050-Uncertain and Incomplete knowledge analysis in 3D surface model processing

Working with 3D images is important in many applications, for example in urban planning or to understand climatic impact in mountainous or icy landscapes. In this context, the satellite is an interesting component thanks to its ability to see large spaces in one sweep, at a lower cost than an airplane. CNES supports many activities in 3D, such as the CO3D project with Airbus, which will aim to map the earth in 3D with dedicated satellites.
CNES has a 3D restitution pipeline which generates, from an image pair, the corresponding Digital Elevation Model (DEM). This 3D tool called CARS is publicly available.This pipeline is composed of the following classical 3D steps:
Epipolar geometry transformation (image alignment)
Dense matching between images to identify homologous points: Pandora tool
Triangulation of homologous points thanks to the image geometric models
Rasterization from a point cloud to a 2.5D image

In each of these stages, uncertainty can appear:
- on the input data (geometric models, noise on the image detectors, etc.)
- on the method for computing epipolar images
- on dense matching method
- on rasterization method

Uncertainty can be linked either to stochastic uncertainty (measurement noise) or to epistemic uncertainty resulting from a lack of knowledge, especially in the models. Currently,  uncertainty is propagated in the 3D pipeline without being precisely quantified or modeled.
While probability distributions are sufficient to model purely stochastic or random uncertainty, many works suggest that it is not sufficient to describe uncertainty due to lack of knowledge or imprecision. This modeling can be done, for example, by using sets of probabilities or fuzzy sets.
This thesis aims at analyzing the different types of uncertainty and to see how to represent them using a wide set of mathematical tools like belief functions, distributions of possibilities, etc. The objective is to apply mathematical tools for modelling and propagate imprecise and uncertain knowledge through the aforementioned pipeline, and to check how classical approaches currently used can be improved to better take into account  and better quantify uncertainty in the final 3D result.

The objectives are to:

Understand the steps of a 3D pipeline and the associated uncertainties  through the CARS tool.
Identify mathematical methods for representing and propagating uncertainties in the 3D pipeline
Define how to represent information of a random or  imprecise nature in the pipeline
Understand how uncertainty propagate within the pipeline
Quantify the impact of uncertainty in the different stages in order to be able to identify which parameters impact the most on the final uncertainty.
Select which uncertainties to primarily reduce according to their characteristics and importance in order to improve the confidence in 3D restitution

Propose solutions for evaluating and improving the quality of a digital surface model, such as:
Generating an uncertainty interval for the elevation measurement and a way to represent uncertainty in the end results to users.
Providing avenues for understanding uncertainty in the 3D pipeline