Integral Geometric Dual Distributions of Multilinear Models
This work provides a method for analyzing uncertainty in feature distributions tied to training data, which is incremental for applications in computer vision and geometry.
The authors tackled the problem of computing dual distributions for multilinear model parameters using an integral geometric approach, resulting in analytical forms derived from maximum likelihood estimator asymptotic normality and generalized Radon transforms.
We propose an integral geometric approach for computing dual distributions for the parameter distributions of multilinear models. The dual distributions can be computed from, for example, the parameter distributions of conics, multiple view tensors, homographies, or as simple entities as points, lines, and planes. The dual distributions have analytical forms that follow from the asymptotic normality property of the maximum likelihood estimator and an application of integral transforms, fundamentally the generalised Radon transforms, on the probability density of the parameters. The approach allows us, for instance, to look at the uncertainty distributions in feature distributions, which are essentially tied to the distribution of training data, and helps us to derive conditional distributions for interesting variables and characterise confidence intervals of the estimates.