Related papers: Shearlets on Bounded Domains
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…
One of the reasons for the success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains of arbitrary shape. In the case of second order…
Most image labeling problems such as segmentation and image reconstruction are fundamentally ill-posed and suffer from ambiguities and noise. Higher order image priors encode high level structural dependencies between pixels and are key to…
Two-region image segmentation is the process of dividing an image into two regions of interest, i.e., the foreground and the background. To this aim, Chan et al. [Chan, Esedo\=glu, Nikolova, SIAM Journal on Applied Mathematics 66(5),…
Microlocal analysis provides deep insight into singularity structures and is often crucial for solving inverse problems, predominately, in imaging sciences. Of particular importance is the analysis of wavefront sets and the correct…
Image segmentation is widely used in a variety of computer vision tasks, such as object localization and recognition, boundary detection, and medical imaging. This thesis proposes deep learning architectures to improve automatic object…
In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and…
The problem of image segmentation is known to become particularly challenging in the case of partial occlusion of the object(s) of interest, background clutter, and the presence of strong noise. To overcome this problem, the present paper…
Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…
Dictionary learning algorithms have been successfully used in both reconstructive and discriminative tasks, where the input signal is represented by a linear combination of a few dictionary atoms. While these methods are usually developed…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
The problem of ensuring constraints satisfaction on the output of machine learning models is critical for many applications, especially in safety-critical domains. Modern approaches rely on penalty-based methods at training time, which do…
The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…
In recent papers the author introduced a simple alternative to isoparametric finite elements of the n-simplex type, to enhance the accuracy of approximations of second-order boundary value problems with Dirichlet conditions, posed in smooth…
While deep Embedding Learning approaches have witnessed widespread success in multiple computer vision tasks, the state-of-the-art methods for representing natural images need not necessarily perform well on images from other domains, such…
This paper is concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to data and a total variation constraint.…
Recent years have witnessed great progress in deep learning based object detection. However, due to the domain shift problem, applying off-the-shelf detectors to an unseen domain leads to significant performance drop. To address such an…
Image segmentation is a fundamental and challenging problem in computer vision with applications spanning multiple areas, such as medical imaging, remote sensing, and autonomous vehicles. Recently, convolutional neural networks (CNNs) have…
Segment Anything Model (SAM) has revolutionized the way of segmentation. However, SAM's performance may decline when applied to tasks involving domains that differ from natural images. Nonetheless, by employing fine-tuning techniques, SAM…