Code, Algorithms and Probabilities

Line Fitting with Gaussian Belief Propagation in Python

What changes when the variables are continuous and the distributions Gaussian, worked through on a piecewise line fit in Python.

By Mario Lüder

Posted on August 21, 2023

Gaussian Belief Propagation is a variant of Belief Propagation and used for inference on graphical models if the underlying distribution is described as a Gaussian. [Read More]

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Image Denoising with Loopy Belief Propagation in Python

A Markov random field over image pixels, with the messages run to convergence in Python — the first example here where the graph really has loops.

By Mario Lüder

Posted on September 24, 2022

I want to continue my previous post with a (useful) example to get more a feel how to use Loopy Belief Propagation in practice. The aim is to remove noise from an image - which is only a toy example. [Read More]

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Loopy Belief Propagation on Factor Graphs, in Python

Message passing on a factor graph, worked through message by message and then in Python, including how the products of the distributions are computed.

By Mario Lüder

Posted on September 17, 2022

This is about how to implement Loopy Belief Propagation in Python and to understand the calculations in detail. [Read More]

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Path Planning with Quintic Polynomials in Frenet Coordinates

How to generate jerk-minimising trajectories for a vehicle in a Frenet frame: the quintic polynomial derived, with the Python that produces the paths.

By Mario Lüder

Posted on February 13, 2022

This is an introduction on how to compute a driving path for an autonomous vehicle. In this article, I focus only the trajectory creation. Obstacle perception and avoidance shall be out of scope. [Read More]

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