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The factor graph representation and analysis lends itself to simplified understanding and reasoning about the relationship between poses, measurements, loop clo

by beambot 10y ago

The factor graph representation and analysis lends itself to simplified understanding and reasoning about the relationship between poses, measurements, loop closures, etc. in a way that is simple and intuitive. Dellaert then uses that intuitive structure to show how to setup the problem in a way that can be efficiently computed using linear algebra. To use another example: Let's say you understand and prefer to use QR factorization for some linear algebra use case. That doesn't mean that Cholesky or SVD are somehow "worthless" tools -- they just provide other useful insights or applications. I personally find Dellaert's decomposition of the problem useful. It doesn't hurt that he was one of the early SLAM "inventors" (along with the likes of Fox, Burguard, et al). And since the topic of the post is (literally) probabilistic graphical models, it seems extremely relevant to this thread. (I read through the article you linked. I do not agree that it is an "easier" or "simpler" formulation.)

rsp1984 10y ago
> Dellaert then uses that intuitive structure to show how to setup the problem in a way that can be efficiently computed using linear algebra. But Dellaert didn't invent Factor Graphs, nor how to map a Factor Graphs to a Least Squares problem. Others did that way before him. My criticism is directed towards his style of writing about SLAM in terms of probabilities and densities, which, IMO, is moot since at the end of the day he's just using Gaussians as everyone else and hence everything boils down to a Least Squares problem again. His probabilistic viewpoint is just a detour, a distraction at that point. If he contributed a different kind of solver that could deal with arbitrary distributions then his probabilistic viewpoint would make a whole lot more sense but as long as it's just Gaussians I just don't see the point.
- utkarshsinha 10y ago
  You're wrong. What you're suggesting is there is no merit in going for an O(n^2) sorting algorithm to O(nlogn) and then to an O(n^1.2534) sorting algorithm. SLAM at a multi-city scale can use mathematical trickery to improve runtime. Sure, a new solver would help - but we don't need it as long as there is another trick up the mathematician's sleeve. Oh, and it's harder to come up with a new solver / technique.

by beambot 10y ago

rsp1984 10y ago

> Dellaert then uses that intuitive structure to show how to setup the problem in a way that can be efficiently computed using linear algebra. But Dellaert didn't invent Factor Graphs, nor how to map a Factor Graphs to a Least Squares problem. Others did that way before him. My criticism is directed towards his style of writing about SLAM in terms of probabilities and densities, which, IMO, is moot since at the end of the day he's just using Gaussians as everyone else and hence everything boils down to a Least Squares problem again. His probabilistic viewpoint is just a detour, a distraction at that point. If he contributed a different kind of solver that could deal with arbitrary distributions then his probabilistic viewpoint would make a whole lot more sense but as long as it's just Gaussians I just don't see the point.

utkarshsinha 10y ago
You're wrong. What you're suggesting is there is no merit in going for an O(n^2) sorting algorithm to O(nlogn) and then to an O(n^1.2534) sorting algorithm. SLAM at a multi-city scale can use mathematical trickery to improve runtime. Sure, a new solver would help - but we don't need it as long as there is another trick up the mathematician's sleeve. Oh, and it's harder to come up with a new solver / technique.