Expressing Bayesian Fusion as a Product of Distributions: Application to Randomized Hough TransformCPradalierauthorFColasauthorPBessiereauthorData fusion is a common issue of mobile robotics, computer assisted
medical diagnosis or behavioral control of simulated character for instance. However
data sources are often noisy, opinion for experts are not known with absolute
precision, and motor commands do not act in the same exact manner on the environment.
In these cases, classic logic fails to manage efficiently the fusion process.
Confronting different knowledge in an uncertain environment can therefore be adequately
formalized in the bayesian framework.
Besides, bayesian fusion can be expensive in terms of memory usage and processing
time. This paper precisely aims at expressing any bayesian fusion process as a
product of probability distributions in order to reduce its complexity. We first study
both direct and inverse fusion schemes. We show that contrary to direct models,
inverse local models need a specific prior in order to allow the fusion to be computed
as a product. We therefore propose to add a consistency variable to each local
model and we show that these additional variables allow the use of a product of the
local distributions in order to compute the global probability distribution over the
fused variable. Finally, we take the example of the Randomized Hough Transform.
We rewrite it in the bayesian framework, considering that it is a fusion process
to extract lines from couples of dots in a picture. As expected, we can find back
the expression of the Randomized Hough Transform from the literature with the
appropriate assumptions.Robotics2003Conference Paper