Open SeanGuo063 opened 7 months ago
Hi @SeanGuo063,
Actually, using the point with the maximum density value is not a good idea for extracting a surface, for several reasons. Please let me explain them below.
If we select the surface with maximum density value, we would extract only a single point from this Gaussian blob, which would be the center point of the Gaussian. However, our brain does not perceive a single point when looking at a Gaussian; we see an ellipsoid, with a fuzzy border. Therefore, "the true surface" as our brain perceives it actually corresponds to a isosurface with a lambda value lower than 1! To select a good lambda value for the isosurface, we have to answer this question: Where should we draw the border that defines the ellipsoid when looking at this image? Intuitively, lambda=0.5 or lambda=0.3 are generally pretty good guesses as you can see in the picture. It turns out that experimental results confirm this intuition, as we show in the paper.
I have a question of mesh extraction. Why using lambda,rather than finding the point with the maximum density value along the ray, since max density should theoretically be corresponding to the true surface.