Guillaume Morel

Guillaume Morel, Lucas Drumetz, Simon Benaïchouche et al.

Normalizing Flows (NF) are powerful likelihood-based generative models that are able to trade off between expressivity and tractability to model complex densities. A now well established research avenue leverages optimal transport (OT) and looks for Monge maps, i.e. models with minimal effort between the source and target distributions. This paper introduces a method based on Brenier's polar factorization theorem to transform any trained NF into a more OT-efficient version without changing the final density. We do so by learning a rearrangement of the source (Gaussian) distribution that minimizes the OT cost between the source and the final density. We further constrain the path leading to the estimated Monge map to lie on a geodesic in the space of volume-preserving diffeomorphisms thanks to Euler's equations. The proposed method leads to smooth flows with reduced OT cost for several existing models without affecting the model performance.

M. Erden, B. Rosa, J. Szewczyk et al.

This paper presents an approach for understanding the soft tissue behavior in surface contact with a probe scanning the tissue. The application domain is confocal microlaparoscopy, mostly used for imaging the outer surface of the organs in the abdominal cavity. The probe is swept over the tissue to collect sequential images to obtain a large field of view with mosaicking. The problem we address is that the tissue also moves with the probe due to its softness; therefore the resulting mosaic is not in the same shape and dimension as traversed by the probe. Our approach is inspired by the finger slip studies and adapts the idea of load-slip phenomenon that explains the movement of the soft part of the finger when dragged on a hard surface. We propose the concept of loading-distance and perform measurements on beef liver and chicken breast tissues. We propose a protocol to determine the loading-distance prior to an automated scan and introduce an approach to compensate the tissue movement in raster scans. Our implementation and experiments show that we can have an image-mosaic of the tissue surface in a desired rectangular shape with this approach.

Mustafa Suphi Erden, Benoît Rosa, Jérome Szewczyk et al.

This paper presents the mechanical design of a distal scanner to perform a spiral scan for mosaic-imaging with a confocal microlaparoscope. First, it is demonstrated with ex vivo experiments that a spiral scan performs better than a raster scan on soft tissue. Then a mechanical design is developed in order to perform the spiral scan. The design in this paper is based on a conic structure with a particular curved surface. The mechanism is simple to implement and to drive; therefore, it is a low-cost solution. A 5:1 scale prototype is implemented by rapid prototyping and the requirements are validated by experiments. The experiments include manual and motor drive of the system. The manual drive demonstrates the resulting spiral motion by drawing the tip trajectory with an attached pencil. The motor drive demonstrates the speed control of the system with an analysis of video thread capturing the trajectory of a laser beam emitted from the tip.