Saturday, May 06, 2006
Optimizing noisy 1-D functions
Who knew such a trivial thing as finding the maximum of a noisy 1-D function would prove an unsurmountable task to modern science! While some people are fusing atoms and creating anti-matter, others are screaming in frustration over non-convergent searches and galloping derivatives when trying to focus a simple lens system in a ray tracer. Stochastic sampling in all honor, but for a tremendously costly function (e.g. ray-tracing a focus area and computing its entropy) you don't want to risk wasting those precious samples in potentially all the wrong places. Yes yes, auto-focusing a ray-tracer using the same focus measures as a normal camera might not be the smartest field to invest time in, but school assignments usually aren't picky about realism. Also, I'm sure there's plenty of other applications of a smart search algorithm for noisy data. Golden Section can't reign supreme forever! Right?