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I have a map of a mountainous landscape, http://skimap.org/data/989/60/1218033025.jpg. It contains a number of known points, the lat-longs of which can be easily found out using google maps. I wish to be able to pin any latitude longitude coordinate on the map, of course within the bounds of the landscape. For this, I tried an approach that seems to be largely failing.

I assumed the map to be equivalent to an aerial photograph of the Swiss landscape, without any info about the altitude or other coordinates of the camera. So, I assumed the plane perpendicular to the camera lens normal to be Ax+By+Cz-d=0. I attempt to find the plane constants, using the known points. I fix my origin at a point, with z=0 at sea level. I take two known points in the landscape, and using the equation for a line in 3d, I find the length of the projection of this line segment joining the two known points, on the plane. I multiply it by another constant K to account for the resizing of this length on a static 2d representation of this 3d image. The length between the two points on a 2d static representation of this image on this screen can be easily found in pixels, and the actual length of the line joining the two points, can be easily found, since I can calculate the distance between the two points with their lat-longs, and their heights above sea level.

I end up with an equation directly relating the distance between the two points on the screen 2d representation, lets call it Ls, and the actual length in the landscape, L. I have many other known points, so plugging them into the equation should give me values of the 4 constants. For this, I needed 8 known points (known parameters being their name, lat-long, and heights above sea level), one being my origin, and the second being a fixed reference point. The remaining 6 points generate a system of 6 linear equations in A^2,B^2,C^2,AB,BC and CA. Solving the system using a online tool, I get the result that the system has a unique solution with all 6 constants being 0. So, it seems that the assumption that the map is equivalent to an aerial photograph taken from an aircraft, is faulty. Can someone please give me some pointers or any other ideas to get this to work? Do open street maps have a Mercator projection?

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No amount of math is going to turn an artist's stylized depiction of a landscape into a photogrammetrically correct image. I think you would be better served obtaining orthorectified aerial imagery and plotting your locations/features of interest on it. It is an interesting problem though. –  blah238 Feb 19 '13 at 14:47
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You might be interested the Piste Maps using Open Street Maps as a solution - wiki.openstreetmap.org/wiki/WikiProject_Piste_Maps if they are missing then add them. –  Mapperz Feb 19 '13 at 15:38
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Are you trying to achieve something like this GPS map for Alta Ski Area: mountaindynamics.com/en/resortm.php. I would say the only accurate way is as suggested above with up to date orthophoto's or go out and GPS the trails yourself for your final product which would be my preference :) –  danagerous Feb 19 '13 at 21:31
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I don't think there is any way to georeference a ski resort map - which are often hand-drawn - in a meaningful way. It's an artistic interpretation of the landscape with high degrees of freedom and a focus on being easy to read.

Maybe if you describe your final goal - e.g. what do you want to do with the georeferenced image? - we can propose a different path to get there.

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i am actually making an iOS app targeted at the skiing audience, so what i plan on is that a user should be able to pin point on that map, a given latitude longitude, which can be obtained from the GPS. I wish to show the user then, where he is on the map, as he goes through the terrain. –  Sonu Jha Feb 20 '13 at 13:45
    
i just came across this magazin.unic.com/en/2012/02/16/… They are doing the same thing, with the difference that they have some 300 known input points to come up with something that does an approximate transformation of a 2-d google map to that piste map. How can one follow this approach...transforming one set of co-ordinates to another. Sorry, if this sounds naive, but I have very limited background on this stuff and the mathematics used. Thanks for your help! –  Sonu Jha Feb 20 '13 at 15:03
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