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The goal of this project is to learn a 3D shape representation that enables accurate surface reconstruction, compact storage, efficient computation, consistency for similar shapes, generalization across diverse shape categories, and…

With the advent of deep neural networks, learning-based approaches for 3D reconstruction have gained popularity. However, unlike for images, in 3D there is no canonical representation which is both computationally and memory efficient yet…

Low-rank approximation models of data matrices have become important machine learning and data mining tools in many fields including computer vision, text mining, bioinformatics and many others. They allow for embedding high-dimensional…

Neural implicit functions have achieved impressive results for reconstructing 3D shapes from single images. However, the image features for describing 3D point samplings of implicit functions are less effective when significant variations…

Recent work in mechanistic interpretability has shown that decomposing models in parameter space may yield clean handles for analysis and intervention. Previous methods have demonstrated successful applications on a wide range of toy…

Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a…

Deep learning approaches to 3D shape segmentation are typically formulated as a multi-class labeling problem. Existing models are trained for a fixed set of labels, which greatly limits their flexibility and adaptivity. We opt for top-down…

Recently, implicit neural representations have gained popularity for learning-based 3D reconstruction. While demonstrating promising results, most implicit approaches are limited to comparably simple geometry of single objects and do not…

Neuro-symbolic neural networks have been extensively studied to integrate symbolic operations with neural networks, thereby improving systematic generalization. Specifically, Tensor Product Representation (TPR) framework enables neural…

This paper proposes a 3D shape descriptor network, which is a deep convolutional energy-based model, for modeling volumetric shape patterns. The maximum likelihood training of the model follows an "analysis by synthesis" scheme and can be…

Building accurate maps is a key building block to enable reliable localization, planning, and navigation of autonomous vehicles. We propose a novel approach for building accurate maps of dynamic environments utilizing a sequence of LiDAR…

Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…

Detailed 3D building models are crucial for urban planning, digital twins, and disaster management applications. While Level of Detail 1 (LoD)1 and LoD2 building models are widely available, they lack detailed facade elements essential for…

We present a simple yet effective method to address loop closure detection in simultaneous localisation and mapping using local 3D deep descriptors (L3Ds). L3Ds are emerging compact representations of patches extracted from point clouds…

Reconstructing high-quality 3D objects from sparse, partial observations from a single view is of crucial importance for various applications in computer vision, robotics, and graphics. While recent neural implicit modeling methods show…

We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of…

Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…

Depth estimation plays a pivotal role in advancing human-robot interactions, especially in indoor environments where accurate 3D scene reconstruction is essential for tasks like navigation and object handling. Monocular depth estimation,…

Neural network training is commonly based on SGD. However, the understanding of SGD's ability to converge to good local minima, given the non-convex nature of loss functions and the intricate geometric characteristics of loss landscapes,…

Modern data sets, such as those in healthcare and e-commerce, are often derived from many individuals or systems but have insufficient data from each source alone to separately estimate individual, often high-dimensional, model parameters.…