Geography Reference
In-Depth Information
capture different fields of view. The average pixel width
for the presented case studies varied from 2 to 15 cm.
Such image resolution and frequency parameters are
inferior to the sophisticated high definition video systems
that are typically employed in conventional PIV. In the
field applications, tradeoffs were necessary between image
quality, speed of data transmission, required storage, and
cost. An additional variable to consider is surface tracers.
Accurate measurements of movement vectors depend on
the presence, visibility, and convection of tracers such as
foam, wood, or water waves (Creutin et al., 2002, Fujita
and Hino, 2003) (Figure 16.1a, b). These tracers need
to be as big or larger than the pixel resolution. When
natural tracers are insufficient, artificial tracers such as
soap, which produces a floating foam, can be added. As
a general note, it is necessary to confirm the accuracy of
the installed videographic system for a given application.
systems can be expressed as (Fujita et al., 1998):
L
1
x
+
L
2
y
+
L
3
z
+
L
4
X
=
(16.1a)
L
9
x
+
L
10
y
+
L
11
z
+
1
L
5
x
+
L
6
y
+
L
7
z
+
L
8
Y
=
(16.1b)
L
9
x
+
L
10
y
+
L
11
z
+
1
where the eleven mapping coefficients
L
1
−
L
11
can be
determined by the least square method using the known
GCPs coordinates. A minimum of 6 GCPs are needed
for conducting the transformation. While more GCPs are
useful for checking errors in survey data, the uncertainty
caused by pixel size is usually greater than that caused
by survey error, and additional points are not necessary
for the analysis (Bradley et al., 2002). Fewer points can
be used if the image coordinates are assumed to be on
the same vertical plane. The size of the non-distorted
image should be nearly the same as that of the original
image. In addition, a reconstruction of the pixel intensity
distribution is made to obtain the ortho-rectified image.
Following Muste et al. (1999), intensity at a pixel in the
transformed image is obtained using a cubic convolution
interpolation of the intensity in 16 neighbouring pixels of
the original image.
16.2.3 Imageortho-rectification
Ground-based cameras have an oblique view angle
(Figure 16.1a), which means that pixel size is variable
and distortion can be an important effect (Hauet et al.,
2008a). As a general rule, images are ortho-rectified prior
to analysis. Ortho-rectification refers to the process by
which image distortion is removed and the image scale
is adjusted to match the actual scale of the water surface
(Figure 16.1b - 1c). Ortho-rectification is accomplished
by applying an appropriate image photogrammetric
transformation (Mikhail and Ackermann, 1976) using
known coordinates of ground control points (GCPs) in
thereal(
X
,
Y
,and
Z
)andtheimage(
x
and
y
) coordinate
systems. The mapping relationships between the two
16.3 Case 1 - Stream gauging
16.3.1 Introduction
The first case study will apply LSPIV to estimate dis-
charges in a systemprone to flash-flooding where gauging
has been historically difficult. Flash-floods occur in the
southern Mediterranean region of France and can result
Camera
(a)
(b)
(c)
Figure 16.1
LSPIV measurement sequence: a) imaging the area to be measured (white patterns indicate the natural or added tracers
used for visualization of the free surface); b) the distorted raw image; c) the undistorted image with estimated velocity vectors
overlaid on the image.
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