Geoscience Reference
In-Depth Information
3.1 Ditch Grouping Based on the Edge-Cutting of Minimal
Spanning Tree
Ditches that are subjected to be typification should be recognized before the
typification process. This procedure identifies that which ditches should be con-
sidered as a whole. This study uses the edge-cutting of the minimal spanning tree
for ditch grouping, the idea of which originates from Zahn (
1971
). This method
has been widely applied to building grouping (Regnauld
2001
; Zhang et al.
2013
).
The definition of the cognition distance between the objects is the key issue to
implement this approach.
3.1.1 Definition of Cognition Distance of Ditches
Ditches run approximately parallel and adjacent to each other tend to be recog-
nized within one group according to visual cognition. This paper combines the
average distance (McMaster
1986
), the angle difference and the overlapping
relationship between two ditches to constitute the cognition distance between
them, as shown in Eq. (
1
).
CognitionDistance
¼
AverDistance
tan 4
:
5
AngleDifference
ð
ð
Þ þ
1
Þ
2
OverlapDegree
ð
Þ
ð
1
Þ
AverDistance is the average distance between two ditches, which is propor-
tional to the CognitionDistance. The smaller AverDistance, the smaller Cogni-
tionDistance. As a result, they are more likely to be divided into the same group.
The calculation of AverDistance can be written as:
AverDistance ¼ 2Area
AB
=
L
A
þ
L
B
ð
Þ
ð
2
Þ
where Area
AB
is the area of those polygons that consist of two ditches and their
endpoints, L
A
is the length of ditch A, and L
B
is the length of Ditch B, as shown in
Fig.
2
a.
AngleDifference is denoted as the angle difference between two ditches. The
smaller AngleDifference, the smaller CognitionDistance. Furthermore, ditches
with smaller AngleDifference are more likely to be divided into one group. The
calculation can be shown as:
AngleDifference ¼ Angle
A
Angle
B
j
j
ð
3
Þ
where Angle
A
is the angle of ditch A, Angle
B
is the angle of ditch B. Angledif-
ference ranges from 0 to 10.
OverlapDegree shows the overlapping relationship between two ditches. In
contrast to AverDistance, OverlapDegree is inversely proportional to Cognition-
Distance, that is, the greater OverlapDegree, the smaller CognitionDistance. Thus,
ditches with greater OverlapDegree are more likely to be divided into a group. The
