Related papers: Complex-order Derivative and Integral Filters and …
Corner detection is widely used in various computer vision tasks, such as image matching and 3D reconstruction. Our research indicates that there are theoretical flaws in Zhang et al.'s use of a simple corner model to obtain a series of…
Medical imaging based prostate cancer diagnosis procedure uses intra-operative transrectal ultrasound (TRUS) imaging to visualize the prostate shape and location to collect tissue samples. Correct tissue sampling from prostate requires…
We introduce a continuous-order integral analog of the Maclaurin expansion that reconstructs analytic functions from fractional derivative data. The operator integrates over continuous order, replacing the discrete sum of integer…
Deep learning-based image processing is capable of creating highly appealing results. However, it is still widely considered as a "blackbox" transformation. In medical imaging, this lack of comprehensibility of the results is a sensitive…
Chromatic derivatives and series expansions of bandlimited functions have recently been introduced in signal processing and they have been shown to be useful in practical applications. We extend the notion of chromatic derivative using…
Many deep learning architectures for semantic segmentation involve a Fully Convolutional Neural Network (FCN) followed by a Conditional Random Field (CRF) to carry out inference over an image. These models typically involve unary potentials…
The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide…
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…
Segmentation of regions of interest in images of patients, is a crucial step in many medical procedures. Deep neural networks have proven to be particularly adept at this task. However, a key question is what type of deep neural network to…
A modification of the standard Boris algorithm, called filtered Boris algorithm, is proposed for the numerical integration of the equations of motion of charged particles in a strong non-uniform magnetic field in the asymptotic scaling…
The set E of functions f fulfilling some conditions is taken to be the definition domain of s-order integral operator J^s (iterative integral), first for any positive integer s and after for any positive s (fractional, transcendental {\pi}…
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…
Composed image retrieval, a task involving the search for a target image using a reference image and a complementary text as the query, has witnessed significant advancements owing to the progress made in cross-modal modeling. Unlike the…
Image restoration problems are typically ill-posed requiring the design of suitable priors. These priors are typically hand-designed and are fully instantiated throughout the process. In this paper, we introduce a novel framework for…
Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questions and employing different methodologies. It is the purpose…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
In many scenarios, a state-space model depends on a parameter which needs to be inferred from data. Using stochastic gradient search and the optimal filter (first-order) derivative, the parameter can be estimated online. To analyze the…
We address the issue of large-order expansions in strong-field QED. Our approach is based on the one-loop effective action encoded in the associated photon polarisation tensor. We concentrate on the simple case of crossed fields aiming at…
The paper considers causal smoothing of the real sequences, i.e.,discrete time processes in a deterministic setting. A family of causal linear time-invariant filters is suggested. These filters approximate the gain decay for some non-causal…
An algorithm for the estimation of multiple targets from partial and corrupted observations is introduced based on the concept of partially-distinguishable multi-target system. It combines the advantages of engineering solutions like MHT…