Program in GIS

Georeferenced State College DRG Screen Capture



Figure 1: Georeferenced State College DRG screen capture with link table.

Source:  Brenton White ArcMap Project 3 screen capture.

Figure 1 shows the georeferenced State College DRG with link table.  We have an RMS error of 0.9031 meters, which is less than one half the width of a cell (see Calculation of "a Reasonable RMS Error" discussion below).  Essentially, the RMS error tells us that the location of a given cell in meters is the location specified +/- 0.9 meters.  Given that a DRG is effectively distortion free, this is not an unexpected result with well placed links.

Close Up Views of State College DRG Links

Upper Left Link	Upper Right Link
Lower Left Link	Lower Right Link

Figure 2: Close up views of DRG links.

Source:  Brenton White ArcMap Project 3 screen capture.

Figure 2 shows close ups of the four links used to georeference the State College DRG.

Georeferenced State College Map Screen Capture

Figure 3: Georeferenced State College map screen capture with link table.

Source:  Brenton White ArcMap Project 3 screen capture.

Figure 3 shows the georeferenced State College Map with link table.  It shows an RMS error of 7.38, which is not a good RMS for the sake of accuracy. However, it is good to note the RMS value in this case so as NOT to rely on the coordinates for work that requires knowing the location of a specific feature (see Diagnostic Value of RMS Error Result discussion below).

Close Up Views of State College Map Links

Upper Left Link	Upper Right Link
Lower Left Link	Lower Right Link

Figure 4: Close up views of map links.

Source:  Brenton White ArcMap Project 3 screen capture.

Figure 4 shows close ups of the four links used to georeference the State College Map.

Georeferenced State College 1963 Screen Capture

Figure 5: Georeferenced State College 1963 screen capture with links.

Source:  Brenton White ArcMap Project 3 screen capture.

Figure 5 shows the georeferenced State College 1963 with link table.

Close Up Views of the State College 1963 L1-L5 Links

Link L1	Link L2
Link L3	Link L4
Link L5

Figure 6: Close up views of the L1-L5 links.

Source:  Brenton White ArcMap Project 3 screen capture.

Figure 6 shows close ups of five of the links used to georeference the State College 1963.

Discussion

Calculation of "a Reasonable RMS Error"—The key here is to determine the length of a cell in map units (in this case, meters) since a reasonable RMS error is defined as:

"...that the RMS error be less than or equal to one half the map unit size of a cell (pixel)"

Given the definition and knowing there are a number of ways to calculate the length of a cell (pixel) in a raster graphic, I used the fact that there are 250 cells per inch, the scale of the map is 1:24000, and took the coordinates off my map (before georeferencing) as follows:

Width of map = 19.375925-2.092211 inches = 17.28371 inches
Total number of cells = 17.28371 inches * 250 cells/inch = 4320.928 cells
Meters represented in map  = 268265.246 - 257730.594 meters = 10534.652 meters
Length of cell in map meters = 10534.652 meters / 4410.425 cells = 2.438 meters/cell

It is interesting to note that the Rectify process gives us the length of a cell (the cell size field) in map meters when you save the rectified image:

Figure 7: Cell size determined by Rectify.

Thus, a reasonable RMS error for the maps is 2.438/2 = 1.219 = 1.22 meters.

Or we could do it Jim's way and just use the scale of the map, figure the inches represented with 250 cells/inch, convert inches to meters and we're on our way.  I just chose to use measurements from my map.

Diagnostic Value of RMS Error Results—the value of the RMS for the DRG and the Map are high.  The DRG has well defined control points that are precisely known.  As such, the RMS (assuming that the FROM points are well placed and haven't been "fudged" to lower the RMS) gives an very good idea of the accuracy of a given point on the map.  This is also true for the Map even though the value is very high.  While the map has good control points, they are not as far apart as for the DRG and there is possible distortion from the scanning process.  The high RMS suggests that one should not use this map for locating features that require a high level of accuracy (each pixel could be a much as about 7 meters off in either direction).

The diagnostic value of the 1963 photo is useless.  The photo is distorted, the control points could have built in errors from the surveying process, the placement of the roads as TO points could have errors, and the transformation equation itself can introduce error.  Thus, one should not use the RMS error value from the 1963 image to get a sense of the accuracy of elements located on or aligned to the image.

What Might Limit Ability to Achieve a Low RMS Error—Some of the elements that might limit one's ability to achieve a low RMS error are:

• Control points (X and Y parameters) are not precisely digitized

• Control point locations are offset from their actual position

• Uncertainties in the Easting and Northing coordinates

• The transformation equation used (1st, 2nd, or 3rd order)

• Reference points that are too closely located or not representative of the landscape

• High distortion in the aerial photograph

• Poorly scanned or damage hardcopy map

Garbage in equals garbage out.  Even with a perfect transformation, source data contains errors (its inevitable) and sets a floor for a true RMS error.  Thus, there are many factors, human, machine, process, that might limit the ability to achieve a low RMS error.  And this doesn't even bring into account the second law of thermodynamics, which states that all systems move to a higher state of disorder (as a Physics major, I had to throw this in)!
 

GEOG 5223: Project 3: Registering an Image for the Purpose of Data Creation. August 2004.