An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

<div>In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.</div>

Projection methods for high numerical aperture phase retrieval

We develop for the first time a mathematical framework in which the class of projection algorithms can be applied to high numerical aperture (NA) phase retrieval. Within this framework, we first analyze the basic steps of solving the high-NA phase retrieval problem by projection algorithms and establish the closed forms of all the relevant projection operators. We then study the geometry of the high-NA phase retrieval problem and the obtained results are subsequently used to establish convergence criteria of projection algorithms in the presence of noise. Making use of the vectorial point-spread-function (PSF) is, on the one hand, the key difference between this paper and the literature of phase retrieval mathematics which deals with the scalar PSF. The results of this paper, on the other hand, can be viewed as extensions of those concerning projection methods for low-NA phase retrieval. Importantly, the improved performance of projection methods over the other classes of phase retrieval algorithms in the low-NA setting now also becomes applicable to the high-NA case. This is demonstrated by the accompanying numerical results which show that available solution approaches for high-NA phase retrieval are outperformed by projection methods.

Deep supervised hashing for gait retrieval

Background: Gait recognition is perceived as the most promising biometric approach for future decades especially because of its efficient applicability in surveillance systems. Due to recent growth in the use of gait biometrics across surveillance systems, the ability to rapidly search for the required data has become an emerging need. Therefore, we addressed the gait retrieval problem, which retrieves people with gaits similar to a query subject from a large-scale dataset. Methods: This paper presents the deep gait retrieval hashing (DGRH) model to address the gait retrieval problem for large-scale datasets. Our proposed method is based on a supervised hashing method with a deep convolutional network. We use the ability of the convolutional neural network (CNN) to capture the semantic gait features for feature representation and learn the compact hash codes with the compatible hash function. Therefore, our DGRH model combines gait feature learning with binary hash codes. In addition, the learning loss is designed with a classification loss function that learns to preserve similarity and a quantization loss function that controls the quality of the hash codes Results: The proposed method was evaluated against the CASIA-B, OUISIR-LP, and OUISIR-MVLP benchmark datasets and received the promising result for gait retrieval tasks. Conclusions: The end-to-end deep supervised hashing model is able to learn discriminative gait features and is efficient in terms of the storage memory and speed for gait retrieval.

J-EDA: A workbench for tuning similarity and diversity search parameters in content-based image retrieval

Similarity searches can be modeled by means of distances following the Metric Spaces Theory and constitute a fast and explainable query mechanism behind content-based image retrieval (CBIR) tasks. However, classical distance-based queries, e.g., Range and k-Nearest Neighbors, may be unsuitable for exploring large datasets because the retrieved elements are often similar among themselves. Although similarity searching is enriched with the imposition of rules to foster result diversification, the fine-tuning of the diversity query is still an open issue, which is is usually carried out with and a non-optimal expensive computational inspection. This paper introduces J-EDA, a practical workbench implemented in Java that supports the tuning of similarity and diversity search parameters by enabling the automatic and parallel exploration of multiple search settings regarding a user-posed content-based image retrieval task. J-EDA implements a wide variety of classical and diversity-driven search queries, as well as many CBIR settings such as feature extractors for images, distance functions, and relevance feedback techniques. Accordingly, users can define multiple query settings and inspect their performances for spotting the most suitable parameterization for a content-based image retrieval problem at hand. The workbench reports the experimental performances with several internal and external evaluation metrics such as P × R and Mean Average Precision (mAP), which are calculated towards either incremental or batch procedures performed with or without human interaction.

Automatic Translation of Music-to-Dance for In-Game Characters

Music-to-dance translation is an emerging and powerful feature in recent role-playing games. Previous works of this topic consider music-to-dance as a supervised motion generation problem based on time-series data. However, these methods require a large amount of training data pairs and may suffer from the degradation of movements. This paper provides a new solution to this task where we re-formulate the translation as a piece-wise dance phrase retrieval problem based on the choreography theory. With such a design, players are allowed to optionally edit the dance movements on top of our generation while other regression-based methods ignore such user interactivity. Considering that the dance motion capture is expensive that requires the assistance of professional dancers, we train our method under a semi-supervised learning fashion with a large unlabeled music dataset (20x than our labeled one) and also introduce self-supervised pre-training to improve the training stability and generalization performance. Experimental results suggest that our method not only generalizes well over various styles of music but also succeeds in choreography for game players. Our project including the large-scale dataset and supplemental materials is available at https://github.com/FuxiCV/music-to-dance.

Sparse phase retrieval via ℓp (0 < p ≤ 1) minimization

In this paper, the [Formula: see text]-analysis model for the phase retrieval problem of sparse unknown signals in the redundant dictionary is extended to the [Formula: see text]-analysis model, where [Formula: see text]. It’s shown that if the measurement matrix [Formula: see text] satisfies the strong restricted isometry property adapted to D (S-DRIP) condition, the unknown signal [Formula: see text] can be stably recovered by analyzing the [Formula: see text] [Formula: see text] minimization model.