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Line segment detection is an essential task in computer vision and image analysis, as it is the critical foundation for advanced tasks such as shape modeling and road lane line detection for autonomous driving. We present a robust…
There is an increasing interest in the study of metamaterials and periodic materials across disciplines. These are anisotropic and their properties present directionality. For example, the wave speed depends on the propagation direction.…
Using the tools of Differential Geometry, we define a new <<fast>> chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e. "quickly") than the usual tools, like Lyapunov Characteristic Numbers…
When the elastic properties of structured materials become direction-dependent, the number of their descriptors increases. For example, in two-dimensions, the anisotropic behavior of materials is described by up to 6 independent elastic…
An efficient method of exploring the effects of anisotropy in the fractal properties of 2D surfaces and images is proposed. It can be viewed as a direction-sensitive generalization of the multifractal detrended fluctuation analysis (MFDFA)…
Most of the existing methods for anomaly detection use only positive data to learn the data distribution, thus they usually need a pre-defined threshold at the detection stage to determine whether a test instance is an outlier.…
By using directional distance sensors that have unknown locations, this paper proposes a method of estimating the shape of a location-unknown target object $T$ moving with unknown speed on an unknown straight line trajectory. Regardless of…
The special problem of transport in 2-dimensional divergence-free stochastic velocity fields is studied by developing a statistical approach, the nested subensemble method. The nonlinear process of trapping determined by such fields…
To understand how the human visual system analyzes images, it is essential to know the structure of the visual environment. In particular, natural images display consistent statistical properties that distinguish them from random luminance…
Symmetry is an important composition feature by investigating similar sides inside an image plane. It has a crucial effect to recognize man-made or nature objects within the universe. Recent symmetry detection approaches used a smoothing…
Anomaly localization in images -- identifying regions that deviate from normal patterns -- is vital in applications such as medical diagnosis and industrial inspection. A recent trend is the use of image generation models in anomaly…
The purpose of this paper is to introduce an algorithm that can detect the most unusual part of a digital image in probabilistic setting. The most unusual part of a given shape is defined as a part of the image that has the maximal distance…
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of…
In recent years, a novel x-ray imaging modality has emerged that reveals unresolved sample microstructure via a "dark-field image", which provides complementary information to conventional "bright-field" images, such as attenuation and…
Two-dimensional materials are a class of atomically thin materials with assorted electronic and quantum properties. Accurate identification of layer thickness, especially for a single monolayer, is crucial for their characterization. This…
In this study, we present a method for predicting the representativity of the phase fraction observed in a single image (2D or 3D) of a material. Traditional approaches often require large datasets and extensive statistical analysis to…
We present a novel method for image anomaly detection, where algorithms that use samples drawn from some distribution of "normal" data, aim to detect out-of-distribution (abnormal) samples. Our approach includes a combination of encoder and…
Road detection is a fundamental task in autonomous navigation systems. In this paper, we consider the case of monocular road detection, where images are segmented into road and non-road regions. Our starting point is the well-known machine…
Detecting and localizing objects in the real 3D space, which plays a crucial role in scene understanding, is particularly challenging given only a monocular image due to the geometric information loss during imagery projection. We propose…
Directional tests to compare incomplete undirected graphs are developed in the general context of covariance selection for Gaussian graphical models. The exactness of the underlying saddlepoint approximation is proved for chordal graphs and…