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Haar-like filters are renowned for their simplicity, speed, and accuracy in various computer vision tasks. This paper proposes a novel algorithm to identify optimal fully dispersed Haar-like filters for enhanced facial feature extraction…

We focus on the analysis of planar shapes and solid objects having thin features and propose a new mathematical model to characterize them. Based on our model, that we call an epsilon-shape, we show how thin parts can be effectively and…

This paper introduces a family of local feature aggregation functions and a novel method to estimate their parameters, such that they generate optimal representations for classification (or any task that can be expressed as a cost function…

In this paper, we attempt to shed light on a new class of nonstationary random fields which exhibit, what we call, local invariant nonstationarity. We argue that the local invariant property has a special interaction with a new generalized…

Fourier-encoded implicit neural representations (INRs) have shown strong capability in modeling continuous signals from discrete samples. However, conventional Fourier feature mappings use a fixed set of frequencies over the entire spatial…

The high-dimensional nature of the 4-D light field (LF) poses great challenges in achieving efficient and effective feature embedding, that severely impacts the performance of downstream tasks. To tackle this crucial issue, in contrast to…

We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of…

Previous work has shown that feature maps of deep convolutional neural networks (CNNs) can be interpreted as feature representation of a particular image region. Features aggregated from these feature maps have been exploited for image…

Scientists at the Berkeley SETI Research Center are Searching for Extraterrestrial Intelligence (SETI) by a new signal detection method that converts radio signals into spectrograms through Fourier transforms and classifies signals…

This paper explains a neural network for image generation from a new perspective, i.e., explaining representation structures for image generation. We propose a set of desirable properties to define the representation structure of a neural…

The convolution layer has been the dominant feature extractor in computer vision for years. However, the spatial aggregation in convolution is basically a pattern matching process that applies fixed filters which are inefficient at modeling…

There is a wide range of applications where the local extrema of a function are the key quantity of interest. However, there is surprisingly little work on methods to infer local extrema with uncertainty quantification in the presence of…

Local algorithms are common tools for estimating intrinsic volumes from black-and-white digital images. However, these algorithms are typically biased in the design based setting, even when the resolution tends to infinity. Moreover, images…

To incorporate spatial (neighborhood) and bidirectional hierarchical relationships as well as features and priors of the samples into their classification, we formulated the classification problem on three variants of multiresolution…

This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…

Resampling is an important signature of manipulated images. In this paper, we propose two methods to detect and localize image manipulations based on a combination of resampling features and deep learning. In the first method, the Radon…

We exploit the Cartan-K\"ahler theory to prove the local existence of real analytic quaternionic contact structures for any prescribed values of the respective curvature functions and their covariant derivatives at a given point on a…

Recent works with an implicit neural function shed light on representing images in arbitrary resolution. However, a standalone multi-layer perceptron shows limited performance in learning high-frequency components. In this paper, we propose…

We show that the Hardy spaces for Fourier integral operators form natural spaces of initial data when applying $\ell^{p}$-decoupling inequalities to local smoothing for the wave equation. This yields new local smoothing estimates which, in…

Local covariant feature detection, namely the problem of extracting viewpoint invariant features from images, has so far largely resisted the application of machine learning techniques. In this paper, we propose the first fully general…