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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…
In this paper we study the realizability question for commuting graphs of finite groups: Given an undirected graph $X$ is it the commuting graph of a group $G$? And if so, to determine such a group. We seek efficient algorithms for this…
In natural image matting, the goal is to estimate the opacity of the foreground object in the image. This opacity controls the way the foreground and background is blended in transparent regions. In recent years, advances in deep learning…
This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann…
In this paper, we study the compositional learning of images and texts for image retrieval. The query is given in the form of an image and text that describes the desired modifications to the image; the goal is to retrieve the target image…
In order to track the moving objects in long range against occlusion, interruption, and background clutter, this paper proposes a unified approach for global trajectory analysis. Instead of the traditional frame-by-frame tracking, our…
Recent advances in AI-powered image editing tools have significantly lowered the barrier to image modification, raising pressing security concerns those related to spreading misinformation and disinformation on social platforms. Image…
Graphical elements: particularly tables and figures contain a visual summary of the most valuable information contained in a document. Therefore, localization of such graphical objects in the document images is the initial step to…
A canonical system of basic invariants is a system of invariants satisfying a set of differential equations. The properties of a canonical system are related to the mean value property for polytopes. In this article, we naturally identify…
Recomputation algorithms collectively refer to a family of methods that aims to reduce the memory consumption of the backpropagation by selectively discarding the intermediate results of the forward propagation and recomputing the discarded…
Convolututional Neural Networks have achieved state of the art in image classification, object detection and other image related tasks. In this paper I present another use of CNNs i.e. if given a set of images and then giving a single test…
Unsupervised image-to-image translation methods learn to map images in a given class to an analogous image in a different class, drawing on unstructured (non-registered) datasets of images. While remarkably successful, current methods…
Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…
We give practical algorithms for computing the divisor class group and the gonality of a curve over a finite field, achieving several orders of magnitude speedup over existing methods for sufficiently large genus or residue field. The…
Image segmentation is a fundamental task in computer vision. Data annotation for training supervised methods can be labor-intensive, motivating unsupervised methods. Current approaches often rely on extracting deep features from pre-trained…
Scene Graph Generation has gained much attention in computer vision research with the growing demand in image understanding projects like visual question answering, image captioning, self-driving cars, crowd behavior analysis, activity…
The analysis of digital images using homological procedures is an outstanding topic in the area of Computational Algebraic Topology. In this paper, we describe a certified reduction strategy to deal with digital images, but preserving their…
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…
We propose the Canonical 3D Deformer Map, a new representation of the 3D shape of common object categories that can be learned from a collection of 2D images of independent objects. Our method builds in a novel way on concepts from…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…