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A Random Graph is a random object which take its values in the space of graphs. We take advantage of the expressibility of graphs in order to model the uncertainty about the existence of causal relationships within a given set of variables.…
3D object detection is a fundamental and challenging task for 3D scene understanding, and the monocular-based methods can serve as an economical alternative to the stereo-based or LiDAR-based methods. However, accurately detecting objects…
This work considers the inclusion detection problem of electrical impedance tomography with stochastic conductivities. It is shown that a conductivity anomaly with a random conductivity can be identified by applying the Factorization Method…
Optical two-dimensional (2D) coherent spectroscopy excels in studying coupling and dynamics in complex systems. The dynamical information can be learned from lineshape analysis to extract the corresponding linewidth. However, it is usually…
We study graphs that are formed by independently-positioned needles (i.e., line segments) in the unit square. To mathematically characterize the graph structure, we derive the probability that two line segments intersect and determine…
Self-similarity is the essence of fractal images and, as such, characterizes natural stochastic textures. This paper is concerned with the property of self-similarity in the statistical sense in the case of fully-textured images that…
Reconstructing magnetizations from measurements of the generated magnetic potential is generally non-unique. The non-uniqueness still remains if one restricts the magnetization to those induced by an ambient magnetic dipole field (i.e., the…
Semantic segmentation consists of predicting a semantic label for each image pixel. While existing deep learning approaches achieve high accuracy, they often overlook the ordinal relationships between classes, which can provide critical…
Aleatoric uncertainty is an intrinsic property of ill-posed inverse and imaging problems. Its quantification is vital for assessing the reliability of relevant point estimates. In this paper, we propose an efficient framework for…
We develop a "multifocal" approach to reveal spatial dissimilarities in cities, from the most local scale to the metropolitan one. Think for instance of a statistical variable that may be measured at different scales, eg ethnic group…
Time-frequency analysis is often used to study non stationary multicomponent signals, which can be viewed as the surperimposition of modes, associated with ridges in the TF plane. To understand such signals, it is essential to identify…
We study random 2-dimensional complexes in the Linial - Meshulam model and find torsion in their fundamental groups at various regimes. We find a simple algorithmically testable criterion for a subcomplex of a random 2-complex to be…
Modeling the distribution of natural images is a landmark problem in unsupervised learning. This task requires an image model that is at once expressive, tractable and scalable. We present a deep neural network that sequentially predicts…
Networks are often characterized by node heterogeneity for which nodes exhibit different degrees of interaction and link homophily for which nodes sharing common features tend to associate with each other. In this paper, we propose a new…
We consider the problem of detecting anomalies in the directional distribution of fibre materials observed in 3D images. We divide the image into a set of scanning windows and classify them into two clusters: homogeneous material and…
We demonstrate that extremely rapid and weak periodic and non-periodic signals can easily be detected by using the autocorrelation of intensity as a function of time. We use standard radio-astronomical observations that have artificial…
Random projection is a common technique for designing algorithms in a variety of areas, including information retrieval, compressive sensing and measuring of outlyingness. In this work, the original random projection outlyingness measure is…
Monocular depth estimation is often described as an ill-posed and inherently ambiguous problem. Estimating depth from 2D images is a crucial step in scene reconstruction, 3Dobject recognition, segmentation, and detection. The problem can be…
A geometrical approach to calculate the electric field due to a uniformly charged rod is presented. The result is surprisingly simple and elegant. Using pure geometrical quantities like length and angle, the direction of the electric field…
Images of spacecraft photographed from other spacecraft operating in outer space are difficult to come by, especially at a scale typically required for deep learning tasks. Semantic image segmentation, object detection and localization, and…