Related papers: The use of discrete gradient methods for total var…
We revisit total variation denoising and study an augmented model where we assume that an estimate of the image gradient is available. We show that this increases the image reconstruction quality and derive that the resulting model…
Intrinsic image decomposition is the process of recovering the image formation components (reflectance and shading) from an image. Previous methods employ either explicit priors to constrain the problem or implicit constraints as formulated…
We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories…
Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently. However, existing methods require the nonconvex regularization to be smooth or simple to ensure convergence. In this paper, we…
Coherent ptychographic imaging experiments often discard over 99.9 % of the flux from a light source to define the coherence of an illumination. Even when coherent flux is sufficient, the stability required during an exposure is another…
We further develop a new framework, called PDE Acceleration, by applying it to calculus of variations problems defined for general functions on $\mathbb{R}^n$, obtaining efficient numerical algorithms to solve the resulting class of…
In this thesis, we offer a thorough investigation of different regularisation terms used in variational imaging problems, together with detailed optimisation processes of these problems. We begin by studying smooth problems and partially…
This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image…
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the…
Gradient methods are frequently used in large scale image deblurring problems since they avoid the onerous computation of the Hessian matrix of the objective function. Second order information is typically sought by a clever choice of the…
Normalization layers are widely used in deep neural networks to stabilize training. In this paper, we consider the training of convolutional neural networks with gradient descent on a single training example. This optimization problem…
Modern deep learning techniques focus on extracting intricate information from data to achieve accurate predictions. However, the training datasets may be crowdsourced and include sensitive information, such as personal contact details,…
Derivatives of computer graphics, image processing, and deep learning algorithms have tremendous use in guiding parameter space searches, or solving inverse problems. As the algorithms become more sophisticated, we no longer only need to…
This paper presents a process for estimating the spatially varying surface reflectance of complex scenes observed under natural illumination. In contrast to previous methods, our process is not limited to scenes viewed under controlled…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
In this paper, we propose several novel deep learning methods for object saliency detection based on the powerful convolutional neural networks. In our approach, we use a gradient descent method to iteratively modify an input image based on…
For fourth-order geometric evolution equations for planar curves with the dissipation of the bending energy, including the Willmore and the Helfrich flows, we consider a numerical approach. In this study, we construct a structure-preserving…
Anisotropic diffusion is a well recognized tool in digital image processing, including edge detection and denoising. We present here a particular nonlinear time-dependent operator together with an appropriate high-order discretization for…
Image segmentation is a key topic in image processing and computer vision with applications such as scene understanding, medical image analysis, robotic perception, video surveillance, augmented reality, and image compression, among many…
A systematic digital-discrete method for obtaining continuous functions with smoothness to a certain order (C^(n)) from sample data is designed. This method is based on gradually varied functions and the classical finite difference method.…