HT and RHT 

HT and RHT

It's a common sense that RHT is faster than HT. For, RHT makes several samples each term to calculate one point in the parameter space in a determined fashion, but RT use only one sample and compute a whole buntch of parameters( a curve or a surface in the parameter space). The higher the dimension is, the slower HT will be. But as the experiments shows that the "randomized" characteristics of the RHT seems to be problematic if there are many sample points. Because, the samples generated by computer is not random enough! So, when I detect long curves using RHT, the sample points tends to be localized on some part of the curve, and the precision of the algorithm is greatly penalized.

So, how to solve this problem?

One IEEE papar proposes a recursive RHT algorithm:
run RHT once, then narrow down the samples and the parameter space and run RHT again using higher precision.

This approach, which I tested by the tile quality checking system below, is still not good enough, although its execution time is very short.

My method is:
run RHT first , narrowing down the parameter space enough.
Then use the brutal HT on it.

Because the RHT, HT can be very fast, and retain its precision.

This optimization is thoroughly discussed in my paper.