should range in the same interval of the geometric metrics
used to ensure compatibility, since both will be combined. In
this paper weights ranged from 0 (totally different) to 1 (per-
fectly similar) like the geometric metrics used in Möller
et al.
(2013). Thus, the
TSI
values also lies between 0 and 1.
Figure 3. Matrix summarizing the thematic similarity weights
between
m
land cover classes.
In practical terms, the three features considered in the
TSI
(the number of classes within an object, their proportion of
coverage, and their thematic similarity) influence the thematic
quality of the object and the
TSI
value summarizes all of the ef-
fects. Figure 4 illustrates two examples to help understand the
TSI
. Figure 4a shows an object under evaluation by two users:
X and Y. The object mixes land cover classes 1 and 2. The user
X is not very sensitive to errors involving these classes, and
thus defined their thematic similarity as 0.9 (w
12
= 0.9). On
contrary, user Y is very sensitive to errors involving these two
classes and defined w
12
= 0.1. Each of the classes occupies ap-
proximately the same proportion of area within the object, and
thus the object is far of being thematically pure (low segmen-
tation quality). Because the object is mixed the
TSI
value for
both users is <1. However, the magnitude of the
TSI
depends
on the sensitivity of the user to the thematic error. Since user
X defined w
12
= 0.9, the
TSI
value of the object is much higher
than that for user Y for whom w
12
= 0.1. Figure 4b shows a
case in which one class dominates most of the object’s area.
Combining Geometric and Thematic Methods
The combination of Möller
et al.
’s (2013) geometric metrics
and the
TSI
before the calculation of a global metric for the
whole segmentation is central to the geometric-thematic
method of segmentation quality assessment. Combining the
geometric metrics that assess areal and positional accuracy of
each object S and the corresponding
TSI
allows the final global
metric to reflect both geometric and thematic proprietaries of
the segmentation (Figure 5).
Figure 5. Combination of the geometric and thematic methods
(dashed outlined areas) to calculate the geometric-thematic
method (solid outlined area). The geometric metrics, G
R
and G
F
,
and the TSI (see main text for details on the TSI
R
and TSI
F
) are
joined together to produce J
R
and J
F
, which are used to calculate
the global metric M
j
.
The geometric metrics, G
R
and G
F
, and the
TSI
are joined to-
gether, forming new metrics designed as J
R
and J
F
. Metrics G
R
and G
F
alone assess geometric quality of each intersection S
whereas J
R
and J
F
assess geometric and thematic quality. How-
ever, the combination of the geometric metrics with the
TSI
is not straightforward. The
TSI
was originally designed to be
calculated for each object directly (object F), whereas metrics
G
R
and G
F
are calculated for each intersection S. As a result,
there is no one-to-one correspondence between the geometric
metrics and the
TSI
. To overcome this issue, the
TSI
value of
each object F is assigned to all intersections S
∈
F, which can
be referred to as TSI
F
. Then, for each S
∈
F, the geometric met-
ric G
F
is combined with the TSI
F
through geometric averag-
ing, originating J
F
. Similarly, the metric G
R
is combined with
the TSI
R
, originating J
R
. However, there is no such
TSI
value
because the
TSI
is calculated only in relation to F and not to R.
For this reason, the
TSI
value of the reference objects R (TSI
R
)
Figure 4. Calculation of the TSI: (a) a circular object is mixing two land cover classes (1 and 2) in similar proportions (P
1
~P
2
), to which an
example of a calculation is presented for two users: X and Y, and (b) a circular object is mixing two land cover classes (1 and 2) in dissimi-
lar proportions (P
1
>>P
2
), to which an example of a calculation is presented for two users: X and Y. Symbols
⟶
, ↑, and ↓ mean “tends to”,
“tends to maximum”, and “tends to minimum”, respectively.
454
June 2015
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
