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This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…

With the advent of deep learning, object detection drifted from a bottom-up to a top-down recognition problem. State of the art algorithms enumerate a near-exhaustive list of object locations and classify each into: object or not. In this…

In order to determine the 3D structure of a thick sample, researchers have recently combined ptychography (for high resolution) and tomography (for 3D imaging) in a single experiment. 2-step methods are usually adopted for reconstruction,…

In this paper we provide rigorous proof for the convergence of an iterative voting-based image segmentation algorithm called Active Masks. Active Masks (AM) was proposed to solve the challenging task of delineating punctate patterns of…

Most advanced unsupervised anomaly detection (UAD) methods rely on modeling feature representations of frozen encoder networks pre-trained on large-scale datasets, e.g. ImageNet. However, the features extracted from the encoders that are…

Ptychography is a data-intensive computational imaging technique that achieves high spatial resolution over large fields of view. The technique involves scanning a coherent beam across overlapping regions and recording diffraction patterns.…

We propose a general alternating minimization algorithm for nonconvex optimization problems with separable structure and nonconvex coupling between blocks of variables. To fix our ideas, we apply the methodology to the problem of blind…

Most unsupervised image anomaly localization methods suffer from overgeneralization because of the high generalization abilities of convolutional neural networks, leading to unreliable predictions. To mitigate the overgeneralization, this…

We address the problems of measuring geometric similarity between 3D scenes, represented through point clouds or range data frames, and associating them. Our approach leverages macro-scale 3D structural geometry - the relative configuration…

To produce cartographic maps, simplification is typically used to reduce complexity of the map to a legible level. With schematic maps, however, this simplification is pushed far beyond the legibility threshold and is instead constrained by…

In this note, we show that the solution to the Dirichlet problem for the minimal surface system in any codimension is unique in the space of distance-decreasing maps. This follows as a corollary of the following stability theorem: if a…

X-ray Computed Tomography (CT) reconstruction from a sparse number of views is a useful way to reduce either the radiation dose or the acquisition time, for example in fixed-gantry CT systems, however this results in an ill-posed inverse…

The cover metric is suitable for describing the resilience against correlated errors in arrays, in particular crisscross errors, which makes it interesting for applications such as distributed data storage (DDS). In this work, we consider…

Theoretical inverse problems are often studied in an ideal infinite-dimensional setting. The well-posedness theory provides a unique reconstruction of the parameter function, when an infinite amount of data is given. Through the lens of…

Rigid registration of multi-view and multi-platform LiDAR scans is a fundamental problem in 3D mapping, robotic navigation, and large-scale urban modeling applications. Data acquisition with LiDAR sensors involves scanning multiple areas…

Diversity maximization is an important geometric optimization problem with many applications in recommender systems, machine learning or search engines among others. A typical diversification problem is as follows: Given a finite metric…

We characterize the fundamental limits of coded aperture imaging systems up to universal constants by drawing upon a theorem of Nazarov regarding Fourier transforms. Our work is performed under a simple propagation and sensor model that…

We study geometric variations of the discriminating code problem. In the \emph{discrete version} of the problem, a finite set of points $P$ and a finite set of objects $S$ are given in $\mathbb{R}^d$. The objective is to choose a subset…

Optimal Morse matchings reveal essential structures of cell complexes which lead to powerful tools to study discrete geometrical objects, in particular discrete 3-manifolds. However, such matchings are known to be NP-hard to compute on…

Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…