Classifying Overlapping Gaussian Mixtures in High Dimensions: From Optimal Classifiers to Neural Nets

We derive closed-form expressions for the Bayes optimal decision boundaries in binary classification of high dimensional overlapping Gaussian mixture model (GMM) data, and show how they depend on the eigenstructure of the class covariances, for particularly interesting structured data. We empirically demonstrate, through experiments on synthetic GMMs inspired by real-world data, that deep neural networks trained for classification, learn predictors which approximate the derived optimal classifiers. We further extend our study to networks trained on authentic data, observing that decision thresholds correlate with the covariance eigenvectors rather than the eigenvalues, mirroring our GMM analysis. This provides theoretical insights regarding neural networks' ability to perform probabilistic inference and distill statistical patterns from intricate distributions.

Multispectral Imaging with Fresnel Lens

This paper presents a Multispectral imaging (MSI) approach that combines the use of a diffractive optical element, and a deep learning algorithm for spectral reconstruction. Traditional MSI techniques often face challenges such as high costs, compromised spatial or spectral resolution, or prolonged acquisition times. In contrast, our methodology uses a single diffractive lens, a grayscale sensor, and an optical motor to capture the Multispectral image without sacrificing spatial resolution, however with some temporal domain redundancy. Through an experimental demonstration, we show how we can reconstruct up to 50 spectral channel images using diffraction physical theory and a UNet-based deep learning algorithm. This approach holds promise for a cost-effective, compact MSI camera that could be feasibly integrated into mobile devices.

Person Recognition using Facial Micro-Expressions with Deep Learning

This study investigates the efficacy of facial micro-expressions as a soft biometric for enhancing person recognition, aiming to broaden the understanding of the subject and its potential applications. We propose a deep learning approach designed to capture spatial semantics and motion at a fine temporal resolution. Experiments on three widely-used micro-expression databases demonstrate a notable increase in identification accuracy compared to existing benchmarks, highlighting the potential of integrating facial micro-expressions for improved person recognition across various fields.

Temporal Super-Resolution using Multi-Channel Illumination Source

While sensing in high temporal resolution is necessary for wide range of application, it is still limited nowadays due to cameras sampling rate. In this work we try to increase the temporal resolution beyond the Nyquist frequency, which is limited by the sampling rate of the sensor. This work establishes a novel approach for Temporal-Super-Resolution that uses the object reflecting properties from an active illumination source to go beyond this limit. Following theoretical derivation, we demonstrate how we can increase the temporal spectral detected range by a factor of 6 and possibly even more. Our method is supported by simulations and experiments and we demonstrate as an application, how we use our method to improve in about factor two the accuracy of object motion estimation.

Illumination-Based Color Reconstruction for the Dynamic Vision Sensor

This work demonstrates a novel, state of the art method to reconstruct colored images via the Dynamic Vision Sensor (DVS). The DVS is an image sensor that indicates only a binary change in brightness, with no information about the captured wavelength (color), or intensity level. We present a novel method to reconstruct a full spatial resolution colored image with the DVS and an active colored light source. We analyze the DVS response and present two reconstruction algorithms: Linear based and Convolutional Neural Network Based. In addition, we demonstrate our algorithm robustness to changes in environmental conditions such as illumination and distance. Finally, comparing with previous works, we show how we reach the state of the art results.