0

What would be a good algorithm or analytical method to approximate a discrete 2D look-up-table (LUT) to a continuous function? That is, given z=LUT[x1][x2] and we wanna come up with a function such that z=f(x1, x2).

Jes
  • 2,614
  • 4
  • 25
  • 45
  • 2
    It just depends what you are trying to approximate. What is your lookup table for? You gave no indication on what you want, other than it maps a space of two variables onto an output of one value. You can just use the continuous function with a set of discrete values, and actually make a lookup table, of course. What are you really trying to do? – Dan Oct 09 '15 at 23:21
  • To elaborate, if the continuous function is a polynomial, then a large enough table will let find the values exactly. Or if it's a trigonometric polynomial. If you have bounds on the derivatives, then you can get better results. If you only have continuity, then all you can do is linearly interpolate. – Teepeemm Oct 10 '15 at 00:02
  • Your two sentences seem contradictory: The first sentence appears to imply that you are trying to approximate a continuous function via a LUT, the second sentence asks for a continuous function that approximates a function specified via LUT. Which case are you actually interested in? – njuffa Oct 10 '15 at 04:51
  • @Jes Take a look at [Reverse complex 2D lookup table](http://stackoverflow.com/a/29227551/2521214) it is very similar problem so it might help. Without knowing the properties of your LUT is **very hard** to estimate the `Z` properly see [Finding the mathematical algorithm to which matches an input and output together](http://stackoverflow.com/a/31510038/2521214) and that is just 1D. If nothing works you still can do piecewise bilinear/bicubic interpolation ... – Spektre Oct 10 '15 at 06:49

0 Answers0