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Image restoration requires a careful balance between noise suppression and structure preservation. While first-order total variation (TV) regularization effectively preserves edges, it often introduces staircase artifacts, whereas…
The conjugate gradient (CG) method is commonly used for the rapid solution of least squares problems. In image reconstruction, the problem can be ill-posed and also contaminated by noise; due to this, approaches such as regularization…
Over the last 30 years a plethora of variational regularisation models for image reconstruction has been proposed and thoroughly inspected by the applied mathematics community. Among them, the pioneering prototype often taught and learned…
We consider the problem of surface segmentation, where the goal is to partition a surface represented by a triangular mesh. The segmentation is based on the similarity of the normal vector field to a given set of label vectors. We propose a…
We present an out-of-core variational approach for surface reconstruction from a set of aligned depth maps. Input depth maps are supposed to be reconstructed from regular photos or/and can be a representation of terrestrial LIDAR point…
We introduce a class of higher-order anisotropic total variation regularisers, which are defined for possibly inhomogeneous, smooth elliptic anisotropies, that extends the Total Generalized Variation (TGV) regulariser and its variants. We…
Riemannian flow matching (RFM) extends flow-based generative modeling to data supported on manifolds by learning a time-dependent tangent vector field whose flow-ODE transports a simple base distribution to the data law. We develop a…
Due to their ability to handle discontinuous images while having a well-understood behavior, regularizations with total variation (TV) and total generalized variation (TGV) are some of the best-known methods in image denoising. However,…
The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV…
In this paper, we are interested in the application to video segmentation of the discrete shape optimization problem involving the shape weighted perimeter and an additional term depending on a parameter. Based on recent works and in…
This work proposes the variable exponent Lebesgue modular as a replacement for the 1-norm in total variation (TV) regularization. It allows the exponent to vary with spatial location and thus enables users to locally select whether to…
We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…
Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the $\ell_1$-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually…
We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…
Total variation (TV) regularization is popular in image restoration and reconstruction due to its ability to preserve image edges. To date, most research activities on TV models concentrate on image restoration from blurry and noisy…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
The objectives of this chapter are: (i) to introduce a concise overview of regularization; (ii) to define and to explain the role of a particular type of regularization called total variation norm (TV-norm) in computer vision tasks; (iii)…
Video Temporal Grounding (VTG) aims to localize the video segment that corresponds to a natural language query, which requires a comprehensive understanding of complex temporal dynamics. Existing Vision-LMMs typically perceive temporal…
We study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems with the image restoration problem as constraint. A general…
This article is the second work in our series of papers dedicated to image processing models based on the fractional order total variation $TV^r$. In our first work of this series, we studied key analytic properties of these semi-norms.…