. 2. Labyrinth 1 (left) and labyrinth 2 (right) [11]
The cognitive maps were analyzed in five different criteria: Number of elements: 3
in Labyrinth 1 and 4 in Labyrinth 2. Form of elements: referring to the correct identi-
fication of the L and T forms in the composition. Position: referring to the correct
orientation of the elements. Placement: referring to the correct distance between the
elements. Symmetry: referring to the correct axial disposition of the elements in the
first labyrinth and the correct central disposition in the second labyrinth.
A map of the real environment is more complex than the labyrinths in figure 2.
There are features such as street names, curves on the streets, different directions,
crosses and so on. Therefore, to evaluate reconstructed cognitive maps of the real
environment, we need a more complex approach.
38 Proceedings SKALID 2012
A Quantitative Evaluation Approach for Cognitive Maps of Blind People
3 Development of the Approach
In this section, we describe how this approach has been developed in detail. There
are 3 steps: in the first step, the criteria were identified with which we can evaluate
the cognitive maps quantitatively; then, we weighted these criteria; and finally, the
method for the quantification of the criteria was chosen.
3.1 Identification of Criteria
In this step, we analysed several cognitive maps which were reconstructed by blind
people in a previous study of us. In this study, ten blind people were asked to con-
struct mental maps after learning three different maps of unknown environments us-
ing three different media (tactile map, iPad and tactile pin device (www.Hyper-
braille.de)). Space restrictions do not allow to go into details here. Nine criteria were
identified by the principle: one mistake should not be counted twice. The criteria were
classified in 4 categories:
• Category 1: number of elements
─ Number of correct street segments (C1): streets are divided in segments by
crosses or branches. Only the correct street segments should be counted.
─ Number of correctly remembered street names (C2): This criterion is just rele-
vant, if we want to evaluate how easy blind people can remember the street
names with the help of technological aids.
• Category 2: property of streets. Property of streets refers to the shape, name and
direction of the streets.
─ Number of correct street shapes (C3): referring to, if a street is straight or has
curves, the number and the directions of the curves.
─ Number of correctly assigned street names (C4): These include the street names
which were not only remembered correctly, but also assigned to the right streets
correctly.
─ Number of correct street direction (C5): A tolerance range for the estimation of
direction is necessary for blind people. On the basis of the 12 division on a
clock face, we define 2 divisions as tolerance range. In the case that a street has
curve(s), we define the direction with reference to the start and end point of the
street, if there is no landmark in between.
• Category 3: arrangement of streets
─ Number of correct crosses and branches (C6): a cross or branch is correct, if it
is found in the original map.
• Category 4: number of errors
─ Number of none existing streets (C7): streets should be counted which do not
exist in the original map.
─ Number of none existing crosses and branches (C8): this refers to the crosses
and branches which are caused by streets which are reconstructed too long, but
not by none existing streets.
Proceedings SKALID 2012 39
Miao & Weber
─ Number of displacements of streets (C9): it refers to the relative position of the
streets. For example, if street A crosses street B after the crossroad, it is a dis-
placement, meaning that street A should cross street B before the crossroad.
It should be pointed out that the length belongs to the property of a street as well.
However, it cannot be used as a criterion extra. Because if a street is reconstructed too
long, then the length will be taken into account in the criterion “Number of none ex-
isting crosses and branches”. Otherwise, if a street is reconstructed too short, then it
will be taken into account in the criterion “Number of correct crosses and branches”.
3.2 Weighting of the Criteria
All of the nine criteria deal with crosses/branches (C1, 6, 7, 8, 9), street names (C2,
4), street shapes (C3), or street directions (C5). In this step, we weighted these four
items with weights w1, w2, w3 and w4 by involving blind people. The weights are speci-
fied as follows:
(1) At first, we had to find out if it is necessary to give the 4 items different
weights. According to the relevance for getting an overview of an environment, 21
blind people were invited to rank the 4 items in order. Two different items can have
the same ranking. Then, the four items are ordered by the average of the rankings
from blind people: crosses/branches (rank at 1), street names (rank at 2), street
shapes (rank at 3), and street directions (rank at 4).
(2) Then, we tested if the rankings of the items are significantly different. The fre-
quency distribution of the four items and rankings was displayed in a 4x4 - contin-
gency table. The items were paired (crosses/branches with street names, street names
with street shapes, and street shapes with street directions) and tested by using the
Chi-square test for homogeneity. The test showed a significant difference between
crosses/branches and street names, street shapes and street directions, but not be-
tween street names and street shapes (df = 3, p=0.95, χ23;0.95 = 7.81). However there is
a significant difference between street names and street directions. Therefore, street
names and street shapes should get the same weight.
(3) Finally, we calculated the weights w1, w2, w3, and w4. The weights are calculated
according to the frequency of rank 1 and 2 of the four items. However, the frequency
of rank 1 should be given more weight than the frequency of rank 2. Therefore, the
frequency of rank 1 should be multiplied by a factor f (1 < f < 3). According to the
rankings from blind people, the item crosses/branches should get the highest weight.
If the frequency of rank 1 is multiplied by 3, the item street names will get the highest
weight. f should be therefore less then 3. In our study, we set f equal 2 (see table 1).
Table 1. Weighted frequency distribution of the four items (ai) of rank 1 and 2 (H: frequency)
items
a1 a2 a3 a4 ∑
rank
1 H11*2 H12*2 H13*2 H14*2 H1. *2
2 H21 H22 H23 H24 H2.
∑ H11*2+ H21 H12*2+ H22 H13*2+ H23 H14*2+ H24 H1. *2+ H2.
40 Proceedings SKALID 2012
A Quantitative Evaluation Approach for Cognitive Maps of Blind People
The weights were calculated as shown in equation (1). So we got following results:
w1 = 0,31, w2= w3 = 0,28, w4 = 0,13.
w (ai) = (H1i * 2 + H2i)/(H1. * 2 + H2.) (1)
3.3 Choice of Method for Quantification
For quantifying the criteria we chose the approach weighted Euclidean distance.
i
d ( x, y ) = ∑ w *(x − y ) = w *(x − y ) +Λ + w *(x − y )
i =1
i i i
2
1 1 1
2
i i i
2
(2)
where x = (x1, x2, … xi), y = (y1, y2, …, yi), wi = weights, and d(x, y) = the distance from
point x to y. In our case, xi is the i-th value of the original map (x7, 8, 9 = 0), while yi is
the i-th value of the reconstructed cognitive map, and wi is the specified weight for i-
th criteria (see table 2). d (x, y) is the distance between the original map and cognitive
map. In other words, we compare these two maps by measuring the distortion be-
tween the original map and the cognitive map. It gives a measure of how similar cog-
nitive map to the original map actually is. The smaller the value, the more similar the
cognitive map to the original map is.
Table 2. Criteria and their weights for evaluating cognitive map
criteria weight Original Cognitive
map map
Number of correct street segments 0.31 x1 y1
Number of correct remembered street names 0.28 x2 y2
Number of correct street shapes 0.28 x3 y3
Number of correct assigned street names 0.28 x4 y4
Number of correct street direction 0.13 x5 y5
Number of correct crosses and branches 0.31 x6 y6
Number of none existing streets 0.31 0 y7
Number of none existing crosses and branches 0.31 0 y8
Number of displacement of streets 0.31 0 y9
As mentioned, if we do not want to evaluate how easy blind people can remember
the street names with the help of technological aids, we can set its (C2) weight 0.
4 Conclusions
This approach has been developed within a study in which the arrangement of streets
was tested with different technological aids. There were no landmarks on the original
map. It is not intended for evaluating cognitive maps according to the structure of
buildings such as an airport. In this case the location of landmarks should be tested,
Proceedings SKALID 2012 41
Miao & Weber
the criteria have to be extended and the weight specified. In addition, we also found
out that the blind people weighted the 4 items in matters of wayfinding differently
than in matters of getting an overview of an environment. This indicates that if route
knowledge is tested, we need other criteria and other weights for them.
Acknowledgements
We would like to thank all of the blind participants and collaborators for spending
their time on our study. We would also like to thank Limin Zeng for the preparation
of the study and Michael Schmidt for useful discussions.
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