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Understanding sequential information is a fundamental task for artificial intelligence. Current neural networks attempt to learn spatial and temporal information as a whole, limited their abilities to represent large scale spatial…
When using Convolutional Neural Networks (CNNs) for segmentation of organs and lesions in medical images, the conventional approach is to work with inputs and outputs either as single slice (2D) or whole volumes (3D). One common…
Purpose AI-based methods for anatomy segmentation can help automate characterization of large imaging datasets. The growing number of similar in functionality models raises the challenge of evaluating them on datasets that do not contain…
This paper presents a semantic planar SLAM system that improves pose estimation and mapping using cues from an instance planar segmentation network. While the mainstream approaches are using RGB-D sensors, employing a monocular camera with…
Let $\mathbb{R}$ be the field of real numbers. We consider the problem of computing the real isolated points of a real algebraic set in $\mathbb{R}^n$ given as the vanishing set of a polynomial system. This problem plays an important role…
Taking projections of high-dimensional data is a common analytical and visualisation technique in statistics for working with high-dimensional problems. Sectioning, or slicing, through high dimensions is less common, but can be useful for…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
In this paper we present new data structures for two extensively studied variants of the orthogonal range searching problem. First, we describe a data structure that supports two-dimensional orthogonal range minima queries in $O(n)$ space…
In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We…
Semantic segmentation is the pixel-wise labelling of an image. Since the problem is defined at the pixel level, determining image class labels only is not acceptable, but localising them at the original image pixel resolution is necessary.…
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…
It is well-known that any sum of squares (SOS) program can be cast as a semidefinite program (SDP) of a particular structure and that therein lies the computational bottleneck for SOS programs, as the SDPs generated by this procedure are…
Simultaneous localization and mapping (SLAM) is a critical capability in autonomous navigation, but memory and computational limits make long-term application of common SLAM techniques impractical; a robot must be able to determine what…
We survey both old and new developments in the theory of algorithms in real algebraic geometry -- starting from effective quantifier elimination in the first order theory of reals due to Tarski and Seidenberg, to more recent algorithms for…
In Computer Vision, edge detection is one of the favored approaches for feature and object detection in images since it provides information about their objects boundaries. Other region-based approaches use probabilistic analysis such as…
Research in Simultaneous Localization And Mapping (SLAM) is increasingly moving towards richer world representations involving objects and high level features that enable a semantic model of the world for robots, potentially leading to a…
This dissertation addresses visual scene understanding and enhances segmentation performance and generalization, training efficiency of networks, and holistic understanding. First, we investigate semantic segmentation in the context of…
The incorporation of cutting planes within the branch-and-bound algorithm, known as branch-and-cut, forms the backbone of modern integer programming solvers. These solvers are the foremost method for solving discrete optimization problems…
We investigate the problem of scanning and prediction ("scandiction", for short) of multidimensional data arrays. This problem arises in several aspects of image and video processing, such as predictive coding, for example, where an image…
We propose Seg&Struct, a supervised learning framework leveraging the interplay between part segmentation and structure inference and demonstrating their synergy in an integrated framework. Both part segmentation and structure inference…