Publications related to Caustic Art

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We propose a semantic shape editing method to edit 3D triangle meshes using parametric implicit surface templates, benefiting from the many advantages offered by analytical implicit representations, such as infinite resolution and boolean or blending opera ...

We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good g ...

Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...

This paper develops a fast algorithm for computing the equilibrium assignment with the perturbed utility route choice (PURC) model. Without compromise, this allows the significant advantages of the PURC model to be used in large-scale applications. We form ...

Photometric stereo, a computer vision technique for estimating the 3D shape of objects through images captured under varying illumination conditions, has been a topic of research for nearly four decades. In its general formulation, photometric stereo is an ...

Modeling the 3D internal crack under compression entails complex fracture mechanics (mode I-II-III fracture), resulting in substantial computational costs and challenges in characterizing fracture morphology characterization for Phase Field Method (PFM) si ...

Detailed modeling of the evolution of neutral hydrogen in the intergalactic medium during the Epoch of Reionization, 5≤z≤20, is critical in interpreting the cosmological signals from current and upcoming 21-cm experiments such as the Low-Frequency Array (L ...

Distributed learning is the key for enabling training of modern large-scale machine learning models, through parallelising the learning process. Collaborative learning is essential for learning from privacy-sensitive data that is distributed across various ...

Recent advancements in deep learning have revolutionized 3D computer vision, enabling the extraction of intricate 3D information from 2D images and video sequences. This thesis explores the application of deep learning in three crucial challenges of 3D com ...

In this paper, we present a new parameterization and optimization procedure for minimizing the weight of ribbed plates. The primary goal is to reduce embodied CO2 in concrete floors as part of the effort to diminish the carbon footprint of the construction ...

The optical domain presents potential avenues for enhancing both computing and communication due to its inherent properties of bandwidth, parallelism, and energy efficiency. This research focuses on harnessing 3-Dimensional (3D) diffractive optics for nove ...

Quantum support vector machines employ quantum circuits to define the kernel function. It has been shown that this approach offers a provable exponential speedup compared to any known classical algorithm for certain data sets. The training of such models c ...

Computing light reflection from rough surfaces is an important topic in computer graphics. Reflection models developed based on geometric optics fail to capture wave effects such as diffraction and interference, while existing models based on physical opti ...

Omnidirectional video streaming is usually implemented based on the representations of tiles, where the tiles are obtained by splitting the video frame into several rectangular areas and each tile is converted into multiple representations with different r ...

Control systems operating in real-world environments often face disturbances arising from measurement noise and model mismatch. These factors can significantly impact the perfor- mance and safety of the system. In this thesis, we aim to leverage data to de ...

We propose ordering-based approaches for learning the maximal ancestral graph (MAG) of a structural equation model (SEM) up to its Markov equivalence class (MEC) in the presence of unobserved variables. Existing ordering-based methods in the literature rec ...

A method for enforcing smoothness constraints on surface meshes produced by a Graph Convolutional Neural Network (GCNN) including the steps of reading image data from a memory, the image data including two-dimensional image data representing a three-dimens ...

In this paper, we present a spatial branch and bound algorithm to tackle the continuous pricing problem, where demand is captured by an advanced discrete choice model (DCM). Advanced DCMs, like mixed logit or latent class models, are capable of modeling de ...

This paper presents a novel distributed approach for solving AC power flow (PF) problems. The optimization problem is reformulated into a distributed form using a communication structure corresponding to a hypergraph, by which complex relationships between ...

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

Caustic Art

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Semantic Shape Editing with Parametric Implicit Templates

The effect of smooth parametrizations on nonconvex optimization landscapes

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

Perturbed Utility Stochastic Traffic Assignment

Aggregating Spatial and Photometric Context for Photometric Stereo

An adaptive phase field approach to 3D internal crack growth in rocks

pyC 2 Ray: A flexible and GPU-accelerated radiative transfer framework for simulating the cosmic epoch of reionization

Optimization Algorithms for Decentralized, Distributed and Collaborative Machine Learning

Advancing Self-Supervised Deep Learning for 3D Scene Understanding

Mesh-based topology, shape and sizing optimization of ribbed plates

3D diffractive optics for linear interconnects and nonlinear processing

The complexity of quantum support vector machines

A Full-Wave Reference Simulator for Computing Surface Reflectance

Quality-Constrained Encoding Optimization for Omnidirectional Video Streaming

Data-Driven Control and Optimization under Noisy and Uncertain Conditions

Novel Ordering-based Approaches for Causal Structure Learning in the Presence of Unobserved Variables

A method and system for enforcing smoothness constraints on surface meshes from a graph convolutional neural network

A Spatial Branch and Bound Algorithm for Continuous Pricing with Advanced Discrete Choice Demand Modeling

Hypergraph-Based Fast Distributed AC Power Flow Optimization

Augmented Lagrangian Methods for Provable and Scalable Machine Learning