Converting a fisheye image into a panoramic, spherical or perspective projection
Transformations like these have wide applicability. Performing optics in software so to speak, is more flexible and cheaper than grinding lenses and building special cameras.I was charged once, with transforming images for projection onto a sphere through special lenses. I didn't know the lens transform, the manufacturer kept that secret.  I did know that the intensity across the spherical surface was of uniform brightness - the manufacturer boasted about this. With that bound I could guess the transform, as each pixel of the source image would have to illuminate an equal surface area of sphere once projected.The manufacturer advertised a service to do this transform on your image, but they wanted $10K for each run! Once I presented my insights and a little math, they capitulated and did it at cost. I never got to write my projection software in the end.