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Deep learning-based medical image segmentation techniques have shown promising results when evaluated based on conventional metrics such as the Dice score or Intersection-over-Union. However, these fully automatic methods often fail to meet…
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…
Factorization machine (FM) variants are widely used for large scale real-time content recommendation systems, since they offer an excellent balance between model accuracy and low computational costs for training and inference. These systems…
This paper is concerned with the $\Gamma$-limits of Ambrosio-Tortorelli-type functionals, for maps $u$ defined on an open bounded set $\Omega\subset\mathbb R^n$ and taking values in the unit circle $\mathbb S^1\subset\mathbb R^2$. Depending…
Given cell-average data values of a piecewise smooth bivariate function $f$ within a domain $\Omega$, we look for a piecewise adaptive approximation to $f$. We are interested in an explicit and global (smooth) approach. Bivariate…
Image segmentation is a critical task in microscopy, essential for accurately analyzing and interpreting complex visual data. This task can be performed using custom models trained on domain-specific datasets, transfer learning from…
Motivated by conforming finite element methods for elliptic problems of second order, we analyze the approximation of the gradient of a target function by continuous piecewise polynomial functions over a simplicial mesh. The main result is…
Hyperspectral images provide a rich representation of the underlying spectrum for each pixel, allowing for a pixel-wise classification/segmentation into different classes. As the acquisition of labeled training data is very time-consuming,…
Semantic segmentation with fine-grained pixel-level accuracy is a fundamental component of a variety of computer vision applications. However, despite the large improvements provided by recent advances in the architectures of convolutional…
As a specific semantic segmentation task, aerial imagery segmentation has been widely employed in high spatial resolution (HSR) remote sensing images understanding. Besides common issues (e.g. large scale variation) faced by general…
Segmenting images of low quality or with missing data is a challenging problem. Integrating statistical prior information about the shapes to be segmented can improve the segmentation results significantly. Most shape-based segmentation…
A non parametric, level set free method is proposed for detecting image boundaries using the shape gradient of the Mumford Shah energy for segmentation. Minimizing the variance in pixel intensities inside and outside a boundary set of…
Image segmentation techniques are predominately based on parameter-laden optimization. The objective function typically involves weights for balancing competing image fidelity and segmentation regularization cost terms. Setting these…
Spectral graph theory is well known and widely used in computer vision. In this paper, we analyze image segmentation algorithms that are based on spectral graph theory, e.g., normalized cut, and show that there is a natural connection…
In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
The approximation of smooth functions with a spectral basis typically leads to rapidly decaying coefficients where the rate of decay depends on the smoothness of the function and vice-versa. The optimal number of degrees of freedom in the…
Segmentations are often necessary for the analysis of image data. They are used to identify different objects, for example cell nuclei, mitochondria, or complete cells in microscopic images. There might be features in the data, that cannot…