non linear regression of a 3D line

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Edward
Edward 2011-11-19
I have a 3D line On which I need to do a non-linear regression. The shape will range from a straight line going from (0,0,0) to (1,1,1) to a line that connects (0,0,0) and (1,1,1) by tracing the x, y and z axes.
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Image Analyst
Image Analyst 2011-11-20
Can the "shapes" be something other than a series of connected line segments? Like some arbitrarily curvy path? If so, why do you call the "shapes" a "3D line"?

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Michael
Michael 2011-11-20
You need a model to fit to the data, if you can come up with one (for example, f(x,y,z; param1, param2 ...) = 0), and have a suitable definition of what a residual is in three dimensions (eg. the nearest distance of the curve from the data point (xi,yi,zi)), you can write a function which returns these residuals and pass it to lsqnonlin which will then minimise it.

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