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FAQ: How do nonlinear conditions affect image warping?

Question

How do nonlinear conditions affect image warping?

Answer

Image warping distorts an image to match a particular surface. Image warping in Java is supported through the use of the JAI polynomial projection, a linear projection algorithm commonly used for displaying images over the past 25 years. Subsequently, if a polynomial can be developed to describe the image transformation in one projection (coordinate system) to the target projection (coordinate system), image warping can be successfully completed. However, projections with a nonlinear condition pose a problem to this method.

A nonlinear condition occurs when the underlying latitudes and longitudes in one coordinate system cannot be linearly transposed to the latitudes and longitudes in the other coordinate system. In other words, the projection cannot be modeled by polynomials without discontinuities; hence, it is not a continuous linear function.

For example:

You have an image covering the entire world with its center at 100 degrees West longitude. Its projection is Geographic Latitude / Longitude in degrees.

You want a projection with Geographic Latitude / Longitude in degrees, but with its center at 100 degrees East longitude.

Given the new center, it is only possible to view an image 40 degrees in longitudal width successfully (centered at 100 degrees East longitude). Anything larger requires cutting the original image and placing part of it on the opposite side (adjacent). This is the nonlinear condition.

As a result, the polynomial transformation of images is utilized on local images instead of larger global images. It can work for global images, but only when the underlying latitude/longitude bases do not shift.