# Integral Geometric Dual Distributions of Multilinear Models

## TL;DR

This paper introduces an integral geometric method to compute dual distributions of parameter estimates in multilinear models, enabling analysis of uncertainty and confidence intervals in feature distributions.

## Contribution

It presents a novel integral geometric approach using Radon transforms to derive analytical dual distributions for various multilinear models.

## Key findings

- Allows computation of dual distributions from parameter estimates
- Enables analysis of uncertainty in feature and training data distributions
- Provides a framework for deriving confidence intervals of model parameters

## Abstract

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.