Mapping Urban Arboreal Topology using Photogrammetric and Geospatial Techniques

Author

Greg Ruszovan
gregruszovan@yahoo.com

American River College
Geography 350 - Data Acquisition in GIS
Spring 2006

Abstract

Measuring the height and volume of trees in an urban setting poses some interesting challenges. Conventional manual methodologies for determining the height of a tree include the use of an inclinometer, a measurement of the distance of the observer from the base of the tree (often done by simply pacing out a distance from the trunk, and an understanding of basic geometry. In an urban setting, intervening buildings and fences make it difficult to determine the distance from the base of the tree. Pacing off each tree in an area would be time consuming in itself.

This study attempts to use photogrammetric techniques, through the use of calibrated photo-imaging, combined with GPS derived positional information and georeferenced aerial photography to ascertain the previously mentioned qualities of distance and therefore calculate height. By allowing a speedier and multipurpose digital photo field survey, avoiding the problem of intervening obstacles, and then using in-the-lab analytical techniques, we will refine a methodology.

In addition, we will investigate the use of this technique in determining the volume of foliage a tree occupies, and eventually the urban arboreal topology of a typical city block.

Introduction

Measuring the heights of trees has practical uses in the fields of forestry and urban tree management. The calculation of harvestable board feet is important in yield determination in the forest products industry. In urban environments, trees are considered a valuable asset and an assessment of tree heights and canopy volumes is helpful in managing this resource. This study focuses on the urban environment, and attempts to create a methodology, using less expensive non-commercial equipment (the exception being the expensive ESRI ArcGIS software products) for inventorying and measuring trees.

Conventional methods of measuring the heights of trees include the use of telescoping poles, and yardsticks held at arms length that provide a ratio multiplier to distance from the tree. Another method uses of inclinometers to determine the angle from the observer to the top of the tree, and is combined some method of determining the distance to the base of the tree, either by pacing off, using a measuring tape, or laser rangefinder. The height is determined using basic trigonometry. Figure 1 shows this type of measurement. (M. Beals, L. Gross, S. Harrell, 2000)

The project explores the use of aerial photography and digital ground based photography as a substitute for the use of an inclinometer, and tape measure. Other methodologies use for extracting large scale tree foliage and volume estimates, including the use of digital orthophotographs in stereo pairs combined with Digital Elevation Models to calculate tree heights (D.R. Miller, et. al., 2005).

In addition, tools were developed in this project to aid in the collection and processing of the ground based digital photography, and to speed the calculation of the tree heights.

Methodology Overview

The methodology includes:

1. Calibrating a digital camera, such that the size of an individual picture element (a pixel) a given distance is known in pixels per foot or pixels per meter.
2. Taking georeferenced pictures of the subject trees using the calibrated camera.
3. Using aerial imagery to determine at what distance from the subject tree the image was taken.
4. Measuring the height of the tree’s image in pixels.
5. Use the determined distance and calibration information to convert the pixel count to a measured height in feet or meters.
6. Displaying tree location and simplified foliage volume in ArcScene.

Calibrating the Camera

The relationship between the size of a pixel, representing a portion of an object within an image and the distance of the object from the camera, needs to be determined. Factors that affect this relationship include the focal length of the lens, the distortion in the lens at a given focal length and the image compression inherent in the camera. A single camera and a single focal length will initially be used, to limit variables, but ultimately, since the focal length used at the time of image capture is automatically recorded in the metadata, the affect of focal length could also be factored in.

1. Photograph object of known width at different known distances and at a fixed image quality and resolution. A fixed focal length should be used. Optional: Vary focal length to determine optimum setting for the least amount of lens distortion.
2. Transfer images to a computer and view in an image viewing program capable of measuring pixels. Record width of known object, and number of pixels in a table. Optional: record focal length.
3. Perform a regression analysis of pixels versus object width. (Focal length)

A backstop in a local park’s baseball field was used as the calibration target. Measured at 34 feet wide, it provided a clear target with well delineated edges, and was visible in the aerial imagery. Location markers were accurately measured with a tape and placed at even intervals out from the backstop. Images of the target were captured by a consumer grade Pentax Optio S4 camera that produces a JPEG compressed file even at its highest quality setting. Images were taken at 3 fixed focal lengths at each distance marker.

Consumer grade GPS units lack the accuracy needed to measure the distance from the target, but a GPS unit was used to record the approximate location of each image to help with later analysis. A demonstration version of a software program, GPS PhotoLink, was used to associate each image with a spatial location and create an ArcGIS shape file. Figure 2 shows aerial imagery with the position of the calibration images shown and sample images.

Figure 2

The aerial imagery used comes from the USGS Urban Areas aerial imagery and was obtained from the USGS / Microsoft collaboration; TerraServer via the GPS PhotoLink software, as acquiring it directly, or from other sources produced projection and georeferencing errors. For comparison, the width of the 34 foot wide backstop was measured in ArcMap from the aerial imagery and found to measure 33.87 feet to the nearest discernable pixel, an error of less that a quarter of a foot. Relative pixel per foot accuracy would increase with the longer distances used in measuring the distance from images to trees.

The following lists the metadata for the aerial imagery:

Projection: North American Datum 1983 / UTM Zone 10N
Provider: U.S. Geological Survey
Resolution: 0.250 meters per pixel
Type: Urban Areas High Resolution Natural Color Imagery

Streets were added for reference from the US Census Bureau’s Tiger data.

Creating Calibration Equations

After acquiring the imagery and moving it to a computer, a program, called Exif Reader, was used to extract the metadata for each image, including the filename, time of capture, and focal length of the lens. Each image was analyzed and the width of the target backstop measured in pixels using the common Microsoft Photo Editor™ included in Windows™. This information was placed in an Excel spreadsheet, and combined with the recorded distances from the target. Regressions were performed on the data, and power equations produced for each of the three focal lengths used in the calibration imagery, as shown in Figure 3.

Figure 3                                                                                                                                 Figure 4

These equations in fact represent a three dimensional solution as shown in Figure 4, as the Feet from the target (Distance) and the focal length both effect the number of pixels per foot.

Calculating an equation to accommodate both variables proved difficult due to a lack of knowledge in what is presumed to be differential equations. Ultimately these equations should be solved simultaneously so that any focal length could be used to take the picture. To simplify this study, only the wide angle setting and equation was used. This resulted in a camera and focal length specific equation of:

Pixels per Foot = 2132.5x ^-0.9802

where x equals the distance from the target in feet.

Using ArcPad to Assist in Image Acquisition.

During preliminary image acquisition tests, it became clear that tools could be used in the field to better identify the trees and to assist in the collection of ancillary information such as tree type, which trees were captured, and the location of the camera for each image. The use of a consumer grade handheld device with GPS capabilities was desired, and a Dell Axim x50v running the Windows Mobile 5 operating system was employed. A free demonstration version of ArcPad 7.0 (which has an annoying but usable twenty minute timeout) was used to develop a simple data entry form and shape file called Tree Notes, as seen in Figures 5. Other municipalities conduct tree inventories, and more sophisticated ArcPad templates exist, free from the ESRI website.

Cambridge Massachusetts is also using PDA type handheld devices and ArcPad for “detailed and comprehensive street tree inventory to track species, size, location, and tree condition easily accessible for managing the maintenance priorities of the tree crews.” This software combines aerial photography with street and building layers, and allows field personnel to inventory and review information which is updated by the central data system (ESRI, ArcNews, 2005).

It should be quite possible to combine these more advanced inventory systems with the Tree Notes spatial data.

During subsequent image capture of the study trees located in the same park, the location of the camera was marked on screen and a line object created in Tree Notes that connected the camera location to the trees being photographed. This helped in keeping track of which trees were photographed and identified the location of the camera, helpful in later analysis.

Tree Image Capture

Due to the inaccuracy of consumer grade GPS units, and the difficulty with getting properly georeferenced aerial imagery, positioning information could not be relied upon to provide accurate distances from the camera to the trees. The georeferenced aerial images would be used as the “yardstick” for measurement, because they have a high degree of internal consistency and accuracy. Because of this, it was important that the location of the camera be visible from the air, and easily and accurately identified. Block corners, with their intersecting sidewalks, made an highly visible “X” that would allow for accurate measurements in ArcMap.

After the field work was completed, the imagery was again imported using GPS PhotoLink, and the resulting Picture shape file imported to ArcMap.

Digitizing Trees

Because of the desire to calculate area and volume of foliage for each tree, the aerial imagery of the study location was reviewed, and a Trees shape file created. The individual trees were digitized, and an x and y easting and northing value for centroids was calculated for each. The centroid information was exported and manipulated in Excel and then re-imported as a point file called Tree Centers, containing centroids for each tree, a surrogate for both the location of the trunk and the location of the maximum tree height. Labels were assigned to each tree consisting of the concatenated integer portions of the centroid values. This gave each tree a unique identifier. The Tree Notes and Picture files were also added.

The results of combining the above data in ArcMap are shown below in Figure 7.

Calculating Tree Heights

The distance from each camera location to the target tree was measured in ArcMap using the measure tool and recorded as an attribute in the Trees data file. The appropriate image to analyze was identified visually on-screen using the Tree Notes and Pictures data. Each appropriate tree image was opened in Microsoft Photo Editor™ and the height of the tree trunk and the total tree was measured in pixels using the selection tool. These values were also entered into the Trees shape file. The tree types (simply classified for this project as palm, deciduous, conifer, and dead) were also entered.

The calibration equations developed previously, were then used to calculate the number of pixels per feet and the heights of the trunks and trees. Unfortunately, the author could not determine the correct method for calculating a power function with a negative exponent, so the pixel height data was exported and height calculations quickly performed in Excel, and then joined back into the Trees file. Heights were calculated in both feet and meters.

Preparing 3D model in ArcScene

To better visualize the topology of the trees measured, the Trees file, along with aerial imagery and supporting files, was used to create an ArcScene file and view. The trunk heights were used as a base from which to extrude the remaining tree height, producing a view with the foliage volume represented as a simple cylinders as shown in Figure 8.

Figure 8

Clicking on the image in Figure 8 will open a window with an animated view of the above scene.

Future Work

1. Improve work flow. While imporovements were made through several iterations, work still needs to be done to speed the process, inclding the use of spatial joins to connect digitized trees to Tree Notes. Digitizing the trees before performing field work may help.
2. Determine differential equation to include focal length. Only one focal length was used during tree image capture. The use of longer focal lengths should decrease relative pixel measurement for tree at a distance, and decrease the number of camera locations. For this to be used, an equation is needed that defines the relationship between focal length, distance, and pixels per foot.
3. Develop a method for determining heights of trees where bottom not visible. Due to time constraints, the study was not extended (as originally intended) to trees where the bottom is not visible, such as those located in back yards. If the camera is level when a picture is taken, we surmise that the center of the image would be at the same height as the camera, giving a ground plane from which the height of the tree can be determined by adding the camera height, to the calculated distance from the image center to the top of the tree.
4. Expand ArcPad forms and Tree Notes. As mentioned above, better tree inventory forms exist, and may prove helpful in the overall task of inventorying trees.
5. Quantify errors. A study of the sources and magnitude of errors, including comparisons to other methods of measurement would be essential before this methodology could be used with confidence.
6. Develop a better representation of tree volume. The 3D scenes rendered in ArcScene assume a cylindrical form for all trees, as would a simple calculation of volume using area and height. A better approximation of volume would use a knowledge of tree geometry and structure.

Summary

This project developed an alternate method for calculating the heights of trees using non-commercial cameras handheld devices and GPS units, relying on photogrammetric principals and camera calibration. Applications for the technology include uses in urban planning and resource management, and maintenance procedures.

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References

M. Beals, L. Gross, S. Harrell, 2000. Alternative Routes to Quantitative Literacy for the Life Sciences. http://www.tiem.utk.edu/~gross/bioed/bealsmodules/triangle.html.

ESRI, ArcNews, Vol. 27 No. 4, Winter 2005/2006, page 39. (No author attributed. Also available online at: http://www.esri.com/news/arcnews/winter0506articles/cambridge-mass.html )

D.R. Miller, A.D. Cameron and G. Zagalikis, 2005, Macaulay Institute, Craigiebuckler, Aberdeen AB15 8QH, Scotland. The monitoring of tree and stand characteristics using digital photogrammetry and image analysis techniques. (http://www.macaulay.ac.uk/workshop/ remotesensing2004/DM_Full_paper.pdf)