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Citation for published item:
Fonstad, M.A. and Dietrich, J.T. and Courville, B.C. and Jensen, J.L. and Carbonneau, P.E. (2013)
'Topographic structure from motion: a new development in photogrammetric measurement.', Earth surface
processes and landforms., 38 (4). pp. 421-430.
Further information on publisher's website:
https://doi.org/10.1002/esp.3366
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This is the accepted version of the following article: Fonstad, M.A., Dietrich, J.T., Courville, B.C., Jensen, J.L.
Carbonneau, P.E. (2013). Topographic structure from motion: a new development in photogrammetric measurement.
Earth Surface Processes and Landforms 38(4): 421-430 which has been published in nal form at
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Topographic Structure from Motion: a new development in photogrammetric
measurement
Mark A. Fonstad
1
, James T. Dietrich
1
, Brittany C. Courville
2
, Jennifer L. Jensen
2
, Patrice E.
Carbonneau
3
1
Department of Geography, University of Oregon, Eugene, OR 97403 USA
2
Department of Geography, Texas State University, TX 78666 USA
3
Department of Geography, Durham University, Durham UK
Submitted to
Earth Surface Processes and Landforms
12 December 2011
1. Introduction
The production of high-resolution topographic datasets is of increasing concern and application
throughout the geomorphic sciences (Butler et al., 2001; Hancock and Willgoose, 2001; Lane,
2003; Bird et al., 2010; Fonstad and Marcus, 2010). A wide range of topographic measurement
methods have evolved to meet this production need. Despite the range of available methods, the
production of high resolution, high quality digital elevation models (DEMs) generally requires a
significant investment in personnel time, hardware and/or software. Image based methods, such
as digital photogrammetry (Chandler, 1999; Lane, 2000; Butler et al., 2002; Chandler et al.,
2002; Baily et al., 2003; Carbonneau et al., 2003; Lane et al., 2003; Westaway et al., 2003;
Gimenez et al., 2009; Marzloff and Poesen, 2009; Lane et al., 2010), have steadily been
decreasing in costs. Photogrammetry is becoming accessible to a wider base of users following
the development of methods allowing for the accurate calibration of non-metric cameras and the
increasingly reliable automation of the photogrammetric process (e.g. Carbonneau et al., 2004;
Chandler, 1999; Chandler et al., 2002). Recent developments should lower the cost of image
based topography even further. Initially developed for the purpose of rapid, inexpensive and
easy three dimensional surveys of buildings or small objects, the Structure from Motion
approach (SfM) is a purely image based method that could deliver a step change if transferred to
the geomorphic sciences.
While a full review of the SfM process is not appropriate for this manuscript (see Snavely et al.
[2006 and 2008] for a basic overview of this computer vision process, and Snavely, [2008] for a
complete description), the following gives a brief overview of the approach in a qualitative
manner. Similarly to traditional photogrammetry, SfM uses images acquired from multiple
viewpoints in order to restitute the three dimensional geometry of an object. However, SfM
diverges significantly from traditional photogrammetry in that in SfM, no ground control is
required to restitute that camera parameters (focal length, distortion and position) and the relative
topographic variations in a scene. This technology is based on progress in the area of automated
image matching. By automatically finding a very large number of conjugate image points in
several images, the colinearity equations which describe the relationship between a three
dimensional object and its projection onto a two dimensional image can be solved and
topography calculated (See Wolf and Dewitt, 2000). In the traditional photogrammetry language,
the bundle adjustment is done after coordinate system rectification using ground control points
(i.e. in real, object space), whereas in the SfM process bundle adjustment occurs before
coordinate system rectification (i.e. in image space). Only after the photogrammetric bundle
adjustment process creates a point cloud are ground control points necessary to rectify the entire
point cloud to a desired coordinate system. Another non-technical distinction to be noted is that
the SfM method can be performed entirely with freely available software packages which are
easily accessible to non-specialists.
Earlier SfM approaches in geomorphology have been previously discussed by Heimsath and
Farid (2002, 2003). However, it should be noted that in recent years, the SfM workflow has
been significantly improved and that current SfM software operates with a significantly higher
level of automation. Additionally, some of the problematic assumptions in this earlier use of
SfM (and noted by Chandler et al., 2003) have since been removed. When the number of photos
of the same areas is quite large, modern SfM algorithms appear to have the same level of
robustness as traditional photogrammetry. This reduces the camera backcalculation errors per
picture. Most importantly, however, has been the rise of standalone, freely-available, and easy-
to-use SfM software, designed for general computer users. The progress in the refining of these
tools over the past two or three years has been stunning, and it seems inevitable that these SfM
approaches will become appropriate to an even wider range of instrument platforms. Verhoeven
(2009) and Verhoeven et al. (2009) have made introductory tests of the modern SfM process
using low-altitude helikites in archaeology. A handful of other recent SfM applications to
topography have been presented previously at professional conferences and published in
abstracts and proceedings (Dietrich, 2010; Fonstad et al., 2010; Dietrich et al., 2011; Fonstad et
al., 2011a, b). Dowling et al. (2009) used SfM and a hand-held camera to study soil erosion over
a 1 m
2
plot. Templeton et al. (2010) used a UAS helicopter and SfM to generate DEMs for
ecohydrological research. Welty et al. (2010) used hand-held camera images taken from a plane
to construct the topography of the Columbia Glacier. Whilst these SfM DEMs are remarkably
easy to produce and visually stunning, the errors and limitations of this new method are not yet
known. Such errors can profoundly influence uses of these DEMs in geomorphology, such as in
sediment budgeting (Wheaton et al., 2010). The crucial research question we address is this:
what is quality of the DEMs produced by the SfM method? First, we will demonstrate that the
SfM approach can be applied in a fluvial geomorphology context in order to restitute high-
resolution topography. Second, we will show that the outputs of the SfM workflow are of equal
quality to those of an independently acquired airborne LiDAR validation dataset.
2. Assessment of Topographic Accuracy
