Summary:
This paper is all about curves and making them as smooth as possible. It begins with some definitions about their equations and some basic mathematic procedure. The next section deals with the basic curvature estimations based mostly on direction change. It goes in depth on how local convexity can be used to add "weight" to a curve and make it much less error-prone. It further goes on to add local monotonicity to the mix. Local monotonicity allows for the convexity to check local points but does not add that convexity unless it's lower than the current minimum value. Ample examples are given to explain this. The paper then shows results of a user study adding each of the elements one at a time, showing how the system gets more accurate and smooth each time a new feature is added, leading to better results.
Discussion:
This paper was slightly confusing the first time through, but it did make sense eventually. The concept of monotonicity really is not a simple one but it is extremely useful. Usually I don't like non-simple solutions but after you understand it it becomes incredibly clear. I think this is probably one of the best curvature estimations that I have seen so far, and really isn't hard to implement, making it my favorite.
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1 comment:
I can understand why you thought that this paper seemed a bit confusing at first. The paper pretty much went straight into the details without what I thought, to be a clear motivation as to why it was done. With how curve estimation was done in the previous papers, I thought the approach done by Kim et al was quite novel in how it computes curvature estimation based on curvatures and its direction in terms of a neighborhood of points. As a consequence, it also has an added benefit of a pseudo-error reducing mechanism. In other words, I think that if there is a point with some noise, its error won't affect the rest of the points as much as if the point's significance was more so computed alone.
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