I have a problem similar in formulation to this post, with a few notable differences:
Like in that post:
- I have a $f(x,y)$ and evaluation of this function is somewhat expensive to compute
Unlike in that post:
I am interested not in the value of the function accurately everywhere, but only in finding a single isocontour of the function.
I can make significant assertions about the autocorrelation of the function, and consequently the scale of smoothness.
Is there an intelligent way to step along/sample this function and find this contour?
The function is the computation of Haralick Features over $N$ pixles surrounding the point, and soft classification by some sort of classifier/regressor. The output of this is a floating point number which indicates which texture/material the point belongs to. The scaling of this number can be estimated class probablities (SoftSVM or statistical methods etc) or something really simple like the output of a linear/logistic regression. Classification/regression is accurate and cheap compared to time taken for feature extraction from the image.
Statistics surrounding $N$ means that the window is typically sampling overlapping regions, and as such there is significant correlation between nearby samples. (Something I can even approach numerically/symbolically) Consequently, this can be thought of as a more complex function of $f(x, y, N)$ where larger $N$ will give an estimate more related to the neighborhood (highly correlated), and a smaller $N$ will give a more variable, but more local estimate.
Things I Have Tried:
Brute Computation - Works well. 95% correct segmentation with constant $N$. The results look fantastic when contoured using any standard method after that. This takes forever. I can simplify the features calculated on a per-sample basis, but ideally I want to avoid this to keep this code general to images with textures who's differences show up in different parts of the feature space.
Dumb Stepping - Take a single pixel "step" in each direction and pick the direction to move based on closeness to iso-line value. Still pretty slow, and it will ignore bifurcation of an isoline. Also, in areas with a flat gradient it will "wander" or double back on itself.
I am thinking I want to do something like the subdivison proposed in the first link, but pruned for boxes which bound the isoline of interest. I feel like I should be able to leverage $N$ also, but I am not sure how to approach that.