Colloquium Computer Science - Phuc Ngo, LORIA, Université de Lorraine

Title: Rigid Motions on Digital Images

Abstract:

In many applications of image processing, computer vision, or data augmentation techniques in deep learning, it requires applying geometric transformations to images. Despite the discrete nature of digital images, these transformations are often applied as continuous transformations, followed by discretization (usually involving sampling and interpolation). However, interpolation paradigms can alter the nature of the image and lead to unwanted visual biases. As for the sampling paradigms, they can cause geometric approximation errors. Other issues concern the topological properties of observed objects, whose preservation is often desirable in image analysis.

In this talk, we will first outline the different issues that can arise when applying geometric transformations to digital images. Then, several solutions that have been proposed in the field of digital geometry will be presented to deal mainly with the problems related to the topological and geometric preservation of transformed images. For this, different notions and tools will be introduced, such as digital convexity, topological invariant, regularity, etc. Examples are given to illustrate the mentioned problems as well as the proposed solutions in the context of digital image processing and analysis.

Additionally, within the presentation, we share recent results derived from the utilization of digital geometry tools in wood image processing, specifically aiming at enhancing tree growth rings. This operator enables diverse applications in estimating wood log quality, such as counting the number of tree rings or determining their average width.