### Bayesian Programming

Probability as an extension of logic

# Perception of shape from motion

PhD thesis of Francis Colas (2006)

Perception can be seen as collecting and confronting various pieces of information in order to understand the environment. Man uses many sensory modalities such as vision, touch, audition, or proprioception. Various kind of information can be conveyed by each sense. For example vision is about texture, colour, shapes or movement. Optic flow is the displacement of the image on the retina.

Man can perceive part of the shapes from optic flow alone. However, extracting structure from motion is a complicated issue.

First, perception is an inverse problem in general. Geometry can give the optic flow given the shape and movement of the objects of the scene.

Then, many configurations can lead to the same optic flow. Such an problem is said ill-posed.

Last, one can seldom be sure of some perception with an arbitrary precision. Perception is therefore an uncertain problem.

In order to solve these issue, we use the Bayesian Programing formalism. It is designed to reason with uncertainty using probabilities. Multiple solutions of an ill-posed problem are taken into account using multi-modal probability distributions. Finally, the symmetry of Bayes’ rule allows for the same inference for either direct or inverse problems.

We propose a Bayesian model of the perception of planes from the optic flow based on some explicit assumptions. The main hypotheses involved in our model are rigidity and stationarity.

Rigidity is a constraint that minimises the relative 3D motion of the observed dots.

Stationarity minimises the absolute 3D motion of the dots. We validate our model with five experiments from the literature.

For each experiment, the model reproduces qualitative features of the results and allows for an explanation of the experimental result based on the functioning of the model.

Finally, we show how to adapt our model to an experiment of perception of a corrugated surface by optic flow. We also present a Bayesian model to generate the input of our perception model and generalise the integration of our model into a more complete system.

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