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Automated 3D Spatial Measurement of 
Short Gravity-Capillary Waves 
By A.P. Graciant$, J-P. Muller}, P.G. Challenor$, M.A. Srokosz$ 
t+ Department of Photogrammetry and Surveying, University College London, Gower street, 
London WC1E 6BT, United Kingdom. Tel (+44) 071-387 7050 x2738 / Fax (+44) 071-380 
0453, INTERNET : agracian@ps.ucl.ac.uk 
$ James Hennell Centre for Ocean Circulation, Gamma house, Chilworth Research Centre, 
Chilworth, Southampton SO1 7NS, United Kingdom. 
Abstract 
The use of close-range stereo wave imagery using photogrammetric cameras is being investigated as a method for 
deriving sea surface micro-topography and spatial statistics. This approach has the advantage over conventional 
wave measurement techniques, such as capacitance wave staffs, in allowing 3D-spatial information rather than data 
at a single point to be obtained. Furthermore it is a non-invasive measurement technique, which is important 
regarding the study of gravity-capillary waves, since any measuring device that penetrates the surface will modify 
the waves in this region of the spectrum. The approach described, differs from previous work primarily in that the 
process of measuring the wave height field from the imagery is automated. The effect of this is to reduce the total 
processing time, thereby making the method more viable and permitting a larger range of ocean-atmosphere 
parameters to be examined. The sea surface micro-topography is derived using a stereoscopic technique, based on 
Otto-Chau's Least Squares Correlation technique. Results of the automated measurement processes are presented, 
together with directional wave spectra. 
KEY WORDS: Close-Range, Stereo-Matching, Gravity-Capillary Waves, Oceanography. 
I. INTRODUCTION 
This paper describes results of a collaborative project on 
interpreting microwave scatterometer interactions with short 
gravity-capillary waves under wind forcing (Gracian et al., 
1990, 1991). One of the main factors that effect microwave 
Bragg resonant backscatter signatures from sea surfaces are the 
surface spatial statistics and elevation wavenumber spectra, in 
the 4 Hz to 8 Hz wave spectrum region. For spaceborne sensors, 
such as the scatterometer that forms part of the Active 
Microwave Instrument on the European Remote Sensing 
Satellite -1 (ERS-1), sea surface waves in the 3 cm to 7 cm 
wavelength range can affect the Bragg-scattered signal (Ulaby et 
al, 1981). At present most algorithms for retrieving 
oceanographic parameters from data received from spaceborne 
sensors are empirical. It is hoped eventually that by analysis of 
coincident stereo imagery and ERS-1 data, a more fundamental 
basis for parameter retrieval can be provided. 
A study of sea surface statistics in relation to the directional 
distribution of ocean-wave momenta and elevation wave number 
spectra is of great technological and fundamental scientific 
interest. For example it is high frequency waves that are 
damped out by surface pollutants such as oil slicks (Lombardini 
et al, 1989). However, there are several problems with 
conventional wave measurement techniques such as capacitance 
probe measurements (Tucker, 1991). The first is the difficulty 
in transforming the temporal frequency spectra directly into 
wave number spectra. This limitation arises from Doppler 
shifting by long wavelength waves of the shorter gravity-cap- 
illary waves (5—50mm range), which are possibly from different 
directions (Kitaigorodskii et al. 1975; Longuet-Higgins, 
1983). The second point is that it is not possible to derive high 
resolution spatial information from point measurements. 
Thirdly, due to physical limitations such as wetting of the 
device and meniscus effects there is an upper limit to the fre- 
quency at which they work. This is generally of the order of 
3Hz, which is into the gravity wave range. 
The use of stereo photography to obtain sea surface micro- 
topography and derive sea surface statistics appears to be a 
possible solution to many of these limitations (Shemdin et al., 
1988; Banner et al., 1989; Gracian et al., 1991). Indeed as far 
back as 1903 the use of stereo photography had been suggested 
by Kohlschuetter as a means of investigating waves (Laas, 
1921). The use of close-range stereo photogrammetry also has 
the benefit of being a non-invasive measurement technique. 
This is important in relation to the study of gravity-capillary 
waves, since any measuring device that penetrates the surface 
will modify the waves in this region of the spectrum. However, 
the labour intensive requirement of manually processing stereo 
images has until now limited its oceanographic application. 
The approach outlined here differs from previous work primarily 
in that an attempt is made to automate the process. The effect of 
this is to reduce the total processing time, thereby making the 
method more viable and permitting a larger range of ocean- 
atmosphere parameters to be examined. 
Section II describes the data acquisition process in terms of the 
photogrammetric cameras used, their synchronisation and 
mounting in relation to water surface, derivation of suitable 
control point information as well as ancillary wave staff 
measurements. The wave staff measurements were made to 
enable an inter-comparison with wavenumber spectra derived 
from the automated measurement process. In section III, stereo- 
matching as a method of automated wave height measurement is 
considered based on an adaptive least squares correlation 
algorithm. Coverage results of the automated matching process 
are presented together with the high frequency sea surface micro- 
topography. The corresponding one sided directional power 
spectral density is then derived in section IV, by the discrete 
Fourier transform of the auto-correlation function for the wave 
height distribution. Directional components of the derived 
spectra are then compared with two sets of point (or omni- 
directional) wavenumber spectra above the spectral peak. 
Finally, sections V and VI discuss the results and future 
developments.