arXiv subjects

Antonin Clerc

Publications and source records attributed to Antonin Clerc.

3 recordsLinked to original sources

arXiv2026

HOT-POT: Optimal Transport for Sparse Stereo Matching

Stereo vision between images faces a range of challenges, including occlusions, motion, and camera distortions, across applications in autonomous driving, robotics, and face analysis. Due to parameter sensitivity, further complications arise for stereo matching with sparse features, such as facial landmarks. To overcome this ill-posedness and enable unsupervised sparse matching, we consider line constraints of the camera geometry from an optimal transport (OT) viewpoint. Formulating camera-projected points as (half)lines, we propose the use of the classical epipolar distance as well as a 3D ray distance to quantify matching quality. Employing these distances as a cost function of a (partial) OT problem, we arrive at efficiently solvable assignment problems. Moreover, we extend our approach to unsupervised object matching by formulating it as a hierarchical OT problem. The resulting algorithms allow for efficient feature and object matching, as demonstrated in our numerical experiments. Here, we focus on applications in facial analysis, where we aim to match distinct landmarking conventions.

cs.CV↗

arXiv2026

Reinterpreting EMML as Mirror Descent for Constrained Maximum Likelihood Estimation

The Expectation--Maximization Maximum Likelihood (EMML) algorithm belongs to the Expectation--Maximization family and is widely used for image reconstruction problems under Poisson noise. In this paper, we reinterpret EMML as a mirror descent method applied to a reparametrized objective function. This perspective allows us to incorporate convex constraints into the algorithm through appropriately chosen Bregman projections, while preserving the multiplicative structure of the EMML updates to ensure computational efficiency. We then establish the convergence of the resulting algorithm toward a solution of the constrained maximum-likelihood problem. Numerical experiments on hyperspectral unmixing problems demonstrate that the constrained EMML converges in fewer iterations than the classical EMML.

math.OC↗

arXiv2026

i-DEQ: A stable inertial deep equilibrium model for image restoration

Deep Equilibrium Models (DEQs) are an established framework for image restoration that learn a problem-adapted regularization by solving a fixed-point (i.e. equilibrium) problem. While flexible and expressive, DEQs are often hindered by high computational cost and training instability. We propose an inertial DEQ (i-DEQ) that learns an explicit nonconvex regularization within the DEQ formulation. By using momentum within the fixed-point iterations, i-DEQ has convergence guarantees and accelerated rates. Moreover, we observe that i-DEQ is significantly more stable during the training and robust to rough initialization than DEQs. Numerical experiments on various linear and nonlinear inverse problems demonstrate that i-DEQ achieves reconstruction quality comparable to state-of-the-art methods, while reducing DEQ's inference time by a factor of two.

math.OC↗