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Spectral embedding based on the Singular Value Decomposition (SVD) is a widely used "preprocessing" step in many learning tasks, typically leading to dimensionality reduction by projecting onto a number of dominant singular vectors and…
Projected entangled pair states (PEPS) on finite two-dimensional lattices are a natural ansatz for representing ground states of local many-body Hamiltonians, as they inherently satisfy the boundary law of entanglement entropy. In this…
There is increasing evidence on the importance of brain morphology in predicting and classifying mental disorders. However, the vast majority of current shape approaches rely heavily on vertex-wise analysis that may not successfully capture…
Pixel-wise regression is probably the most common problem in fine-grained computer vision tasks, such as estimating keypoint heatmaps and segmentation masks. These regression problems are very challenging particularly because they require,…
Understanding the orientation of geological structures is crucial for analyzing the complexity of the Earths' subsurface. For instance, information about geological structure orientation can be incorporated into local anisotropic…
The problem of object pose and shape estimation has seen key advancements lately. Encoder-decoder (e.g., SAM3D, LRM, CRISP) and diffusion-based models (e.g., InstantMesh, Zero123, SceneComplete) have shown category-agnostic shape encoding…
Blind inverse problems arise in many experimental settings where both the signal of interest and the forward operator are (partially) unknown. In this context, methods developed for the non-blind case cannot be adapted in a straightforward…
We give complete geometric invariants of cobordisms of framed fold maps. These invariants consist of two types. We take the immersion of the fold singular set into the target manifold together with information about non-triviality of the…
In this paper we consider two topological transforms that are popular in applied topology: the Persistent Homology Transform (PHT) and the Euler Characteristic Transform (ECT). Both of these transforms are of interest for their mathematical…
In single molecule orientation localization microscopy, valuable information about the orientation and longitudinal position of each molecule is often encoded in the shape of the point spread function (PSF). This shape, though, can be…
We study formally determined inverse problems with passive measurements for one dimensional evolution equations where the goal is to simultaneously determine both the initial data as well as the variable coefficients in such an equation…
Adaptive optics (AO) system performance is improved using post-processing techniques, such as point spread function (PSF) deconvolution. The PSF estimation involves characterization of the different wavefront (WF) error sources in the AO…
The orthogonal matching pursuit (OMP) is an algorithm to solve sparse approximation problems. Sufficient conditions for exact recovery are known with and without noise. In this paper we investigate the applicability of the OMP for the…
Plantar pressure mapping is essential in clinical diagnostics and sports science, yet large heterogeneous datasets often contain outliers from technical errors or procedural inconsistencies. Statistical Parametric Mapping (SPM) provides…
Existing Object Pose Estimation (OPE) methods for stacked scenarios are not robust to changes in object scale. This paper proposes a new 6DoF OPE network (NormNet) for different scale objects in stacked scenarios. Specifically, each…
We study a surprising phenomenon related to the representation of a cloud of data points using polynomials. We start with the previously unnoticed empirical observation that, given a collection (a cloud) of data points, the sublevel sets of…
6D pose estimation of rigid objects is a long-standing and challenging task in computer vision. Recently, the emergence of deep learning reveals the potential of Convolutional Neural Networks (CNNs) to predict reliable 6D poses. Given that…
The use of parameters measuring order-parameter fluctuations (OPF) has been encouraged by the recent results reported in \cite{RS} which show that two of these parameters, $G$ and $G_c$, take universal values in the $\lim_{T\to 0}$. In this…
In this paper, we consider the problem of planar graph-based simultaneous localization and mapping (SLAM) that involves both poses of the autonomous agent and positions of observed landmarks. We present CPL-SLAM, an efficient and…
Existing deep calibrated photometric stereo networks basically aggregate observations under different lights based on the pre-defined operations such as linear projection and max pooling. While they are effective with the dense capture,…