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This thesis surveys the research in patch-based synthesis and algorithms for finding correspondences between small local regions of images. We additionally explore a large kind of applications of this new fast randomized matching technique.…
We present a method for estimating the maximal symmetry of a continuous regression function. Knowledge of such a symmetry can be used to significantly improve modelling by removing the modes of variation resulting from the symmetries.…
The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions), which are complete in general position and continuous under…
We introduce a novel two-step approach for estimating a probability density function (pdf) given its samples, with the second and important step coming from a geometric formulation. The procedure involves obtaining an initial estimate of…
Object recognition in humans depends primarily on shape cues. We have developed a new approach to measuring the shape recognition performance of a vision system based on nearest neighbor view matching within the system's embedding space.…
We introduce an approach based on moving frames for polygon recognition and symmetry detection. We present detailed algorithms for recognition of polygons modulo the special Euclidean, Euclidean, equi-affine, skewed-affine and similarity…
In this paper we observe that information theoretical concepts are valuable tools for extracting information from images and, in particular, information on image symmetries. It is shown that the problem of detecting reflectional and…
As a fundamental topic in graph mining, Densest Subgraph Discovery (DSD) has found a wide spectrum of real applications. Several DSD algorithms, including exact and approximation algorithms, have been proposed in the literature. However,…
In this paper we propose a global optimization-based approach to jointly matching a set of images. The estimated correspondences simultaneously maximize pairwise feature affinities and cycle consistency across multiple images. Unlike…
In this work, we describe a generic approach to show convergence with high probability for stochastic convex optimization. In previous works, either the convergence is only in expectation or the bound depends on the diameter of the domain.…
We present a new method for estimating the 6D pose of rigid objects with available 3D models from a single RGB input image. The method is applicable to a broad range of objects, including challenging ones with global or partial symmetries.…
Approximate convex decomposition aims to decompose a 3D shape into a set of almost convex components, whose convex hulls can then be used to represent the input shape. It thus enables efficient geometry processing algorithms specifically…
Robotic grasping is facing a variety of real-world uncertainties caused by non-static object states, unknown object properties, and cluttered object arrangements. The difficulty of grasping increases with the presence of more uncertainties,…
Most recent 6D object pose estimation methods first use object detection to obtain 2D bounding boxes before actually regressing the pose. However, the general object detection methods they use are ill-suited to handle cluttered scenes, thus…
Detecting changes in high-dimensional vectors presents significant challenges, especially when the post-change distribution is unknown and time-varying. This paper introduces a novel robust algorithm for correlation change detection in…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
Digitising the 3D world into a clean, CAD model-based representation has important applications for augmented reality and robotics. Current state-of-the-art methods are computationally intensive as they individually encode each detected…
Particle tracking is common in many biophysical, ecological, and micro-fluidic applications. Reliable tracking information is heavily dependent on of the system under study and algorithms that correctly determines particle position between…
This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. In this paper, we…
We introduce Patchwork, a new general-purpose shape representation capable of modeling 2D and 3D geometry with a small number of parameters. Patchwork is grounded in a rigorous mathematical framework, providing provable complexity bounds…