U.S. Department of the Interior

U.S. Geological Survey

Prepared in cooperation with Northern Arizona University

Automated Remote Cameras for Monitoring Alluvial 

Sandbars on the Colorado River in Grand Canyon, 

Arizona

By Paul E. Grams, Robert B. Tusso, and Daniel Buscombe

Open-File Report 2018–1019
ii

Cover image: Photograph of sandbar that is photographed daily by remote digital camera (in 

foreground) along the Colorado River in Grand Canyon National Park, Arizona.
U.S. Department of the Interior

U.S. Geological Survey

Prepared in cooperation with Northern Arizona University

Automated Remote Cameras for Monitoring Alluvial 

Sandbars on the Colorado River in Grand Canyon, 

Arizona

By Paul E. Grams, Robert B. Tusso, and Daniel Buscombe

Open-File Report 2018–1019
iv

U.S. Department of the Interior

RYAN K. ZINKE, Secretary

U.S. Geological Survey

William H. Werkheiser, Deputy Director

exercising the authority of the Director

U.S. Geological Survey, Reston, Virginia: 2018

For more information on the USGS—the Federal source for science about the Earth,

its natural and living resources, natural hazards, and the environment—visit

https://www.usgs.gov/ or call 1–888–ASK–USGS (1–888–275–8747).

For an overview of USGS information products, including maps, imagery, and publications,

visit https://store.usgs.gov/.

Any use of trade, firm, or product names is for descriptive purposes only and does not imply

endorsement by the U.S. Government.

Although this information product, for the most part, is in the public domain, it also may

contain copyrighted materials as noted in the text. Permission to reproduce copyrighted items

must be secured from the copyright owner.

Suggested citation:

Grams, P.E., Tusso, R.B., and Buscombe, D., 2018, Automated remote cameras for monitoring alluvial 

sandbars on the Colorado River in Grand Canyon, Arizona: U.S. Geological Survey Open-File Report 

2018–1019, 50 p., https://doi.org/10.3133/ofr20181019. 

ISSN 2331-1258 (online)
v

Acknowledgments

We thank the many individuals who have contributed to the development, construction, and maintenance of the 

remote camera systems described in this report. Glen Bennett and Ted Melis initiated the transition from film to the 

new digital cameras in 2008 and the original 12 cameras (most of which are still in service) were built by Rian Bogle. 

Tim Dealy assisted with building many of the cameras currently in use. Many cooperators and volunteers have 

assisted with servicing the cameras and exchanging memory cards in the field including Matt Kaplinski, Ryan Lima,

Tom Sabol, Ron Griffiths, and Joel Unema. Joseph Hazel, Keith Kohl, Rob Ross, and Rod Parnell surveyed the 

locations of cameras and panels used for image rectification. Julaire Scott and Caleb Ring assisted with organizing 

the thousands of scanned images from the original film cameras. Finally, Tom Gushue, Tim Andrews, Taylor 

Johnson, and James Hensleigh, developed the tools to display and serve the images online. This work was 

supported by the Glen Canyon Dam Adaptive Management Program and the U.S. Department of Interior Bureau of 

Reclamation.
vi

Contents

Acknowledgments.......................................................................................................................................................... v

Abstract..........................................................................................................................................................................1

Introduction ....................................................................................................................................................................1

Study Area and Monitoring Locations ............................................................................................................................2

Description of Remote-Camera Systems.......................................................................................................................6

Film-Camera Systems................................................................................................................................................6

Digital-Camera Systems.............................................................................................................................................7

Image Processing and Analysis .....................................................................................................................................9

Image Processing and Web-Based Image Viewer.....................................................................................................9

Qualitative Analysis of Sandbar Deposition and Erosion .........................................................................................11

Method Validation................................................................................................................................................14

Results of Visual Estimates of Sandbar Change.................................................................................................17

Quantitative Analysis of Sandbar Area.....................................................................................................................19

Image Registration and Rectification...................................................................................................................19

Delineation of Sandbar Area ...............................................................................................................................23

The RCSandSeg Program...................................................................................................................................25

Sandbar Area at RC0307 Between October 2009 and October 2015 .........................................................................30

References Cited .........................................................................................................................................................37

Appendix 1. Normalized Changes in Sandbar Area, Volume, and Composite Sandbar Size on the Colorado River in 

Grand Canyon National Park, Arizona, Determined from Repeat Topographic Surveys......................................40

Appendix 2. Estimated Changes in sandbar size on the Colorado River in Grand Canyon National Park, Arizona, 

from Remote-Camera Images for the 2012, 2013, 2014, and 2016 Controlled Floods Released from Glen 

Canyon Dam.........................................................................................................................................................41

Appendix 3. Example Python Computer Program for Finding the [x,y] Translation Vector Between Two RemoteCamera Images Used for Monitoring Sandbars on the Colorado River in Grand Canyon National Park, Arizona, 

Using Two-dimensional Fast Fourier Transform (2D-FFT) ...................................................................................49

Appendix 4. Example Python Computer Program for Finding the Area of a Polygon in Projected [x,y] Coordinates ..50
vii

Figures

Figure 1. Map of Colorado River corridor in Glen Canyon National Recreation Area and Grand Canyon 

National Park, Arizona, showing the locations of sandbar monitoring sites with remote cameras.................3

Figure 2. Photograph of debris fan and downstream eddy showing typical alluvial sandbar formations 

along the Colorado River in Grand Canyon National Park, Arizona...............................................................4

Figure 3. Photographs of remote-camera systems used along the Colorado River in Grand Canyon 

National Park, Arizona...................................................................................................................................7

Figure 4. Graph of discharge of the Colorado River at Lees Ferry, Arizona ......................................... 12

Figure 5. Photographs of sandbars along the Colorado River in Grand Canyon National Park, Arizona, 

from before and after the 2014 controlled flood released from Glen Canyon Dam...................................... 13

Figure 6. Graphs of visual estimates of change in sandbar size in remote-camera images from 

monitoring sites along the Colorado River in Grand Canyon National Park, Arizona, following controlled 

floods released from Glen Canyon Dam...................................................................................................... 19

Figure 7. Example of the image-registration workflow used for sandbar monitoring along the Colorado 

River in Grand Canyon National Park, Arizona............................................................................................ 20

Figure 8. Example of the image rectification workflow used for sandbar monitoring along the Colorado 

River in Grand Canyon National Park, Arizona............................................................................................ 21

Figure 9. Example oblique photograph taken by a remote camera used for sandbar monitoring along 

the Colorado River in Grand Canyon National Park, Arizona ...................................................................... 23

Figure 10. Time series of oblique imagery from a sandbar monitoring site (RC0307R) along the 

Colorado River in Grand Canyon National Park, Arizona ............................................................................ 24

Figure 11. Screenshots from the RCSandSeg program used to process remote-camera images for 

sandbar monitoring along the Colorado River in Grand Canyon National Park, Arizona............................. 26
viii

Figure 12. Screenshots from the green tab of the RCSandSeg program used to process remote-camera 

images for sandbar monitoring along the Colorado River in Grand Canyon National Park, Arizona ........... 27

Figure 13. Graph of time lag, in hours, between discharge at each remote-camera site and the nearest 

upstream gaging station along the Colorado River in Grand Canyon National Park, Arizona...................... 27

Figure 14. Example interactive segmentation in the RCSandSeg program (Buscombe, 2017) used to 

process remote-camera images for sandbar monitoring along the Colorado River in Grand Canyon National 

Park, Arizona............................................................................................................................................... 29

Figure 15. Time series of oblique remote-camera imagery..................................................................... 33

Figure 16. Graph of the relation between survey-derived and image-derived sandbar area above the 

river stage associated with a flow rate of 10,000 cubic feet per second along the Colorado River in Grand 

Canyon National Park, Arizona.................................................................................................................... 34

Figure 17. Graphs showing time series since 1990 of total-station survey-derived and image-derived 

sandbar areas above the river stage associated with a flow rate of 10,000 cubic feet per second along the 

Colorado River in Grand Canyon National Park, Arizona ............................................................................ 35

Figure 18. Images showing comparisons between rectified sandbars used for sandbar monitoring along 

the Colorado River in Grand Canyon National Park .................................................................................... 36

Tables

Table 1. Sandbar monitoring sites with remote camera systems along the Colorado River in Grand 

Canyon National Park, Arizona......................................................................................................................5

Table 2. Digital-camera models used in remote camera systems along the Colorado River in Grand 

Canyon National Park, Arizona......................................................................................................................8

Table 3. Periods of image record at sandbar monitoring sites where camera locations have changed 

along the Colorado River in Grand Canyon National Park, Arizona............................................................. 10
ix

Table 4. Visually estimated changes in sandbar size in remote-camera images taken along the 

Colorado River in Grand Canyon National Park, Arizona ............................................................................ 14

Table 5. Comparison between visual estimates of sandbar change in remote-camera images and 

measured sandbar change at monitoring sites ............................................................................................ 16

Table 6. Matrix of agreement and disagreement between measured change in normalized sandbar 

size and visually estimated change in sandbar size in remote camera images at monitoring sites along the 

Colorado River in Grand Canyon National Park, Arizona. ........................................................................... 17
x

Conversion Factors

U.S. customary units to International System of Units

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square foot (ft2) 0.09290 square meter (m2)

Flow Rate

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

International System of Units to U.S. customary units

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square meter (m2) 10.76 square foot (ft2) 

Flow rate

cubic meter per second (m3/s) 35.31 cubic foot per second (ft3/s)

Datum

Vertical coordinate information is referenced to the Geodetic Reference System 1980 (GRS 80) ellipse defined by the North 

American Datum of 1983 (NAD 83) (2011).

Horizontal coordinate information is referenced to NAD 83 (2011) and projected to State Plane Coordinate System, Arizona 

Central Zone, in meters.

Elevation, as used in this report, refers to distance above the Geodetic Reference System 1980 (GRS 80) ellipse defined by the 

North American Datum of 1983 (NAD 83) (2011).
xi

Abbreviations

2D-FFT two-dimensional fast Fourier transform

DC direct current

Exif exchangeable image file format

GCMRC Grand Canyon Monitoring and Research Center

GCP ground control point

GUI graphical user interface

ft3/s cubic feet per second

RANSAC random sample consensus

RM river mile

RMSE root-mean-square error

RCSandSeg Remote Camera Sandbar Segmentation computer program

SIFT scale invariant feature transform

USGS U.S. Geological Survey
1

Automated Remote Cameras for Monitoring Alluvial 

Sandbars on the Colorado River in Grand Canyon, 

Arizona

By Paul E. Grams1, Robert B. Tusso1, and Daniel Buscombe2

Abstract

Automated camera systems deployed at 43 remote locations along the Colorado River 

corridor in Grand Canyon National Park, Arizona, are used to document sandbar erosion and 

deposition that are associated with the operations of Glen Canyon Dam. The camera systems, which 

can operate independently for a year or more, consist of a digital camera triggered by a separate 

data controller, both of which are powered by an external battery and solar panel. Analysis of 

images for categorical changes in sandbar size show deposition at 50 percent or more of monitoring 

sites during controlled flood releases done in 2012, 2013, 2014, and 2016. The images also depict 

erosion of sandbars and show that erosion rates were highest in the first 3 months following each 

controlled flood. Erosion rates were highest in 2015, the year of highest annual dam release volume. 

Comparison of the categorical estimates of sandbar change agree with sandbar change (erosion or 

deposition) measured by topographic surveys in 76 percent of cases evaluated. A semiautomated 

method for quantifying changes in sandbar area from the remote-camera images by rectifying the 

oblique images and segmenting the sandbar from the rest of the image is presented. Calculation of 

sandbar area by this method agrees with sandbar area determined by topographic survey within 

approximately 8 percent and allows quantification of sandbar area monthly (or more frequently).

Introduction

Sandbars that occur along the banks of the Colorado River in Grand Canyon National Park 

and Glen Canyon National Recreation Area, Arizona, have long been recognized as integral 

components of the riverine landscape and an important resource. Sandbars serve as the primary 

boat landing and camping sites for the thousands of overnight visitors to the river corridor each 

year (Stewart and others, 2003). Sandy alluvium provides substrate for riparian vegetation, which 

forms the terrestrial riparian ecosystem (Ralston, 2005). The morphological characteristics of some 

sandbars create streambank irregularities that are low-velocity habitat for native fish (Valdez and 

Ryel, 1995; Converse and others, 1998). The bare sand exposed on sandbars is also a source of 

windblown sand for upland aeolian dune fields that contain historical and archeological sites (East 

 

1U.S. Geological Survey.

2Northern Arizona University.
2

and others, 2016). For all of these reasons, sandbars and changes in sandbar size and character are 

of interest to resource managers and the public.

Scientific investigations have described sandbar characteristics (Schmidt, 1990), 

mechanisms of sandbar erosion (Budhu and Gobin, 1995; Alvarez and Schmeeckle, 2013), and rates 

and magnitudes of deposition (Hazel and others, 1999, 2010; Schmidt and others, 1999). Sandbars 

have eroded, decreasing in size and number since the completion of Glen Canyon Dam in 1963 

(Dolan and others, 1974; Schmidt and Graf, 1990; Schmidt and others, 2004; Ross and Grams, 

2015). Schmidt and others (2004) estimated the extent of exposed sand decreased by 

approximately 25 percent. Erosion was associated with a corresponding decrease in campsites 

available to river recreationists (Kearsley and others, 1994). In 1996, the U.S. Department of the 

Interior began experiments with controlled flood releases from Glen Canyon Dam to rebuild eroded 

sandbars (Webb and others, 1999). That initial experiment and subsequent experimental releases 

in 2004 and 2008 demonstrated that controlled floods under the appropriate conditions of 

sediment supply were an effective tool for rebuilding eroded sandbars (Schmidt and Grams, 2011). 

Building on these findings, the U.S. Department of the Interior adopted a protocol for releasing 

controlled floods annually, depending on resource conditions (Wright and Kennedy, 2011; U.S. 

Department of the Interior, 2012). Preliminary findings indicate continued effectiveness of this 

approach (Grams and others, 2015).

Assessment of sandbar condition and response to the controlled floods of 1996, 2004, and 

2008 has been based primarily on annual (or more frequent) topographic surveys of a collection of 

long-term monitoring sites (Hazel and others, 2010). These surveys consist of measurements of 

sandbar topography above the elevation associated with a discharge of 8,000 cubic feet per second 

(ft3/s). The topographic maps derived from these surveys are used to calculate sandbar area and 

sandbar volume for each site. Although these surveys are accurate and reliable, data collection 

requires a 16-day river expedition with a crew of 12 or more scientists, technicians, and boat 

operators (Hazel and others, 2010). Processing and analysis of the data requires an additional 8 to 

12 weeks of office time for one or two scientists. Although the accuracy and level of detail provided 

by the surveys was essential for documenting the effects of the initial controlled floods (Hazel and 

others, 1999; Hazel and others, 2010; Schmidt and Grams, 2011), conducting preflood and postflood

release survey expeditions for every subsequent controlled flood is prohibitively time consuming 

and expensive. As an alternative, the U.S. Geological Survey (USGS) Grand Canyon Monitoring and 

Research Center (GCMRC) in partnership with Northern Arizona University established a network 

of remotely deployed digital cameras to collect daily images of selected monitoring sites. These 

cameras are used to document the depositional (or erosional) response of controlled floods and to 

document changes to sandbars that occur following controlled floods. This report describes the 

remote camera systems, the locations where those cameras are maintained, analyses performed on 

the images to document sandbar changes, and image-based assessment of controlled floods 

conducted in 2012, 2013, 2014, and 2016.

Study Area and Monitoring Locations

The sandbar-monitoring sites discussed in this report are along the Colorado River corridor 

within Grand Canyon National Park. Locations are referenced by the GCMRC river mile (RM) system, 

which is distance in miles along the channel centerline downstream from Lees Ferry, Arizona. Lees 

Ferry (RM 0) is located 15.5 miles (mi) (21.4 kilometers, km) downstream from Glen Canyon Dam, 
3

and 1 mi (1.6 km) upstream of the mouth of the Paria River and the northeastern boundary of 

Grand Canyon National Park (fig. 1). Units of streamflow are reported in cubic feet per second.

Figure 1. Map of Colorado River corridor in Glen Canyon National Recreation Area and Grand Canyon National 

Park, Arizona, showing the locations of sandbar monitoring sites with remote cameras. RM, river mile—distance in 

miles along the channel centerline downstream from Lees Ferry. The study area within Grand Canyon National Park 

is divided into five segments based on the locations of streamflow and sediment gaging stations.

All of the monitoring sites contain sandbars that are deposited in an eddy, or zone of 

recirculating flow. Most eddies occur downstream from channel constrictions created by tributary 

debris fans (Howard and Dolan, 1981; Schmidt, 1990). Sandbars that mantle the downstream edge 

of the debris fan are termed separation bars (Schmidt, 1990), because they occur near the point of 

streamflow separation, and sandbars that occur in the central part of the eddy are termed 

reattachment bars because they form near the point where downstream flow reattaches to the river 

bank (fig. 2). Sandbars that occur in eddies upstream from debris fans are termed upper pool 

deposits. Sandbars that lack the distinctive morphology of separation or reattachment bars are 

termed “undifferentiated” sandbars (Schmidt, 1990).
4

Figure 2. Photograph of debris fan and downstream eddy showing typical alluvial sandbar formations along the 

Colorado River in Grand Canyon National Park, Arizona.

An initial set of 33 sandbar-monitoring sites was established in 1990. These sites were 

selected to achieve a spatial distribution of monitoring sites and representation among different 

sandbar types (Beus and Avery, 1993). Additional sites were added in 2002 and 2008 (Hazel and 

others, 2010) to reach the current set of 44 long-term monitoring sites. Topographic surveys of 

these sites continue to be conducted annually in September or October. Because the controlled 

floods are typically released in November, these surveys document the condition of sandbars 10 to 

11 months following the most recent controlled flood. The purpose of the remote cameras is to 

supplement the annual monitoring with more frequent (daily) observations. The current set of 43 

remote cameras were installed at most of the long-term monitoring sites between 2008 and 2012 

(table 1). Cameras were not installed at three of the long-term monitoring sites, because these sites 

do not have suitable locations for a camera and solar panel. Instead, cameras were installed at two 

sites that are not included in the set of sandbars monitored with annual topographic surveys.
5

Table 1. Sandbar monitoring sites with remote camera systems along the Colorado River in Grand Canyon 

National Park, Arizona, with periods of film records, digital-image records, and topographic surveys.

[L, left; R, right; NA, not applicable]

Site ID Site name River 

mile

River 

side

Number of 

camera 

locations

Begin film 

record

End film 

record

Begin 

digital 

record

Topographic 

surveys

0025L Cathedral Wash 2.5 L 1 Mar 1992 Feb 2010 Feb 2010 1990–present

0081L Jackass Camp 8.1 L 2 Mar 1992 Feb 2010 Feb 2012 1990–present

0089L 9-Mile 8.9 L 1 NA Oct 2012 Oct 2012 2008–present

0166L Hot Na Na Wash 16.6 L 1 Mar 1992 Nov 2004 Nov 2004 1990–present

0220R 22-Mile 22.0 R 3 Feb 1996 Oct 2004 Feb 2010 1990–present

0235L Lone Cedar 23.5 L 1 NA NA Feb 2013 2002–present

0295L Silver Grotto 29.5 L 0 NA NA NA 1990–present

0307R Sand Pile 30.7 R 6 NA NA Aug 2008 1990–present

0319R South Canyon 31.9 R 1 NA NA Feb 2012 1990–present

0333L Redwall Cavern 33.3 L 1 NA NA Oct 2013 1990–present

0351L Nautiloid 

Canyon

35.1 L 0 NA NA NA 1990–present

0414R Buck Farm 41.4 R 1 Sep 2002 Feb 2010 Feb 2010 1990–present

0434L Anasazi Bridge 43.4 L 1 Mar 1992 Apr 1994 Oct 2012 1990–present

0445L Eminence 44.5 L 1 Mar 1993 Feb 2010 July 2008 1990–present

0450L Willie Taylor 45.0 L 1 NA NA Feb 2008 2002–present

0476R Saddle 47.6 R 2 NA NA Feb 2011 1990–present

0501R Dinosaur 50.1 R 1 Jan 1996 Oct 2011 Oct 2011 1990–present

0515L 51-Mile 51.5 L 1 NA NA Feb 2008 1990–present

0559R Kwagunt Marsh 55.9 R 1 Feb 1996 Feb 2010 Feb 2010 1991–present

0566R Kwagunt Beach 56.6 R 1 NA NA Oct 2012 2002–present

0629R Crash Canyon 62.9 R 1 NA NA Feb 2013 1993–present

0651R Carbon 65.1 R 1 NA NA Oct 2012 1996–present

0658L Above LavaChuar65.8 L 1 NA NA Feb 2008 2008 only

0661L Palisades 66.1 L 4 NA NA Feb 2011 2008 only

0688R Tanner Rapid 68.7 R 1 Dec 1990 Oct 2011 Oct 2011 1990–present

0701R Lower Basalt 70.1 R 1 Feb 2008 standby April 2013 2008–present
6

Site ID Site name River 

mile

River 

side

Number of 

camera 

locations

Begin film 

record

End film 

record

Begin 

digital 

record

Topographic 

surveys

0817L Grapevine 81.7 L 1 Apr 1992 Feb 2010 Feb 2010 1990–present

0846R Clear Creek 84.6 R 1 NA NA Oct 2013 2002–present

0876L Upper Cremation 87.7 L 1 Jan 1996 Aug 2012 NA 1990–present

0917R Above Trinity 

Camp

91.7 R 1 Jan 1996 Oct 2012 Oct 2012 1990–present

0938L Granite 93.8 L 1 NA NA Feb 2012 1990–present

1044R Emerald 104.5 R 1 Jan 1996 Oct 2012 Oct 2012 1990–present

1194R Big Dune 119.4 R 1 Mar 1992 Feb 2010 Feb 2010 1990–present

1227R 122-Mile 122.8 R 1 Mar 1992 Feb 2011 Feb 2011 1990–present

1233L Upper Forster 123.3 L 3 NA NA Oct 2013 1990–present

1377L Football Field 137.7 L 1 Apr 1992 Feb 2010 Feb 2010 1990–present

1396R Fishtail 139.6 R 1 Jan 1996 Feb 2010 NA 1990–present

1459L Above Olo 145.9 L 1 Mar 1992 Feb 2010 Feb 2010 1990–present

1671L Lower National 167.1 L 1 NA NA Feb 2013 2002–present

1726L Below Mohawk 172.6 L 2 NA NA Feb 2010 1990–present

1833R Below Chevron 183.3 R 1 Mar 1992 Feb 2011 Feb 2011 1990–present

1946L Hualapai Acres 194.6 L 1 Jan 1996 Feb 2010 Feb 2010 1990–present

2023R 202-Mile 202.3 R 1 Jan 1996 Feb 2010 Feb 2010 1990–present

2133L Pumpkin Springs 213.3 L 1 Jan 1996 Oct 2013 Oct 2013 1990–present

2201R Middle 220-Mile 220.1 R 1 NA NA Oct 2013 1990–present

2255R Above Last 

Chance

225.5 R 2 Feb 2010 Feb 2010 Feb 2010 1990–present

Description of Remote-Camera Systems

Film-Camera Systems

Although the primary purpose of this report is to describe the digital-camera systems that 

are currently in use, daily images were collected periodically at many of the same sites between 

1990 and 2008 with film cameras (Cluer, 1995). These systems consisted of a film camera with 

integrated intervalometer mounted in a weatherproof enclosure (fig. 3). All film systems used a 

Pentax IQZ 105 camera and either 24 or 36 exposure diapositive (slide) film. These cameras only 

allowed use of single, fixed intervals with a maximum interval of 1 day, which was used for all 

deployments. The time of day the image was taken was determined by the time of day the camera 
7

was visited and set to trigger. At each visit, camera batteries were replaced, old film was retrieved, 

new film loaded, and the interval triggered. The number of images (and number of days of images) 

was limited to the number of exposures available. Occasionally, field visits were scheduled to 

maintain the cameras, but for most sites there are many gaps in the record of images for the 1990 to 

2008 period, which represent lapses between field visits. Table 1 lists the periods during which film 

cameras were present at each site; however, images are not available continuously for the period of 

record.

Figure 3. Photographs of remote-camera systems used along the Colorado River in Grand Canyon National Park, 

Arizona—A, vertically mounted; B, horizontally-mounted; and C, close-up view of system components.

Digital-Camera Systems

All monitoring sites currently instrumented with remote cameras use a system based on the 

automated camera system described by Bogle and others (2013). This system consists of a digital

SLR camera, programmable controller, voltage-regulation switch, and 12-volt rechargeable battery 

all in a weatherproof enclosure and an external solar panel. All systems use a camera in the Canon 

EOS Digital RebelTM series (table 2), which have the ability to be configured for: (1) direct current 

(DC) power input and (2) a wired remote shutter trigger. These cameras also have a mechanical 

power switch that can be left in the on position so that the camera can be turned on and off by 

controlling the DC power supply. All cameras are equipped with the Canon EF-S 18-55 millimeter 

auto-focusing zoom lens. A Campbell Scientific CR-200 series data logger is programmed to (1) 

supply and cut power to the camera at specified intervals and (2) trigger the camera shutter within 
8

the period the power is on. The voltage-regulation switch is used to manually turn the camera on 

for servicing. Power is supplied with a 12 amp-hour, 12-volt sealed lead-acid battery that is charged 

by a 20-watt solar panel. System wiring diagrams and specifications for the voltage-regulation 

switch are in Bogle and others (2013). The system components are installed in a 34×30×16 

centimeter (cm) enclosure in two different configurations (fig. 3). The vertically oriented 

configuration was originally designed for mounting on a pole or other constructed mounting system 

(Bogle and others, 2013). The horizontal configuration is generally better suited for mounting 

directly on bedrock or boulders (fig. 3).

Table 2. Digital-camera models used in remote camera systems along the Colorado River in Grand Canyon 

National Park, Arizona.

[All cameras are in the Canon Digital RebelTM series]

Camera model Memory card type1 Resolution (megapixels) Battery model

Rebel XTi CF (side) 10.1 NB-2LH

Rebel XS SD (side) 10.1 LP-E5

Rebel XSi SD (side) 12.2 LP-E5

Rebel T3 SD (bottom) 12.2 LP-E10

Rebel T3i SD (side) 18 LP-E8

Rebel T4i SD (side) 18 LP-E8

Rebel T5i SD (side) 18 LP-E8

1“Side” indicates memory card is accessed on side of camera; “bottom” indicates memory card is accessed on 

bottom of camera.

All remote cameras are mounted as close to the ground as possible and with a maximum use 

of natural materials to minimize visual impact. In most cases, the enclosures are simply glued to 

boulders with silicone adhesive and painted with colors to match the surrounding terrain (fig. 3B). 

To minimize the visibility of solar panels, they are mounted flush with the ground. Although this 

often results in less than optimal exposure to sunlight, even heavily shadowed solar panels provide 

sufficient charge to meet the low power requirements of the system. The cameras are set to autoexposure (landscape mode) and manual focus. Manual focus is used because the auto-focus may 

occasionally focus on foreground objects rather than the subject of interest, as well as to maintain 

consistency throughout the image series.

The earliest versions of this system were installed in February 2008. Since that time, an 

increasing number of off-the-shelf time-lapse digital-camera systems have become available. 

Although some of these systems may present a lower-cost alternative, the Bogle and others (2013) 

system still offers two main advantages. The first advantage is programming flexibility. The data 

logger can be programmed for any conceivable condition. We program most cameras to take five 

photographs each day at 2-hour intervals between 8 a.m. and 4 p.m. This provides a range of light 

and flow conditions for each day. Most time-lapse systems can only be configured for regular 

intervals, resulting in many nighttime exposures. The other advantage is the robust power system 

that can keep the system running indefinitely. Although we attempt to visit sites approximately 

every 6 months, some sites are only visited annually. The combination of the rechargeable power 
9

supply and the flexible programming, which allows collecting ample (but not too many) images,

results in a system that can operate without servicing and without filling a memory card for a year 

or longer.

Most of the 43 systems we have installed have operated without failure since initial 

installation with only periodic battery replacement. We have found that the sealed lead-acid 

batteries begin to lose ability to hold charge after 3 to 4 years. Batteries tend to fail over the winter, 

when there is less solar radiation hitting the solar panels, and when the cold temperatures make 

charging less efficient. Over a decade, 8 systems at 7 different locations have been damaged or 

destroyed by rockfall, and 4 otherwise-undamaged systems have suffered water damage. Water 

infiltration has typically resulted when the conduit used to protect the wire connecting the solar 

panel to the system creates a pathway for water to flow into the enclosure. For this reason, it is 

recommended to mount the solar panel lower in elevation than the camera enclosure.

Image Processing and Analysis

Image Processing and Web-Based Image Viewer

A series of processing steps are followed to organize and serve the images on-line following 

retrieval of memory cards from the field. The first step is to rename all images in a standardized 

naming convention so that all relevant information is contained in the filenames. The naming 

convention we use is RCLLLLS_YYYYMMDD_hhmm, where RC stands for remote camera and is fixed, 

LLLLS is the five-character location identifier explained below, YYYY is the four-digit year, MM is the 

two-digit month, DD is the two-digit day of month, hh is the two-digit hour (24-hour format), and 

mm is the two-digit minute. Zeros are padded (extra zero added to have a consistent four-digit 

format) to allow files to be sorted by filename. The location identifier is based on the GCMRC river 

mile system, which consists of a river centerline that is subdivided into 0.1 mi increments. River 

Mile (RM) zero is at Lees Ferry (fig. 1). The “L” characters specify the RM to the 0.1 mi, with padded 

zeroes in front and omitting the decimal. The “S” character specifies the side of the river, when 

looking downstream of the subject sandbar (not the camera itself). For example, RC0089L is 

installed to image the sandbar that is at RM 8.9 on the left bank. For sites where installation 

locations have changed (table 1), lowercase letters are appended to follow the side character (table 

3). All full-resolution images (.jpeg format, captured at each cameras maximum resolution) are 

renamed according to this format. Copies are also made at fixed web resolution (1,000×667 pixels), 

and thumbnail resolution (200×133 pixels). The file renaming and copying are done using batch 

processing routines that extract the image date and time from the exchangeable image file format 

(Exif) information from each original image file. The user supplies the location information.
10

Table 3. Periods of image record at sandbar monitoring sites where camera locations have changed along the 

Colorado River in Grand Canyon National Park, Arizona.

[Left bank; R, right bank; NA, not applicable; a–f, letters codes for each of 2–5 cameras at each listed site] 

Site CameraLocation Begin film record End film record Begin digital record End digital record

0081L a Mar 1992 Feb 2012 Feb 2012 active

0081L b Oct 1999 Sept 2002 NA NA

0220R a Feb 1996 Feb 2010 Oct 2004 active

0220R b NA NA Oct 2004 Feb 2010

0220R c NA NA Feb 2008 Feb 2010

0307R a Feb 2010 Feb 2010 Oct 2004 Jul 2006

0307R b NA NA Oct 2004 Jul 2006

0307R c NA NA July 2006 Aug 2008

0307R d NA NA July 2006 Aug 2008

0307R e NA NA Feb 2008 Aug 2008

0307R f NA NA Aug 2008 active

0445L1 Mar 1993 Feb 2010 July 2006 active

0445L1 0446La Nov 1994 Feb 2010 NA NA

0445L1 0446Lb NA NA July 2006 Feb 2010

0476R a Mar 1992 Feb 2011 NA NA

0476R b NA NA Feb 2011 active

0661L a Feb 2008 Feb 2011 NA NA

0661L b NA NA Oct 2004 Jan 2005

0661L c NA NA Jan 2005 Feb 2006

0661L d NA NA Feb 2011 active

1233L a Mar 1992 Feb 2008 NA NA

1233L b NA NA Feb 2008 Feb 2010

1233L c NA NA Oct 2013 active

1726L a Dec 1990 Feb 2010 NA NA

1726L b NA NA Feb 2010 active

2255R a Mar 1996 Feb 2010 Feb 2010 active

2255R b NA NA Feb 2008 Feb 2010

1The site labels for the three camera locations used at 0445L are 0445L (current site), 0446La, and 0446Lb.
11

All images from the film cameras were professionally scanned and archived on compact disk 

at the time of film processing. Because these images do not contain Exif information, the digital files 

(usually high-resolution tiff files) were manually renamed according to the naming convention 

described above. If the film camera imprinted a timestamp on an image, this time was manually 

entered into the hhmm part of the filename. If no timestamp was present, 1200 was used. Copies of 

the original high-resolution tiff files were made at the same web and thumbnail resolutions 

described above.

A subset of the web-resolution images consisting of one image per day is copied to a web 

server and these images are made publically available in a map-based viewing application 

(https://grandcanyon.usgs.gov/gisapps/sandbarphotoviewer/RemoteCameraTimeSeries.html). 

This application includes images from the film and digital records.

Qualitative Analysis of Sandbar Deposition and Erosion

One of the primary uses of the images from the remote cameras is to document the effects of 

controlled floods on the sandbar-monitoring sites as soon as possible following each release. As 

soon as it is possible to retrieve the memory cards from the field, the files are processed and saved 

online. To provide a summary of sandbar response, the images are viewed by an experienced 

technician familiar with each site. The technician selects images from before and after the 

controlled flood that have similar lighting conditions and show the site at approximately the same 

discharge (fig. 4). The technician then assigns a five-category rating to the sandbar change—large 

deposition (value of +2), moderate deposition (+1), negligible change (0), moderate erosion (−1), or 

large erosion (−2).
12

Figure 4. Graph of discharge of the Colorado River at Lees Ferry, Arizona (U.S. Geological Survey gaging station 

09380000 Colorado River at Lees Ferry, AZ), from January 2008 to January 2009, including the controlled flood 

released from Glen Canyon Dam in early March. Four topographic surveys of the sandbars along the Colorado River 

in Grand Canyon National Park were conducted during this period, on the dates shown by the grey vertical bars. 

Photographs of these sandbars from the same dates of the surveys were used to estimate changes in sandbar size.

The assessment of erosion and deposition takes into account both changes in sandbar area 

and sand volume to create an all-inclusive characterization of relative sandbar size (fig. 5). During a 

controlled flood, some sandbars gain significant area, while exhibiting little or no growth in the 

vertical direction (or even emerge with a lower bar-surface elevation). Other sandbars experience 

significant vertical deposition, while maintaining nearly the same area. Over the subsequent 

months, some of these sandbars can increase in area as the newly deposited sand is reworked by 

wind and human foot traffic. The particular changes that take place hold different levels of 

importance depending on how one considers the resource. For example, a sandbar that underwent 

2 meters (m) of deposition, while maintaining the same area, would make an excellent source of 

windblown sand to protect archeological sites, but might be separated from the river by a steeply

eroding cutbank, making use as a campsite difficult. Because of the diverse patterns of flood 

sedimentation and postflood morphological change existing from sandbar to sandbar, it is 

necessary to assign each sandbar a simple change value—size.
13

Figure 5. U.S. Geological Survey photographs of sandbars along the Colorado River in Grand Canyon National 

Park, Arizona, from before and after the 2014 controlled flood released from Glen Canyon Dam. These illustrate the 

categorical assessment of change in sandbar size made by visual assessment. A, Example of large deposition (“+2”) 

observed at river mile (RM) 119.4R; B, Example of moderate deposition (“+1”) observed at RM 30.7R; C, Example of 

negligible change (“0”) observed at RM 172.6L; D, Example of moderate erosion (“−1”) observed at RM 41.4R; and E, 

Example of large erosion (“−2”) observed at RM 65.8L.
14

Method Validation

To validate the qualitative analysis of sandbar change, sandbar photographs were assigned 

change values, then compared with topographic-survey data collected over the same period. Four 

topographic surveys of the sandbar monitoring sites were conducted in 2008. One survey was 

conducted February 1–18, a month before the controlled flood, and repeat surveys were conducted 

1, 2, and 7 months after the controlled flood (April 1–13, May 15–31, and October 15–26). For each 

of the 22 sites with operational remote cameras in 2008, photographs were extracted for each day a 

topographic survey was collected (fig. 4). Without knowledge of the changes measured in the 

surveys, size relative to the condition before the controlled flood was estimated (table 4).

Table 4. Visually estimated changes in sandbar size in remote-camera images taken along the Colorado River in 

Grand Canyon National Park, Arizona, from March 2008 (before 2008 controlled flood) to April, May, and November 

2008.

[Left bank; R, right bank; 2, large deposition; 1, moderate deposition; 0, negligible change; −1, moderate 

erosion; −2, large erosion; --, no data]

Site ID March to April 2008 March to May 2008 March to November 2008

0081L 1 0 --

0220Ra 2 2 -1

0307Ra 2 2 1

0445L 2 -- 1

0446Lb 2 2 1

0476Ra 2 1 --

0510R 1 1 −1

0559R −1 −1 −2

0688R 2 1 1

0817L 1 1 --

0876L 1 0 −1

0917R 1 1 0

1194R 2 1 0

1227R 2 1 1

1233La −1 -1 −1

1377L 1 1 0

1396R 0 -- 0

1459L 1 0 0

1726La 2 1 --

1946L 1 1 0
15

Site ID March to April 2008 March to May 2008 March to November 2008

2023R 1 0 --

2133L 1 0 0

The topographic measurements were used to calculate sandbar area and sand volume at 

each of the 22 sites. The sandbar area was calculated as the area exposed above the 8,000 ft3/s 

water surface elevation (Hazel and others, 2009) and sand volume was calculated as the volume 

above a plane defined by the same elevation. The values for the three postflood surveys were then 

normalized against the values for that site measured on the preflood survey. Normalized sandbar 

area, An,was calculated as

AAn = AAs

AApre

, (1)

where

As is sandbar area measured on the date of survey, and

Apre is sandbar area measured before the controlled flood. 

Similarly, normalized sand volume Vn was calculated as:

VVn = VVs

VVpre

, (2)

where

Vs is sand volume measured on the date of survey, and 

Vpre is sand volume measured before the controlled flood.

These normalized values were then averaged to derive a composite-normalized-sandbar 

size, Sn, with equal weight to areal and volumetric changes: 

SSn = AAn+VVn

2 . (3)

Normalized sandbar size was compared to the visual estimates made from the images. For 

comparison, the normalized metrics were divided into five classes based on change in normalized

sandbar size. Increase in normalized size greater than 10 percent was classified as “large 

deposition.” Increase in normalized size less than 10 percent and greater than 3 percent was 

classified as “moderate deposition.” Decrease in normalized size greater than 10 percent was 

classified as “large erosion.” Decrease in normalized size less than 10 percent and greater than 3 

percent was classified as “moderate erosion.” Changes in normalized size less than 3 percent were 

classified as “negligible change.” The values for normalized sandbar area, normalized sand volume, 

and normalized size for each survey at each site are listed in appendix 1.

All three metrics—sandbar area, sand volume, and normalized sandbar size—were used to 

evaluate the accuracy of the visual estimates of sandbar change. To simplify the comparison, the 

moderate and large depositional classifications (+2 and +1) were merged, as were the moderate and 

large erosional classifications (−2 and −1). This created 3 estimate classes and 3 measurement 

classes, which after comparison yielded 9 possible outcomes (table 5). Although there was general 

agreement between the visual estimates and measurements for all metrics, agreement was 

strongest for normalized-sandbar size. This metric resulted in agreement in 41 out of 54 

comparisons. In the 13 cases of disagreement, most occurred when the visual estimate was 
16

negligible change and the survey measurements indicated significant change. In only one case were 

the estimated and measured changes in direct opposition.

Table 5. Comparison between visual estimates of sandbar change in remote-camera images and measured 

sandbar change at monitoring sites along the Colorado River in Grand Canyon National Park, Arizona.

[NC, negligible change]

Categorized sandbar change Visual estimate compared 

with sandbar area

Visual estimate compared 

with sand volume

Visual estimate compared 

with normalized sandbar 

size

Visual 

estimate

Topographic 

survey

Number Percentage Number Percentage Number Percentage

Agreement

Deposition Deposition 16 30 32 59 31 57

NC NC 4 7 0 0 2 4

Erosion Erosion 9 17 4 7 8 15

Disagreement

Deposition NC 10 19 0 0 2 4

Deposition Erosion 8 15 2 4 1 2

NC Deposition 0 0 8 15 4 7

NC Erosion 7 13 3 6 5 9

Erosion Deposition 0 0 1 2 0 0

Erosion NC 0 0 4 7 1 2

Although the technician was not evaluating the photographs specifically for areal change, it 

is noteworthy that the manual estimates correlated most poorly with the area measurements—only 

54 percent were in agreement. This can be attributed to the viewing angle—the photographs are 

oblique rather than overhead and the vast majority of them are at an angle closer to the water 

surface than to zenith. For more accurate areal estimates, cameras would ideally be positioned as 

high as possible above each sandbar, but this goal has to be balanced with the need for safe and 

efficient access for field technicians. Areal measurements also likely correlated poorly because of 

the inability to perfectly match water levels. The cameras cannot be controlled to take photographs 

when the stage is exactly 8,000 ft3/s, and small changes in stage can mean large changes in subaerial 

sandbar area, especially at sites that are broad and flat.

Based on these comparisons, the visual estimates of deposition shown in camera images are 

more reliable than the visual estimates of sandbar erosion shown in camera images (table 6). 

Deposition was correctly identified in 89 percent of the cases and was never mistaken for erosion. 

Erosion was correctly recognized in 57 percent of the cases. This tendency toward better visual 

recognition of deposition can be attributed to the oblique camera angle (as discussed above), to the 

bulbous shape newly deposited sandbars exhibit after floodwaters recede, and the varied ways 
17

sandbars can change as they are subjected to subaerial sediment transport processes and human 

foot traffic.

Table 6. Matrix of agreement and disagreement between measured change in normalized sandbar size and 

visually estimated change in sandbar size in remote camera images at monitoring sites along the Colorado River in 

Grand Canyon National Park, Arizona.

Measured change Percent estimated

Deposition No change Erosion

Deposition 89 11 0

No change 40 40 20

Erosion 7 36 57

This qualitative method of change detection has proven to be a reasonably effective way to 

assess the effects of controlled-flood events on sandbars along the Colorado River. The manual 

estimates agreed with survey measurements 76 percent of the time (89 percent for sandbars that 

aggraded) and wholly disagreed 2 percent of the time (table 5). Compared to traditional groundsurvey methods, the low cost, high temporal resolution, and quick data-processing time of visually 

estimating geomorphic change using remote-camera images make it a useful way to assess such 

changes.

Results of Visual Estimates of Sandbar Change

Visual estimates of sandbar change were made for each of the controlled-flood releases from 

Glen Canyon Dam in November of 2012, 2013, 2014, and 2016. Although the categories of moderate 

and large change were used in the assessment (appendix 2), these categories were lumped together 

for reporting, consistent with the method validation. Immediately following each controlled flood, 

deposition was observed at 50 percent or more of the monitoring sites (fig. 6), consistent with 

results from previous controlled floods (Hazel and others, 2010; Schmidt and Grams, 2011). Each 

controlled flood resulted in erosion at about 10 percent of the monitoring sites. The estimates of 

sandbar size made from images from February through October indicate that rates of erosion are 

highest in the first 3 months following each controlled flood. In two of the years (2013 and 2014), 

10 to 20 percent of the sites were still larger 11 months after the controlled flood of the previous 

year. Post-controlled-flood erosion rates were highest in 2015 (following the November 2014 

controlled flood), which was also the year of highest annual release volume from Glen Canyon Dam.
18
19

Figure 6. Graphs of visual estimates of change in sandbar size in remote-camera images from monitoring sites 

along the Colorado River in Grand Canyon National Park, Arizona, following controlled floods released from Glen 

Canyon Dam, plotted with the hourly discharge of the Colorado River at Lees Ferry. A, 2012 controlled flood; B, 2013

controlled flood; C, 2014 controlled flood; and D, 2016 controlled flood.

Quantitative Analysis of Sandbar Area

Although the qualitative analysis described above provides a useful and necessary 

characterization of sandbar response to the controlled floods, it is less useful for measuring rates of 

sandbar erosion and comparison of sandbar size among different events and different years. Here, 

we outline the methods that are currently in development to extract measures of sandbar area from 

the images.

There are three major aspects to creating a time series of sandbar area from a time series of 

oblique photographs at a site. First, the oblique image must be rectified, which is the process of 

creating a planform-perspective image in a projected-coordinate system. Second, the sandbar pixels

must be segmented from the image, which is the process of identifying all sandbar pixels and 

delineating the sandbar as a foreground object from the rest of the background image. Third, 

relations must be established between the above-water area of a visible portion of the sandbar at a 

given time (for example, an arbitrary flow stage), and at a reference flow stage (such as that 

associated with a discharge of 8,000 ft3/s), for comparative purposes. The third aspect of 

establishing relations between survey- and image-derived sandbar areal estimates involves 

extrapolating the visible area of sand in an image (for example, above the instantaneous waterline) 

to an area that would correspond to a common reference stage (the stage associated with 8,000 

ft3/s is commonly used).

Image Registration and Rectification

When cameras are moved during routine maintenance, or for any other reason, they no 

longer take pictures of exactly the same scene. Therefore, all images must be remapped into a

common image reference system in a process called image registration. If images were not 

registered, a separate rectification would have to be developed for each set of images between 

significant camera movements. Registration is the procedure of realigning a given sample image so 
20

that it has the same image-coordinate-reference frame as a single reference image. The purpose is 

to place all images for a given site in a common image-reference frame. Our approach is to find the 

translation of the sample image in two dimensions (x and y) relative to a reference image, using 

frequency domain methods. First, we calculate the cross-correlation function between the master 

and given sample image, by means of the two-dimensional fast Fourier transform (2D-FFT) and 

locating its peak (fig. 7). An example Python program for this computation is given in appendix 3. 

The peak in two dimensions represents the shift in x and y locations, which are accordingly applied 

to the sample image to register it (fig. 7). It is therefore a “translation only,” frequency-domain 

image transformation. It is reasonably fast (an image takes only as long as a few seconds to process, 

on a single >2 gigahertz computer processor) and responds well to lighting variations. We tested 

another approach in the spatial domain, which involved finding translations based on the pixel 

locations of common-scale invariant features seen in both master and sample images, implementing 

the scale invariant feature transform (SIFT; Lowe, 2004) algorithm for detecting identical features 

in pairs of images, using random sample consensus (RANSAC; Fischler and Bowles, 1981) to filter 

spurious features, according to the algorithm detailed in Solem (2012). However, the 2D-FFT

approach was deemed superior, both in accuracy and speed.

Figure 7. Example of the image-registration workflow used for sandbar monitoring along the Colorado River in 

Grand Canyon National Park, Arizona. A, a reference photograph against which all other images from remote 

cameras at a site are compared; B, a given sample (unregistered) image; C, the two-dimensional cross-correlation 

between reference and sample image, identifying the peak, the location of which represents the shift in two horizontal 

directions; D, the registered sample image; and E, three images showing a small subsection of the image from, top, 

the reference; middle, the unregistered sample; and bottom, the registered sample images.
21

When a set of images from a particular camera system have been registered, these images 

are then rectified. This step involves computation of a transformation matrix from the pixel 

coordinates in the oblique image to real-world coordinates to create a planform image in a 

projected-coordinate system (fig. 8). The resulting transformed image is referred to as the rectified 

image. The approach we have adopted is to find the homography between two sets of points—(1) 

ground-control points (GCPs) in an image reference system (their pixel coordinates) and (2) their 

corresponding real world coordinates. Note that only two-dimensional points [x,y] are considered. 

The same transformation matrix will apply to all images from a camera deployment observing a 

particular site. 

Figure 8. Example of the image rectification workflow used for sandbar monitoring along the Colorado River in 

Grand Canyon National Park, Arizona. A, a registered oblique photograph from a remote camera; B, the rectified 

image; C, the rectified georeferenced image overlaying a 2013 aerial image; and D, the surveyed extent of the 

sandbar at that location and time (shown in red), overlaying the rectified georeferenced image.

First, we find the perspective transformation matrix, which is a 3×3 matrix, h, which 

describes the mapping or image coordinates [x',y'] to real world coordinates [x,y] in a projected 

coordinate system using the following equation, where w is a scalar:

�

wwww

wwww

ww

� = �

hh1111 hh1111 hh1111

hh hh hh

hh hh hh

��

′

′

11

� . (4)

Matrix h is found by establishing the correspondences between at least n=4 real-world 

coordinate pairs [x,y] and their equivalent image coordinates [x',y']. From equation (4) we can write 

the following homogenous linear system, Ah=0 such that:
22

⎣

⎢

⎢

⎢

⎡ 11 11 11 00 00 00 − 11

′ 11 − 11′ 11 − 11′

00 00 00 11 11 11 − 11

′ 11 − 11′ 11 − 11′

⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮

nn nn 11 00 00 00 − nn

′ nn − nn′ nn − nn′

00 00 00 nn nn 11 − nn

′ nn − nn′ nn − nn′ ⎦

⎥

⎥

⎥

⎤

⎣

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎡

hh1111

hh1111

hh1111

hh

hh

hh

hh

hh

hh ⎦

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎤

=

⎣

⎢

⎢

⎢

⎡

00

00

⋮

00

00⎦

⎥

⎥

⎥

⎤

. (5)

This is an optimization problem with a least-squares solution given by:

mmmmmm‖AA − 00‖ , (6)

which is solved as the eigenvector of ATA with the smallest eigenvalue, where T denotes matrix 

transpose. The problem may be formally stated, where ee

→

λλ

and λλ are eigenvectors and eigenvalues, 

respectively, of matrix ATA

min

λλ

AATTAAee

→λλ = λλ ee→λλ

which, using the identity I we may rewrite as a null-space problem:

AATTAAee

→λλ = II ee→λλ ⇒ (AATTAA − λλ ) ee→λλ =0

→

This has a solution if |AATTAA − λλ | = 0. The eigenvalues are found as the roots of the characteristic 

polynomial pp(λλ) = |AATTAA − λλ | and the eigenvectors associated with each eigenvalue λλii are the 

vectors in the null space of the matrix (AATTAA − λλiiII).

Once the transformation matrix has been obtained, an oblique image is rectified using the 

OpenCV library (http://opencv.org/) function warpPerspective (OpenCV, 2014).

To establish correspondences between real-world and image coordinates, GPC panels (30 

square centimeters, cm2) are placed in the image field-of-view (fig. 9) and surveyed with a total 

station. The image coordinates of these GCPs are related to their real-world coordinates using the 

transformation matrix described above. Additional GCPs are obtained from backshore and bank 

areas by identifying large immobile features, such as rocks, in oblique imagery and either surveying 

these features in the field or extracting their coordinates from georeferenced aerial imagery (fig. 9).

GCPs should not be positioned in a straight line in either real-world or image coordinates, and they 

should ideally be spread across the entire image. Although theoretically only four GCPs are 

required, our experience is that a minimum of six GCPs on and around the sandbar are required to 

establish an accurate homography.
23

Figure 9. Example oblique photograph taken by a remote camera used for sandbar monitoring along the 

Colorado River in Grand Canyon National Park, Arizona. Locations of checkerboard panels (within black circles and 

inset) used to build a homography between real-world and image coordinates are shown. Survey tripods and other 

objects with a known horizontal (easting, northing) location, such as the tripod on the far left of the scene (red circle), 

may also be used to constrain or check a solution.

Delineation of Sandbar Area

Below we describe the process of segmenting the sandbar from the background in an 

oblique (unrectified) image. When the coordinates associated with the boundary of the sandbar 

have been extracted, these coordinates are transformed into a projected coordinate system using 

the same transformation matrix that is used to rectify the image. Delineating the sandbar from the 

rectified image would also be possible, but because the oblique image contains more sand pixels 

than the rectified version, the sandbar outline is better resolved using the oblique image. In 

addition, keeping sandbar boundary coordinates in an image reference frame means that the 

segmentation need only be carried out once, even if the transformation matrix is changed (for 

example, if new GCPs become available and the homography is recomputed).

In our diverse set of imagery, there is no typical sandbar size, shape, color/shade, or relative 

position within images. Between sites, there is enormous variety in the extent of nonsandbar 

features such as scree, vegetation, rock-face texture, water-surface texture, reflection, boats, people, 

and sky. Because of changing weather, position of the sun in the sky, and therefore the extent and 

intensity of shadows from canyon walls, there can be a large variety in image intensities at a given 

pixel location at a particular site (fig. 10). Even on a particular sandbar, color and texture of the 

sand might vary in time because of subtle changes in light or degree of groundwater saturation. 
24

These factors make a single approach to automatically detecting and segmenting sandbars, with 

sufficient accuracy, an extremely challenging computer vision task.

Figure 10. Time series of oblique imagery from a sandbar monitoring site (RC0307R) along the Colorado River in 

Grand Canyon National Park, Arizona, taken during the November 2012 controlled flood release from Glen Canyon 

Dam. Time increases from left to right and from top to bottom.

Any algorithm used to identify sand pixels might be (in order of preference) fully automated 

(unsupervised), semiautomated (supervised), or manual. We have developed a supervised 

approach, based on considering the trade-off between accuracy and speed (a fully manual approach 

is highly accurate but too slow and an unsupervised approach is fast but not sufficiently consistent 

in its accuracy). An interactive graphical program, Remote Camera Sandbar Segmentation

(RCSandSeg), has been developed in the Python programming language that allows the user to 

select a set of images, filter them by date/time and stage, interactively segment the sandbar from 

the image, and store the coordinates of the bar outline. This program is available as a GitHub 

repository at https://github.com/dbuscombe-usgs/RCSandSeg (Buscombe, 2017). The sandbar 
25

outline is extracted using image processing techniques that are relatively invariant to large changes 

in light and shadow, water, color, and the spectrum of image textures associated with different 

surface types. These image-processing procedures are detailed below. An operator supervises the 

process and carries out on-the-fly quality control. Each image takes 10–60 seconds to process by an 

experienced operator.

This partially automated workflow results in accurate sandbar outlines and areas. However, 

given the large and ever-growing database of images (at present consisting of >488,000 images), a 

fully automated workflow will eventually be necessary. Because of the extreme difficulties 

associated with identifying sand pixels based on color and texture metrics alone, further work is 

required to develop a completely automated (unsupervised) sandbar segmentation that is as 

reliable as the partially supervised method detailed above. Several approaches are currently being 

investigated.

The RCSandSeg Program

RCSandSeg (Buscombe, 2017) is a Python program with a graphical user interface (GUI) that 

enables a user to interactively segment a sandbar from an image (a registered image still in an 

image reference frame, unrectified) or series of images. The user selects a set of images, and 

interactively segments them, one by one. The results from each image are saved in a binary Python 

format (a so-called pickled object), one file per image. There are three tabs in the program, each 

with slightly different functionality (fig. 11). The first (gold) tab allows the user to select multiple 

arbitrary files, make a movie of them (which greatly facilitates the visual detection of sandbar 

changes over time), and (or) process them. The act of processing in this case refers to the 

interactive segmentation that is explained below. The second (green) tab allows the user to find 

images from the database, based on site or camera deployment, date range, time of day (including 

the ideal time for a given site, predetermined based on average lighting conditions at a particular 

site), and discharge level (fig. 12). The discharge at a particular site is then estimated using 

empirical relations developed for each site based on the average lag time between the discharge at 

the nearest upstream gage. These relations were constructed by running the Wiele and Griffin 

(1998) unsteady flow model over the full range of flows for each of the five Colorado River gages 

upstream from the study sites. The predicted hydrograph at the cross section closest to each site 

was then cross correlated with the hydrograph of the nearest upstream gage (fig. 13). The program 

will find images within a user-specified tolerance of the desired discharge level at the nearest gage

(the default is ±100 ft3/s). Again, once the images are found based on the user’s criteria, the user 

can process and make a movie of these images (the movie this time will include a plot of the 

discharge curve for the selected date range). The third (purple) tab allows the user to find images 

from the database, based on site/deployment, date range, and time of day (including the ideal time 

for a given site). In other words, it does the same as the green tab, except the specification of 

discharge.
26

Figure 11. Screenshots from the RCSandSeg program (Buscombe, 2017) used to process remote-camera images 

for sandbar monitoring along the Colorado River in Grand Canyon National Park, Arizona. A, The user launches the 

program and selects a working directory, subdirectories contain images per camera site; B, the gold tab of the 

program allows the user to select and process arbitrary collections of images; C, the green tab of the program allows 

the user to select and process imagery based on site, date range, discharge level, and time of day; and D, the purple 

tab of the program allows the user to select and process imagery based on site, date range, and time of day.
27

Figure 12. Screenshots from the green tab of the RCSandSeg program (Buscombe, 2017) used to process 

remote-camera images for sandbar monitoring along the Colorado River in Grand Canyon National Park, Arizona. A,

View of the terminal window that prints activity to screen; B, the graphical user interface (GUI) window; C, the 

instructions window; and D, a window showing a list of files that correspond with the filtering criteria set in the GUI 

window.

Figure 13. Graph of time lag, in hours, between discharge at each remote-camera site (marker) and the nearest 

upstream gaging station (dashed lines, U.S. Geological Survey gaging stations identifiers shown at top) along the 

Colorado River in Grand Canyon National Park, Arizona. The lines and equations are least-squares linear models.

River miles are distance in miles along the channel centerline downstream from Lees Ferry.
28

The program is used in the following way. A window appears containing the image. The user 

draws a box around the sandbar by dragging the mouse over the image, then presses the “n” key on 

the keyboard. The program makes an initial estimate of the sandbar location within the box and 

displays this within a second window (fig. 14). When the user presses “n” again, the program 

updates its estimate. After a few presses of the “n” key, the estimate of the sandbar location no 

longer changes. At that point, the user can accept the sandbar segmentation by visually comparing 

the segmentation with the input image and making a subjective decision about whether or not it is 

of acceptable accuracy. Sometimes, no additional input is necessary (fig. 14A). Then, the program 

saves the result (the coordinates, in the image reference frame, of the sandbar boundary) and 

moves on to the next image. If the segmentation is unsatisfactory, the user gives the program new 

information that allows it to improve its estimate. This is done by specifying what is foreground 

(sandbar) or background in the image, by drawing on the image with the mouse. Foreground 

marking is carried out by pressing the “1” key and then drawing on the image where there is 

sandbar the program has missed. Background marking is carried out by pressing the “0” key, then 

drawing on the image where there is no sandbar. The program refines its estimate of the sandbar 

location based on this new information (fig. 14B).
29

Figure 14. Example interactive segmentation in the RCSandSeg program (Buscombe, 2017) used to process 

remote-camera images for sandbar monitoring along the Colorado River in Grand Canyon National Park, Arizona. A,

The user draws a blue bounding box around an image (left), and the resulting segmentation (right) is perfect; B, the 

user draws a bounding box around the bar in this image with strong shadows, and annotates foreground (white) and 

background (black) with the mouse (left). The resulting segmentation is on the right.

The program is built on the GrabCut algorithm (Rother and others, 2004) which is a 

powerful and widely used interactive image segmentation approach (Szeliski, 2010). Starting with a 

user-specified bounding box around the sandbar to be segmented, the algorithm estimates the color 

distribution of the pixels within the bounding box, and also that of the background (outside the 

bounding box), using a Gaussian mixture model (Bishop, 2006). A graph is built, in which each node 

represents a unique pixel in the image. Two additional nodes are created, the “source” and “sink”

nodes, representing the foreground and background, respectively, and which are initially connected 

to every other node. The image is segmented by connecting each node to either the source or sink 

node. Any information provided by the user (the foreground/background annotations) are set as 

hard constraints (individual nodes are assigned a label which cannot change). All other nodes are 

assigned a probability of being in the foreground or background. An energy cost function is 

incorporated into the graph as weights between pairs of pixel nodes and between pixel nodes and 
30

source or sink nodes. Similarly colored neighboring pixels are encouraged to have the same label by 

assigning relatively large weights between their nodes. Strong gradients in color between pairs of 

pixels are given relatively small weights. A min-cut/max-flow algorithm (Boykov and others, 2001) 

is used to cut the graph. The algorithm determines the minimum cost cut that will separate the 

source and sink nodes. The cost of a cut is the sum of the weights of the links between nodes that 

are cut. To segment the image, all nodes connected to the source become foreground and all nodes 

connected to the sink become background. Segmentations are further refined by the user by 

pointing out misclassified regions and rerunning the energy function (assigning values to weights) 

and recutting the graph.

Sandbar Area at RC0307 Between October 2009 and October 2015

Site RC0307 (camera location f), which is located 30.7 miles downstream of Lees Ferry, AZ, 

in Lower Marble Canyon, was chosen to demonstrate the process of estimating time series of 

sandbar area from a sequence of oblique photographs. Registered images taken between October 

2009 and October 2015 when the river discharge was 10,000±50 ft3/s were selected. Out of this 

subsample of registered imagery, those images taken closest in time to a total station survey were 

processed using RCSandSeg to extract sandbar outline. The images and sandbar outline were 

subsequently rectified (fig. 15) and sandbar areas estimated using the Shoelace formula (Braden, 

1986), the implementation of which is shown in appendix 4. The comparison between estimated 

sandbar areas and equivalent survey areas (above the stage associated with 10,000 ft3/s) was 

satisfactory (fig. 16), with a coefficient of determination, R2, of 0.907, and a root-mean-square error 

(RMSE) of 212.83 square meters (m2), which is equivalent to an average error of 8 percent. The 

main sources of error are (1) actual differences in sandbar area due to physical processes occurring 

between image time and survey time (2009: 19 days; 2011: 67 days; 2012: 59 days; 2013:5 days;

2014: 1 day; and 2015: 4 days); (2) error in the digitized outline of the sandbar output from the 

RCSandSeg program; (3) discrepancy in sandbar area associated with imprecision in flow stage; (4) 

error in the registration process; (5) error in the rectification process; and (6) error in the totalstation survey-derived sandbar area. All of these sources of error are planned to be investigated, 

quantified and, where possible, minimized, in subsequent studies. Having established a reasonable 

relation between observed and image-derived sandbar area above the 10,000 ft3/s stage, the 

remaining images were processed using RCSandSeg and sandbar areas estimated. Figure 17 shows

the results from that analysis, within the context of the survey-derived sandbar area time series that 

extends back to 1990 (Hazel and others, 2010). It is apparent that very significant changes to 

sandbar area occur on a subannual timescale, as previously reported by Cluer (1995). Indeed, close 

inspection of the time series reveals times where highly episodic large-magnitude erosion of 

sandbars occurs over just a few days or weeks. Some of these events are shown graphically in figure

18.
31
32
33

Figure 15. Time series of oblique remote-camera imagery (A–F, left), with identified sandbar outlines (red lines),

used for sandbar monitoring along the Colorado River in Grand Canyon National Park, Arizona, and their 

corresponding rectified image overlaying aerial imagery from May 2013 (right). This time series is associated closest 

in time to total-station surveys, is near the river stage associated with a flow rate of 10,000 cubic feet per second, and 

the derived sandbar areas are used to construct figure 16. Date format is two-digit month and day followed by year 

(MM/DD/YEAR).
34

Figure 16. Graph of the relation between survey-derived and image-derived sandbar area above the river stage 

associated with a flow rate of 10,000 cubic feet per second along the Colorado River in Grand Canyon National Park, 

Arizona. The year of the annual total-station survey is also shown for reference.
35

Figure 17. Graphs showing (A) time series since 1990 of total-station survey-derived (black circles) and imagederived (red dots) sandbar areas above the river stage associated with a flow rate of 10,000 cubic feet per second

along the Colorado River in Grand Canyon National Park, Arizona, and (B) a close-up of the period 2009–2015 

(inclusive).
36

Figure 18. Images showing comparisons between rectified sandbars (overlaying 2013 aerial imagery) used for 

sandbar monitoring along the Colorado River in Grand Canyon National Park, before and after an erosional event or 

period, showing the magnitudes and time-scales of episodic high-magnitude sandbar erosion. Date format is two-digit 

month and day followed by year (MM/DD/YEAR).
37

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40

Appendix 1. Normalized Changes in Sandbar Area, Volume, and Composite 

Sandbar Size on the Colorado River in Grand Canyon National Park, Arizona, 

Determined from Repeat Topographic Surveys

[L, left bank; R, right bank; --, no data; Site ID is appended with camera location code (a.b) for sites that have had 

cameras at multiple locations]

Site

ID

Normalized area change Normalized volume change Normalized size change

March to 

April 2008

March to 

May 2008

March to 

Nov. 2008

March to 

April 2008

March to 

May 2008

March to 

Nov. 2008

March to 

April 2008

March to 

May 2008

March to 

Nov. 2008

0081L 0.1 -- 0.02 0.23 -- 0.11 0.16 -- 0.06

0220Ra −0.05 −0.06 −0.22 0.15 0.08 0 0.05 0.01 −0.11

0307Ra 0.38 0.52 0.2 0.89 0.8 0.35 0.63 0.66 0.28

0445L 0.03 -- −0.01 0.17 -- 0.05 0.1 -- 0.02

0446Lb 0.12 -- 0.2 0.41 -- 0.36 0.26 -- 0.28

0476Ra 0.68 0.46 −0.37 0.8 0.56 0.28 0.74 0.51 0.32

0501R −0.03 −0.02 −0.04 0.1 0.07 0.08 0.03 0.03 0.02

0559R −0.23 −0.22 −0.16 0 0 0 −0.11 −0.11 −0.08

0688R 0.29 0 −0.02 0.37 0.16 0.13 0.33 0.08 0.05

0817L 0.03 0.02 0.02 0.22 0.17 0.13 0.12 0.01 0.07

0876L −0.16 -- −0.13 −0.07 -- −0.05 0.12 -- −0.09

0917R −0.23 -- −0.3 −0.09 -- −0.12 −0.16 -- −0.21

1194R 0.04 −0.05 −0.17 0.44 0.28 0.11 0.24 0.12 −0.03

1227R −0.02 0.16 0.07 0.26 0.28 0.22 0.12 0.22 0.15

1233La −0.31 −0.32 −0.15 −0.06 −0.1 −0.03 −0.19 −0.21 −0.09

1377L −0.14 -- −0.02 0.19 -- 0.08 0.03 -- 0.03

1396R −0.32 -- −0.17 −0.14 -- −0.04 −0.23 -- −0.1

1459L 0.02 0.01 −0.01 0.22 0.17 0.07 0.12 0.09 0.03

1726La 0.01 0.07 0.02 0.29 0.27 0.22 0.15 0.17 −0.12

1946L 0.01 0 0.02 0.11 0.1 0.09 0.06 0.05 0.05

2023R −0.11 −0.16 −0.17 0.17 0.04 −0.03 0.03 −0.06 −0.1

2133L 0.11 −0.14 −0.11 0.37 0.18 0.08 0.24 0.02 −0.01
41

Appendix 2. Estimated Changes in sandbar size on the Colorado River in Grand 

Canyon National Park, Arizona, from Remote-Camera Images for the 2012, 2013, 

2014, and 2016 Controlled Floods Released from Glen Canyon Dam

[L, left bank; R, right bank; --, no data]

Site ID

November 2012 controlled flood

Preflood to 

late Nov. 2012

Preflood to 

Feb. 2013

Preflood to 

May 2013

Preflood to 

Nov. 2013

0025L 1 0 0 0

0081L 1 0 0 0

0089L 1 0 0 0

0166L 0 0 0 0

0220R 2 0 0 1

0307R 1 1 1 1

0319R 1 1 0 0

0414R 0 1 1 1

0434L 0 0 0 0

0445L 0 0 0 0

0450L 2 1 1 1

0476R 0 −1 −1 −1

0501R 0 0 0 0

0515L −1 0 0 0

0559R 0 0 0 0

0651R 2 1 1 −1

0658L 0 0 0 1

0661L 1 0 1 1

0688R 1 1 1 0

0817L 1 0 0 0

0876L 0 −1 −1 0

0917R −1 −1 −1 0

0938L 1 1 1 0

1044R 1 1 0 0
42

Site ID

November 2012 controlled flood

Preflood to 

late Nov. 2012

Preflood to 

Feb. 2013

Preflood to 

May 2013

Preflood to 

Nov. 2013

1194R 2 1 1 0

1227R 0 0 0 0

1377L 0 −1 −1 0

1459L 1 1 1 0

1726L −1 −1 −1 −1

1833R 1 −1 −1 −1

1946L 0 −1 −1 0

2023R 1 1 1 0

2255R 0 0 0 0
43

Site ID

November 2014 controlled flood

Preflood to 

late Nov. 2014

Preflood to 

Feb. 2015

Preflood to 

May 2015

Preflood to 

Nov. 2015

0025L 2 1 1 1

0081L 1 −1 0 0

0089L 2 0 0 −1

0166L 0 0 −1 −1

0220R 1 0 1 −1

0235L 1 0 0 0

0307R 0 −1 0 −1

0319R 2 1 0 0

0333L 0 0 0 −1

0414R −1 −1 −1 0

0434L 0 0 0 0

0445L 0 0 0 −1

0450L 0 −1 −1 −1

0476R 1 1 1 1

0501R 1 0 0 0

0515L 2 1 1 1

0559R 0 0 0 0

0566R 1 0 0 0

0629R 0 0 0 0

0651R 2 1 1 0

0658L −1 −1 −1 0

0661L 1 1 1 −1

0688R 2 0 0 −1

0817L 1 0 0 0

0845R 0 0 0 0

0876L 0 0 0 −1

0917R −2 −2 −2 −2

0938L 0 −1 0 0

1044R 0 −1 −1 0
44

Site ID

November 2014 controlled flood

Preflood to 

late Nov. 2014

Preflood to 

Feb. 2015

Preflood to 

May 2015

Preflood to 

Nov. 2015

1194R 2 1 1 0

1227R 1 1 1 0

1232L −1 −2 −2 −1

1377L −1 −1 0 −1

1459L 1 0 0 0

1671L 1 1 1 −1

1726L 1 1 1 0

1833R 1 −1 −1 −1

1946L 1 0 −1 −1

2023R 2 1 1 0

2132L 0 0 0 0

2201L 0 0 0 0

2255R 0 0 0 0
45

Site ID

November 2014 controlled flood

Preflood to 

late Nov. 2014

Preflood to 

Feb. 2015

Preflood to 

May 2015

Preflood to 

Aug. 2015

Preflood to 

Sept. 2015

0025L 1 0 −1 0 0

0081L 1 1 1 0 0

0089L 0 0 0 −1 −1

0166L 1 1 1 0 0

0220R 0 0 0 0 0

0235L 2 1 1 1 0

0307R 1 1 0 0 −1

0319R 1 0 0 0 0

0333L −1 −1 −1 −1 −1

0414R −1 −1 −1 −1 −1

0434L 0 0 0 0 0

0445L 0 0 −1 −1 −1

0450L 1 0 −1 0 0

0476R 2 -- -- -- 0

0501R 0 −1 −1 −1 1

0515L −1 −1 −2 −2 −2

0559R 1 1 1 1 0

0566R 2 1 0 0 0

0629R 1 1 1 1 0

0651R 1 -- -- -- 0

0658L −2 −2 −2 −2 −2

0661L 2 1 1 0 0

0688R 1 0 0 0 0

0817L 1 0 0 0 0

0845R 1 0 −1 0 −1

0876L 0 0 0 0 --

0917R 0 −1 −1 −1 −1

0938L 0 0 0 0 0

1044R 1 0 0 0 0
46

Site ID

November 2014 controlled flood

Preflood to 

late Nov. 2014

Preflood to 

Feb. 2015

Preflood to 

May 2015

Preflood to 

Aug. 2015

Preflood to 

Sept. 2015

1194R 2 1 1 0 0

1227R 2 1 0 0 −1

1232L 0 0 −1 0 0

1377L −1 −1 0 −1 −1

1459L 1 −1 −1 −1 −1

1671L 1 1 0 0 0

1726L 0 0 0 1 0

1833R 1 0 −1 −1 −1

1946L 0 0 0 0 0

2023R 1 0 −1 −1 −1

2132L 1 1 −1 −1 −1

2201L 0 0 0 0 0

2255R 0 0 0 −1 −1
47

Site ID

November 2016 controlled flood

Preflood to 

late Nov. 2016

Preflood to 

Feb. 2017

Preflood to 

April 2017

0025L 1 −1 −1

0081 1 0 0

0089L 1 0 0

0166L 0 0 0

0220R 0 0 0

0235L 1 0 0

0307R 2 0 1

0319 2 0 0

0333L 0 0 0

0414R −2 −2 −2

0434L 0 0 0

0445L 0 0 0

0450L 2 0 0

0476R 1 1 1

0501R 0 0 0

0515L −1 0 0

0559R 1 1 1

0566R 1 0 0

0629R 0 -- 0

0651R 2 0 0

0658L −2 −2 −1

0661L 1 0 0

0688R 1 0 0

0701R 2 1 1

0817L 1 0 0

0845 1 0 0

0876L 0 0 0

1917R 0 0 0
48

Site ID

November 2016 controlled flood

Preflood to 

late Nov. 2016

Preflood to 

Feb. 2017

Preflood to 

April 2017

0938L 1 0 0

1044R 0 -- --

1194R 2 1 1

1227R 0 0 0

1232L 1 1 1

1377L −1 0 0

1459L 1 0 0

1671L 1 1 0

1726L 0 0 0

1833R 1 0 0

1946L −1 −1 −1

2023R 0 0 0

2132L 1 0 0

2201L 0 0 0

2255R 1 0 0
49

Appendix 3. Example Python Computer Program for Finding the [x,y] 

Translation Vector Between Two Remote-Camera Images Used for 

Monitoring Sandbars on the Colorado River in Grand Canyon National 

Park, Arizona, Using Two-dimensional Fast Fourier Transform (2D-FFT)

Inputs: 

im0 = master (or reference) image (8-bit numpy array) 

im1 = sample image (8-bit numpy array) 

(im0 and im1 must be the same size) 

Outputs: 

t0 = translation of im1 relative to im0 in x (horizontal) coordinate 

t1 = translation of im1 relative to im0 in y (vertical) coordinate 

# import required libraries 

import math 

import numpy as np 

# find shape of master image 

shape = im0.shape 

# compute 2D FFT of master image 

f0 = np.fft.fft2(im0) 

# compute 2D FFT of sample image 

f1 = np.fft.fft2(im1) 

# compute 2D cross-correlation function 

ir = abs(np.fft.ifft2((f0 * f1.conjugate()) / (abs(f0) * abs(f1)))) 

# find the [x,y] location of the peak 

t0, t1 = np.unravel_index(np.argmax(ir), shape) 

if t0 > shape[0] //2: 

 t0 -= shape[0] 

if t1 > shape[1]//2: 

 t1 -= shape[1]
50

Appendix 4. Example Python Computer Program for Finding the Area of a 

Polygon in Projected [x,y] Coordinates

Inputs: 

x = polygon coordinates in x direction (Easting, m) 

y = polygon coordinates in y direction (Northing, m) 

Outputs: 

a = area in m2 

# import required libraries 

import numpy as np 

# compute area 

A = 0.5*np.abs(np.dot(x, np.roll(y,1))-np.dot(y, np.roll(x,1)))