Doubt about my geo referencing procedure

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05-07-2014 10:45 AM
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Occasional Contributor
I just completed creating 8 links to rectify a 1948 aerial photo TIFF to 2013 NAIP imagery, using Arc 10.2   I'm skeptical of the Residual (RMS) error, which I use to judge how effective the links are. Please see the attached screen capture. I believe that the RMS error is in the units of the arc map session, in this case, Meters. Specifically, I'm skeptical of the 0000884777 Total RMS error. Does this look reasonable?  I'm linking points on the 1948 TIFF to the same points that I've ID'd on the 2013 NAIP. Should I be linking: TIFF to Imagery? Alternatively, should I create some vector point features, overlaid on the 2013 NAIP, and then link: TIFF to point features?
Ken
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Esri Notable Contributor
Hi Ken,

My rough approximation of degrees-to-meters is to say that the 4th decimal place is about 30m, so you're seeing a fit around 3 m or less.

If you can, it's sometimes better to georeference directly to the native coordinate system of the raster. Then reproject it if necessary. It's more necessary as scale gets smaller (larger area is represented).

Melita

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Esri Notable Contributor
RMS is in the units of the coordinate system which is, in this case, decimal degrees (your links are lat/lon).

Melita
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Melita,
  Thank you for responding. I realize the X & Y figures in the link table are lat & long. My doubt is about the total RMS error. Is that a reasonable RMS error to you (meters, in the map units)?  I just tried creating point features on the NAIP imagery and then linked the 1948 tiff to those. 7 of these links resulted in a higher RMS error, although still well below 0.0  In geo referencing I've done before it required a lot of links to get just to a 0 RMS; course that work was with GIS 9.3
Ken
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Esri Notable Contributor
Perhaps I'm not understanding something. It's been a while since I georeferenced data. The total RMS values are in decimal degrees, because that's what the target links are in. If you want RMS in meters, you're going to have georeference to a map that's in a projected coordinate system or use links with target values in meters.

Melita
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My original questions remain un answered.  Is the RMS error, in the original attachment, realistic; does it tell me anything?  Is it right to link pts in a tiff directly to a image raster?  Can someone suggest how I might optimize the settings in the attached capture Rectify window?  Please see attached.
Ken
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Esri Notable Contributor
Hi Ken,

My rough approximation of degrees-to-meters is to say that the 4th decimal place is about 30m, so you're seeing a fit around 3 m or less.

If you can, it's sometimes better to georeference directly to the native coordinate system of the raster. Then reproject it if necessary. It's more necessary as scale gets smaller (larger area is represented).

Melita

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Melita,
   Your last note was key to helping me understand how I need to think of the RMS in terms of degrees error. I've tried, unsuccessfully, to reverse engineer your approx. math, where you came up with 3 meters of error: degrees to meters. Would you please tell me what is wrong with my conversion math:

1 degree =  111 kilometers.  To convert our RMS error: (0.0000884777 * 111) * 1000m = 9.8 meters of error

Instead of re projecting the imagery, to gain more accuracy, can we not just change the arcmap session to the native projection, of the imagery, to eliminate the error as ArcMap projects the imagery on the fly?
Ken
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Esri Notable Contributor
My conversion comes from:

6378137 * 2 * PI / 360 = 111.319 km (length of a degree at the equator)

111.319 km / 3600 (seconds in a degree) = 30.922 m (length of a second at the equator)

1" =  2.7777777777777777777777777777778e-4 degrees = 0.000277 degrees

So you're closer!

Melita
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Melita,
   It made my whole day to see your math in the last note! I was able to use it to arrive at my earlier calc, done with diff math, of
9.8m.  It re assures, and makes sense, to me to get a realistic result, like 9.8 meters of error,  for the tiff I geo referenced, instead of the really small number I misinterpreted.  Thanks so much, Melita, from me and the other 3 gis analysts on our team, for helping us understand this process better. We have hundreds of historical tiffs to geo reference in the next year.

For the other folks following this discussion: let me try to sum up the process of interpreting the RMS error reported in  the link table, using Melita's math :

determine that the figures under the X & Y map columns are lat and long coords  The RMS error is then in decimal degrees.

Our RMS error * 3600 seconds = converts the decimal degrees figure to seconds.  The RMS seconds * 30.922 = the error, in meters  Of course, this is the error at the equator and should be converted to your lat, if you need the extra accuracy. I'll post a follow up thread, showing my RMS error corrected for my lat, after I figure out how to convert it.

I think the definition of the RMS error: the error between the coords of the link points set on the tiff and the coords of the  link points set at the same position on the NAIP imagery. I hope someone will feel free to correct my definition, if I'm in error.

Ken
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MVP Frequent Contributor
As a rough approximation (ie on a sphere), just multiply your distance at the equator by the Cosine of the Latitude of where the data is to get the actual distance.
And to further underline Melita's point, you should always georeference into the correct projected coordinate system of the data. Not directly into GCS.
Good luck,
Neil
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