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REMOTE SENSING 2000 in progress...
PROJECT:
The
Scale Limits of the Landsat TM Apparatus
in
the Detection of Small Vegetated Areas in the Urban Context
-BACKGROUND
ON REMOTE SENSING
STATEMENT
OF THE PROBLEM
RATIONALE
METHOD
OF INQUIRY
PROCEDURE
-WARPING
ANALYSIS
OF THE CO-REGISTERED IMAGES
-AREA
CALCULATION
-SPECTRAL PROFILE ANALYSIS
RESULTS
CONCLUSION
REFERENCES
CLASS
LABS
Background
Information
Lab
1 Optical Reflectance and Atmospheric Effects: NYC
Lab
2 Landsat Sensors MSS vs. TM, Spatial, and Spectral Resolution
I: NYC
Lab
3 Landsat Sensors MSS vs. TM, Spatial, and Spectral Resolution
II: Viet Nam
Lab
4 Supervised
Classification: SW Brooklyn, NY
Lab
5 Principle Component Analysis: SW Brooklyn, NY
Lab
6 Georeferencing, Band Ratio-ing, Image Filtering and Decorrelation
Stretching: Canon City, CO
Lab
7 Georeferencing, Scale, Transformations for Vegetation Assessment
(NDVI, Band Ratios), Hyperspectral Analysis (PPI), Transects: Bighorn Basin,
WY
Lab
8 Digital Elevation Model, 3-D Surface and
Fly
Through: Bighorn Basin, WY
THESIS
PROJECT 2000 construction just started...
Brooklyn
Bridge Park Aerial Photo Base Map
MAP
PROJECTS from Spring 1996
Lab
3 Tourist Map of Washington DC
Lab
6 Map for BCUE in Prospect Park, Brooklyn NY
Satellite
Image of the New York City metropolitan area Out of commission
Remote Sensing Project: The Scale Limits of the Landsat TM Apparatus in the Detection of Small Vegetated Areas in the Urban Context
by Dan Wiley
Landsat Thematic Mapper (TM) imagery is a powerful tool for detecting vegetation changes in large landscapes over time, but how effective is it in measuring vegetation on a smaller scale in the urban context? More specifically: at what scale is an area of vegetated green space in New York City recognizable in a Landsat TM image?
In the first sentence above "scale" is used in the sense of geographic scale, which is the spatial extent of the area: satellite imagery is better at representing things that occur on a large scale, in other words, it is better at representing large areas such as agricultural plots or forests etc. The second sentence above uses scale interchangeably with size. Another use of the word "scale" is in the sense of cartographic or map scale: a larger scale map [generally] provides more detailed information (Quatruchi, 14). "Generally" is the operative term here: we expect large scale maps to give us more detail. Bad maps may not. Who would require a poster size print of a fire floor plan posted near an elevator? This project however, will do just that kind of thing: blow up a subset (small crop) of a Landsat TM image data to a large scale to compare it to the NYC DEP map generally used at large scales, so much so that Brooklyn, NY alone is divided into __ tiles, whereas in the examined Landsat TM image, Brooklyn is but one quadrant of a single image.
This paper then will consider scale focusing on spatial resolution, the size of the smallest distinguishable part of a spatial data set. Generally, smaller units are termed "finer scale." The Landsat TM uses a relatively "rough" scale: the spatial resolution of the Landsat TM image is 30 x 30 meters for bands 1-5 and 7 (and 120 x 120 for the thermal band 6, which is not important in this context).
Illustrated
below is the starkest contrast in spatial resolution I could find (which
is considered in this paper): the Landsat TM unit compared with an
equal area of the NYC Department of Environmental Protection (DEP) Orthorectified
Aerial Photograph.
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1 pixel
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Thus, a picture element ("pixel") of information of a TM image (below right center gray square) is about the size of four typical NYC row house ("brownstone") building lots (below left):
Before doing any tests, one could hypothesize that the "sampling theorem" would apply. The sampling theorem states that one should sample at no less than twice the frequency of variation. It is typically applied in the spectral realm in remote sensing: it is necessary to sample at twice the frequency of the shortest wavelength of interest. So for instance, if one is interested in the blue (wavelength of .45-.50 µm), one must sample the electromagnetic radiation fluctuation in the .22-.25 µm range or less (or half so to sample twice the during one wavelength fluctuation). This is also known as the Nyquist Frequency. Sampling at less than the Nyquist frequency will guarantee that the information at this wavelength will be lost. (Sampling at the Nyquist frequency does not guarantee an accurate description since the phase of the signal becomes crucial at this frequency --the difference between optimal sampling at the peaks and troughs or awful sampling in the middle of the fluctuation which would give no indication.) Sampling at less than the Nyquist frequency is a distortion we are all used to seeing in movies where the wagon wheels appear to be moving backwards even thought they are moving forward. That is because the sampling rate of the film camera (shudder speed) is taking samples (exposures) at less than the Nyquist frequency of the spinning wheel giving us a distorted view of its motion.
We
can apply this theorem to spatial variations (patterns) on the ground.
Take the roof example. We have a white roof and a black roof alternating
in a row of four houses. The frequency of the pattern along the short
interval, house to house, is 25 feet. The sampling
theorem
would dictate that the minimum pixel size to capture this variation reliably
would be less than half that, or 12.5 feet, so that the frequency of sampling
brightnesses would be at least twice along the the interval (width of a
roof). In the case of the image on the left, an Aerial Photograph
from the NYC DEP map is at 1 foot resolution, so that we can clearly make
out contrasting objects of two feet (on the short dimension) or larger
on the roof. In the Landsat TM image on the right (warped to the
geographic coordinates within 15 meters see explanation
below) the pixel size is almost four times the 25 foot interval,
so the sampling is not anywhere near twice the roof interval (frequency
if you will, of what's observed). Rather the sample is four times
as large as the interval, instead of half or less. Thus we cannot distinguish
the alternating roof pattern in the TM image at right.
We
however can say that the four houses have on average a gray equivalent
albedo. This could mean that the end members could:
-all be gray
-be alternating black and white
-be black, dark gray, light gray and white etc.
So we can see that we would not use TM data to survey row house roof patterns. (Note that this exercise is analogous to describing the resolution of film for a camera by line pairs that can be discerned; in this case uniformly skinny roofs serve as line pairs.) On the other hand we can learn something from analyzing this TM data, even though it is at eight times the minimum sampling frequency for reading the patters of these roofs. Since roofs tend to be painted one of two colors mostly, black tar and silver tar (black and white), one can generalize some observations based on this knowledge. We could quantify in the aggregate what portion of total roof area is black and white as long as the signature of "painted roof" was distinguishable in terms of available band readings from the universe of other things on the ground.
Similarly, since plants read high albedos in band 4, the near infrared (NIR or also referred to as Short Wave Infrared, SWIR), and are thus easily distinguishable from other things, we can infer their presence in areas even smaller than the minimum recognizable at the spatial resolution of the TM imaging system dictated by the Nyquist frequency of occurrence (60 meters). In in the case of green parcels smaller in one dimension than 60 meters while one may not be able to discern pattern (or exact shape), one can quantify its amount, just not the distribution of that amount (as in the roof example).
I
chose to examine a few vegetated areas on the Downtown Brooklyn, NY waterfront:
in
the inter bridge area between the Brooklyn and Manhattan Bridges
also
known as "DUMBO" Down Under the Manhattan Bridge Overpass
Shots from a plane September 17th, 2000.
Click Here to examine unclose
June
1996 NYC DEP Aerial Photograph used for comparison with Landsat
The largest green park in the area is Empire/Fulton Ferry State Park (also
seen at center in the aerials above)
A
smaller area of green is near the Brooklyn Bridge on its south side, at
Fulton Ferry Landing (see the trees unfortunately cut off to the left of
the woman's head, looking from a boat). This is a mini park created
and maintained by the River Cafe in exchange for being moored on City Property.
To scale with the above larger area aerial photo.
These aerial photographs, which are geo referenced, were used as the base map for warping the Landsat TM images, to scale them up to the same size and orientation. Ground control points were selected on the base map and the Landsat TM image to execute the Resampling, Scaling, and Translation warp. This enabled the two images to be fitted over each other to a degree of accuracy less than 15 meters for interactive overly and comparison.
Then the scale at which the various sizes of green space in the image can be discerned and the minimum size at which green patch identifiable in the TM image can be determined. In cases where the green spaces are smaller than the TM pixel, end members that make up the TM pixels are closely observed. Thus analysis of the scatter plots of the selected wave bands can be more prickly analyzed for what they signify on the ground (their end-members).
Various
ENVI functionalities on the TM image, such as Transformations for Vegetation
Assessment (NDVI, Band Ratios), Hyperspectral Analysis (PPI) and compare
the results pixel by pixel.
The Downtown Brooklyn site was chosen over the areas below (Sunset Park and Bedford Stuyvesant) because the aerial photo data for DUMBO above was taken in June 1996 when grass is greener and leaves are on trees. (This is due to a fluke that the DUMBO air photo happens to be grouped with the Manhattan set of tiles, which were shot in June.) The aerials below are from the Brooklyn set of tiles, shot in April, a time of yellower grass and "leaf off."
Sunset
Park's Waterfront "Brownfield"
(click here to see preliminary work)
Some
preliminary work was done especially in illustrating the technique of how
exactly ground control points were chosen for image warping.
A
Bedford Stuyvesant Block with Community Gardens
(click here to see preliminary work)
Further
work could be done using this image to test the discernability of three
gardens of varying size on one block.
Further
work is possible using these above two data sets in conjunction with photographs
on the ground and on roofs during a "leaf on" period. (Click on each
above to see them)
Warping
the Landsat Satellite TM Image to the Orthorectified Aerial Photograph
To
co-register the NYC DEP Ortho Photo 1996, and the Landsat TM 1999 images
exactly for interactive analysis, we must compare their header information:
| NYC DEP Ortho Photo 1996 | Landsat TM 1999 |
| Pixel = 0.30 Meters2 | Pixel = 30 Meters2 |
| Magic Pixel = 303276.607
E
58674.117 N Projection: State Plane (NY, Long Island) Datum: North America 1983 |
Upper
Left Corner = 6285, 1382
Projection: UTM, Zone
18 North
|
Since the above right header information does not have the same type of georeferencing to register the two types of images together, one is warped to the other by selecting ground control points. Even if the "nominal center" (in ENVI the "magic pixel"), the geocoded pixel that allows one to determine the geographic location of all the other pixels (as one knows the projection information and scale), one could still not accurately co-register the two images because the key geocoded pixel in the TM image is not accurate enough. In the case of Landsat 7, it is off 30-50 meters, and in Landsat 5, where this data comes from, it is off by considerably more than 50 meters. The amount it is off is found below.
Below,
the TM image is to the left to the Ortho Photo to the right.
Four
Ground Control Points were selected.
Well
defined corners of sharply contrasting structures were selected: corners
of piers and a bright roof of a federal building were used. (See the small
numbered and circled cross hairs below)
| This is a regular photograph all be it aerial, and used
the three primary visible wave bands: R GB.
While the spatial resolution is far greater in this image, the image to the right has a greater spectral range with seven wave bands to choose from. |
For a natural color composite assigned display colors:
Red
to B7 (mid infrared) because one associates
soil (and its minerals) with red; Green to B4 (reflective infrared) 0.76-0.90 µm, because nothing sends back near infrared like vegetation; and Blue to B2 (visible green) 0.52-0.60 µm to stand in for the whole visible spectrum since it is in the middle band of the three visible bands (and is interfered with by atmosphere less than band 1). |
The a subset of the resultant warped TM image is on the
right below:
| NYC DEP Ortho Photo 1996 | Landsat TM 1999 (after warping) |
For
an illustration of how the two images above fit each other in an interactive
overlay click here.
.
AREA CALCULATION
Interestingly, in trying to quickly measure the green area of the park, I made a quick rectangle as the region of interest guessing at the approximate equal area by cutting off as much green as non-green I include in the rectangle (instead of drawing an exact multi faceted polygon to trace the exact shape. I was surprised to realize that the Landsat sensor had done almost exactly the same thing: the predominantly green (band 4) pixels clustered at the park in a 2 x 4 rectangle close to identical to what I drew to measure the green area! Of course, it was also lucky that the phase interval of the pixels lined up well with the edges of the park.
So the 30 x 30 meter (900 sq. meter) pixels x 8 = 7200 sq. meters.
The extra area can be accounted for by factoring in the lower right pixel touching the rectangle. This is a "mixed pixel," a rough visual guess (to make it simple) would be 1/3 of the band 4 value in the unmixed center ones.
This would translate into 1/3 of the full area: 900 x .33 = 297.
So the 8 "pure" pixels which are 7200 sq. meters + 297 for the "mixed" pixel = 7497.
If we consider that the upper right pixel is not pure and subtract for the percentage of its contamination with non vegetation, we will come up with an answer very close to the measurement above and the actual area of vegetation! An algorithm can be developed to measure area of say grass by setting of the equation to do what was done above. The Pure pixel of green would have its value of band 4 assigned 100% area of the pixel. Any pixel with a value below that say 60% of the pure pixel would contribute 60% of it's area, etc. This would be a precise way to measure sunny grass. Of course a human would have to adjust for clouds or shadows cast by buildings, etc.
The above park is the ideal size cut-off in its short dimension for aerial vegetation patch recognition in a Landsat TM image. It is two pixels wide, just complying with minimum dictated by the sampling theorem.
Now a more exacting measurement of the area of green vegetation,
using a complex polygon, instead of the simple rectangle above.
Only off by 17.5 square meters using the simple rectangle
above.
Note: the aerial photo above was taken in 1996, but the
Landsat image below was taken in 1999 when the grass was greener in the
light patches above (see other photos above).
.
SPECTRAL PROFILE ANALYSIS
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That about the smaller green space?
The River Cafe park is primarily a cluster of trees a
little bigger than a Landsat TM pixel. Thus it is less than one half
the minimum size for shape recognition according to the sampling theorem.
In this much of the park falls within a TM pixel, but
some of that pixel is also roof at the upper right portion:
Project
Still in Progress...
The sampling theory proved true for pattern and clear shape recognition of green spaces, they to be at least two pixels (60 meters) in their shortest dimension. For smaller parks their presence could be detected, as well as their amount of area, in spite of their exact shape and distribution in space remaining a mystery behind the pixel. There are other factors to contend with in an urban setting, such as shadowing from surrounding buildings, which did not effect the examined waterfront parks because of being in a formerly industrial, relatively open space. Further investigation can proceed with small green spaces in a land locked context, such as Bedford Stuyvesant, Brooklyn (click to view).
Another limiting factor is that pixels don't represent a 30 x 30 meter area on the ground evenly. They tend to favor the centroid and less the edges. In addition, they also take in some of the surrounding area so that a bright object just outside the edge of the pixel can contaminate it. The degree of these effects are determined in part by how the data was originally sampled. More work can be done on how the pixel is constituted under different sampling methods, such as nearest neighbor, vs. bilinear interpolation, vs. cubic convolution.
The general theme though is simple, to avoid having to
worry about these factors, if we want to know the spatial pattern of vegetation
on on the ground, it needs to be at least two pixels in width. If
we are just concerned with amount sub pixel size is acceptable to a point
due to centroid favoritism and edge contamination. That point is
beyond the scope of the present paper but worthy of further research.
Jensen,
John R. 2000. Remote Sensing of the Environment; and Earth Resource
Perspective.
Upper Saddle River, New Jersey: Prentice Hall.
Quattrochi,
D. A. & Goodchild, M. F. 1997. Scale in Remote Sensing and GIS.
New York: CRC Press Inc., Lewis Publishers.
G70.212.S28