Histogram Distance Research Articles

A First Approach to Quantum Logical Shape Classification Framework

Quantum logic is a well-structured theory, which has recently received some attention because of its fundamental relation to quantum computing. However, the complex foundation of quantum logic borrowing concepts from different branches of mathematics as well as its peculiar settings have made it a non-trivial task to devise suitable applications. This article aims to propose for the first time an approach using quantum logic in image processing for shape classification. We show how to make use of the principal component analysis to realize quantum logical propositions. In this way, we are able to assign a concrete meaning to the rather abstract quantum logical concepts, and we are able to compute a probability measure from the principal components. For shape classification, we consider encrypting given point clouds of different objects by making use of specific distance histograms. This enables us to initiate the principal component analysis. Through experiments, we explore the possibility of distinguishing between different geometrical objects and discuss the results in terms of quantum logical interpretation.

Ab initio dispersion potentials based on physics-based functional forms with machine learning.

In this study, we introduce SAPT10K, a comprehensive dataset comprising 9982 noncovalent interaction energies and their binding energy components (electrostatics, exchange, induction, and dispersion) for diverse intermolecular complexes of 944 unique dimers. These complexes cover significant portions of the intermolecular potential energy surface and were computed using higher-order symmetry-adapted perturbation theory, SAPT2+(3)(CCD), with a large aug-cc-pVTZ basis set. The dispersion energy values in SAPT10K serve as crucial inputs for refining the abinitio dispersion potentials based on Grimme's D3 and many-body dispersion (MBD) models. Additionally, Δ machine learning (ML) models based on newly developed intermolecular features, which are derived from intermolecular histograms of distances for element/substructure pairs to simultaneously account for local environments as well as long-range correlations, are also developed to address deficiencies of the D3/MBD models, including the inflexibility of their functional forms, the absence of MBD contributions in D3, and the standard Hirshfeld partitioning scheme used in MBD. The developed dispersion models can be applied to complexes involving a wide range of elements and charged monomers, surpassing other popular ML models, which are limited to systems with only neutral monomers and specific elements. The efficient D3-ML model, with Cartesian coordinates as the sole input, demonstrates promising results on a testing set comprising 6714 dimers, outperforming another popular ML model, component-based machine-learned intermolecular force field (CLIFF), by 1.5 times. These refined D3/MBD-ML models have the capability to replace the time-consuming dispersion components in symmetry-adapted perturbation theory-based calculations and can promptly illustrate the dispersion contribution in noncovalent complexes for supramolecular assembly and chemical reactions.

Unsupervised Change Detection in HR Remote Sensing Imagery Based on Local Histogram Similarity and Progressive Otsu

Unsupervised change detection of land cover in multispectral satellite remote sensing images with a spatial resolution of 2–5 m has always been a challenging task. This paper presents a method of detecting land cover changes in high-spatial-resolution remote sensing imagery. This method has three characteristics: (1) Extended center-symmetric local binary pattern (XCS-LBP) is used to extract image features to emphasize spatial context information in initial change detection. Then, spectral information is combined to improve the accuracy of change detection. (2) The local histogram distance of XCS-LBP features is used as the change vector to improve the expression of change information. (3) A progressive Otsu method is developed for threshold segmentation of the change vector to reduce the false detection rate. Four datasets with different landscape complexities and seven state-of-the-art unsupervised change detection methods were used to test the performance of the proposed method. Quantitative results showed that the proposed method reduced the false detection rate and improved the accuracy of the detection of land cover changes. The F1 score achieved by the proposed method reached 0.8688, 0.8867, 0.7725, and 0.6634, respectively, which are higher than the highest corresponding F1 score achieved by the benchmark methods (0.8533, 0.8549, 0.6545, and 0.5895, respectively).

Hyperuniformity in two-dimensional periodic and quasiperiodic point patterns.

We study hyperuniform properties in various two-dimensional periodic and quasiperiodic point patterns. Using the histogram of the two-point distances, we develop an efficient method to calculate the hyperuniformity order metric, which quantifies the regularity of the hyperuniform point patterns. The results are compared with those calculated with the conventional running average method. To discuss how the lattice symmetry affects the order metric, we treat the trellis and Shastry-Sutherland lattices with the same point density as examples of periodic lattices, and Stampfli hexagonal and dodecagonal quasiperiodic tilings with the same point density as examples of quasiperiodic tilings. It is found that the order metric for the Shastry-Sutherland lattice (Stampfli dodecagonal tilings) is smaller than the other in the periodic (quasiperiodic) tiling, meaning that the order metric is deeply related to the lattice symmetry. Namely, the point pattern with higher symmetry is characterized by the smaller order metric when their point densities are identical. Order metrics for several other quasiperiodic tilings are also calculated.

Evaluation of drone surveys for ungulates in southwestern rangelands

AbstractDrone platforms are increasingly used for aerial wildlife surveys, but the validity of population counts has not been fully evaluated in all environments. Aerial surveys generally undercount the true population size and one must estimate detection probability (p) to correct for missed individuals. Detection probability for visual observers is influenced by vegetation and terrain characteristics, but the use of thermal cameras as the observer may also introduce additional factors influencing detection probability. We conducted diurnal, thermal‐based drone surveys for ungulates during February–April 2020 in South Texas, USA, on sites with varying degrees of woody cover and terrain. We examined histograms of georeferenced perpendicular distances to determine the effect of habitat on detection probabilities. We also examined precision in population estimates and variation in repeated surveys. Finally, we compared drone population estimates to independent estimates derived from helicopter, spotlight, and trail‐camera surveys. Distributions of perpendicular distances from the transect were affected by habitat characteristics. A flat grassland site had relatively few detections near the transect because thermal (solar) reflectance in the center of the footage obscured detections. A hilly brushy site had a uniform p (1.00) but resulted in a severe undercount due to the inability of the drone to follow contours of hills. The flat brushy site had a lower p (0.63), indicating visibility bias. Two additional flat, brushy sites were surveyed repeatedly (n = 5 and 9 surveys, respectively). All combinations of up to 3 repeated surveys were pooled to meet the recommended minimum number of detections for distance sampling analyses (≥60 detections). Population estimates had acceptable precision (CV ≤ 20%) 80.7% of the time and variation among repeated surveys was acceptable (CV = 9% and 23%, respectively). Drone‐based population estimates were comparable with estimates generated from corrected helicopter, spotlight, and trail‐camera surveys. Overall, diurnal drone surveys can generate population estimates for large ungulates on southwestern rangelands after accounting for visibility bias, but may be limited by terrain and thermal conditions.

Security analysis of a reversible data hiding scheme in encrypted images by redundant space transfer

Redundant space transfer (RST) encryption can effectively enhance the security and embedding capacity of reversible data hiding in encrypted images. To demonstrate the security risks of RST encryption in the cloud environment, according to the known plaintext image and marked encrypted image(MEI) pairs, this paper proposes a known plaintext attack (KPA) based on hamming-weight of bit block. The proposed KPA method includes two stages. The first stage is to find the correct ciphertext image. For possible block sizes, all possible ciphertext images of MEI are reconstructed by deleting the embedded secret data. The Hamming weight image (HWI) of plaintext and all possible ciphertext images is calculated in m×8n domain (m, n is the image size). When the histogram distance between the plaintext HWI and a possible ciphertext HWI is the minimum, the correct ciphertext image is found. The second stage is to estimate the permutation keys. The bit block characteristic matrix (BBCM) is defined by using that the bit values of plaintext and ciphertext remain unchanged in the process of RST encryption. Based on the intersection of BBCM’s index set, the block permutation key is directly estimated. Then, the bit plane permutation key in each image block is further estimated. Experimental results show that for RST encryption, when the block size is not less than 3 × 3, the block permutation and bit plane permutation key can be estimated in less than 3 min by using one pair of plain–ciphertext. The estimation accuracy of block permutation key is more than 50%, and the estimation accuracy of bit plane permutation key is 10% for Qin’s RST algorithm, most of the content information of the ciphertext image is leaked.

Automatic Brain Tumor Detection and Volume Estimation in Multimodal MRI Scans via a Symmetry Analysis

In this study, an automated medical decision support system is presented to assist physicians with accurate and immediate brain tumor detection, segmentation, and volume estimation from MRI which is very important in the success of surgical operations and treatment of brain tumor patients. In the proposed approach, first, tumor regions on MR images are labeled by an expert radiologist. Then, an automated medical decision support system is developed to extract brain tumor boundaries and to calculate their volumes by using multimodal MR images. One advantage of this study is that it provides an automated brain tumor detection and volume estimation algorithm that does not require user interactions by determining threshold values adaptively. Another advantage is that, because of the unsupervised approach, the proposed study realized tumor detection, segmentation, and volume estimation without using very large labeled training data. A brain tumor detection and segmentation algorithm is introduced that is based on the fact that the brain consists of two symmetrical hemispheres. Two main analyses, i.e., histogram and symmetry, were performed to automatically estimate tumor volume. The threshold values used for skull stripping were computed adaptively by examining the histogram distances between T1- and T1C-weighted brain MR images. Then, a symmetry analysis between the left and right brain lobes on FLAIR images was performed for whole tumor detection. The experiments were conducted on two brain MRI datasets, i.e., TCIA and BRATS. The experimental results were compared with the labeled expert results, which is known as the gold standard, to demonstrate the efficacy of the presented method. The performance evaluation results achieved accuracy values of 89.7% and 99.0%, and a Dice similarity coefficient value of 93.0% for whole tumor detection, active core detection, and volume estimation, respectively.

Accurate prediction of global-density-dependent range-separation parameters based on machine learning.

In this work, we develop an accurate and efficient XGBoost machine learning model for predicting the global-density-dependent range-separation parameter, ωGDD, for long-range corrected functional (LRC)-ωPBE. This ωGDDML model has been built using a wide range of systems (11 466 complexes, ten different elements, and up to 139 heavy atoms) with fingerprints for the local atomic environment and histograms of distances for the long-range atomic correlation for mapping the quantum mechanical range-separation values. The promising performance on the testing set with 7046 complexes shows a mean absolute error of 0.001 117 a0-1 and only five systems (0.07%) with an absolute error larger than 0.01 a0-1, which indicates the good transferability of our ωGDDML model. In addition, the only required input to obtain ωGDDML is the Cartesian coordinates without electronic structure calculations, thereby enabling rapid predictions. LRC-ωPBE(ωGDDML) is used to predict polarizabilities for a series of oligomers, where polarizabilities are sensitive to the asymptotic density decay and are crucial in a variety of applications, including the calculations of dispersion corrections and refractive index, and surpasses the performance of all other popular density functionals except for the non-tuned LRC-ωPBE. Finally, LRC-ωPBE (ωGDDML) combined with (extended) symmetry-adapted perturbation theory is used in calculating noncovalent interactions to further show that the traditional abinitio system-specific tuning procedure can be bypassed. The present study not only provides an accurate and efficient way to determine the range-separation parameter for LRC-ωPBE but also shows the synergistic benefits of fusing the power of physically inspired density functional LRC-ωPBE and the data-driven ωGDDML model.

Road potholes detection from MLS point clouds

The extraction of pavement damage information is one of the major difficulties in the application research of mobile laser scanning point cloud data. To address the problem of inaccurate detection results by using only relative distance to detect potholes, this paper proposes a novel pothole detection method that combines directed distance and skewed distribution. Firstly, the rapid positioning of the pothole is realized by the directed distance, which is calculated from the points and the local fitted plane. And monomerization and denoising of potential potholes are achieved by density clustering. Then, the new accurate plane is fitted by the surrounding pavement points of the potential pothole to obtain accurate directed distances. The negative skewed distribution of the directed distance histogram and the skewness coefficient are used for the accurate determination of the pothole. Finally, the three-dimensional geometric features of the pothole are extracted. Experiments were carried out on a road with poor road conditions. The experimental results validated the effectiveness and practicality of the proposed method. It can achieve automatic detection of potholes with different shapes and deformation degrees, and has effectively improved the efficiency of automatic road inspection.

Learning system parameters from turing patterns.

The Turing mechanism describes the emergence of spatial patterns due to spontaneous symmetry breaking in reaction-diffusion processes and underlies many developmental processes. Identifying Turing mechanisms in biological systems defines a challenging problem. This paper introduces an approach to the prediction of Turing parameter values from observed Turing patterns. The parameter values correspond to a parametrized system of reaction-diffusion equations that generate Turing patterns as steady state. The Gierer-Meinhardt model with four parameters is chosen as a case study. A novel invariant pattern representation based on resistance distance histograms is employed, along with Wasserstein kernels, in order to cope with the highly variable arrangement of local pattern structure that depends on the initial conditions which are assumed to be unknown. This enables us to compute physically plausible distances between patterns, to compute clusters of patterns and, above all, model parameter prediction based on training data that can be generated by numerical model evaluation with random initial data: for small training sets, classical state-of-the-art methods including operator-valued kernels outperform neural networks that are applied to raw pattern data, whereas for large training sets the latter are more accurate. A prominent property of our approach is that only a single pattern is required as input data for model parameter predicion. Excellent predictions are obtained for single parameter values and reasonably accurate results for jointly predicting all four parameter values.

Arrival-time detection with histogram distance for acoustic emission signals

Arrival-time picking is a fundamental step in time-of-arrival (TOA)-based localisation in current and future acoustic emission (AE), microseismic and seismic localisation systems. The accurate detection of TOA is of great importance for high localisation accuracy. This work presents a histogram distance-based method for TOA detection of elastic wave signals. The authors treat an original elastic waveform that includes the arrival as two different locally stationary segments, namely the intervals following and preceding arrival. To determine the optimal separation of these two stationary segments, ie the arrival time, histograms of these intervals are calculated and a measure of the distance between them modified from the Bhattacharyya coefficient is proposed. The performance of the proposed method is evaluated using TOA picking for AE. The method is shown to provide accurate and robust picks on AE signals under various signal-to-noise ratios. To evaluate the adaptability of the method to other TOA picking scenarios, it is applied to detect the seismic P-phase. The detection accuracy is adequate and errors are constrained to within a few seconds. Factors that influence the detection accuracy are discussed. The results suggest that the proposed method has the potential to detect TOA in various fields.

Dynamic Mode Decomposition for the Comparison of Engine In-Cylinder Flow Fields from Particle Image Velocimetry (PIV) and Reynolds-Averaged Navier–Stokes (RANS) Simulations

Validation of Reynolds-averaged Navier–Stokes (RANS) simulation results against experimental data such as flow measurements from particle image velocimetry (PIV) remains a challenge for the development of thermal propulsion systems. This is partly due to cycle-to-cycle variations (CCVs) in the air motion and partly due to uncertainties in the PIV measurement technique, complicating the question of what constitutes a fair validation target for the RANS model. Indeed, an inappropriate validation target can misguide subsequent adjustments of a RANS model. In this work, the ensemble-averaged PIV field is first investigated for its suitability as a validation target for RANS simulations. The relevance index and the velocity histogram distance are used as quantitative metrics to assess the similarity of the ensemble-averaged field to the full dataset of individual PIV cycles. While a high similarity is seen between the average PIV flow field and the individual cycles on the tumble plane, the similarity is lower and more variable on the cross-tumble plane, where there are significant CCVs. Standard (space-only, phase-dependent) proper orthogonal decomposition (POD) is employed as an alternative method of data processing with the aim of providing a fairer comparison to RANS simulations. The cycle-dependence of the standard POD modes is shown to be an aspect that results in many validation targets and an excessively broad validation range, limiting its utility in this context. Dynamic mode decomposition (DMD) and sparsity-promoting dynamic mode decomposition (SPDMD) are then proposed as alternative solutions, capable of extracting flow structures at specific frequencies. The background 0 Hz SPDMD modes exhibit an ability to produce more realistic flow fields with velocity magnitudes that are significantly closer to the individual cycles.

HDR Map Reconstruction From a Single LDR Sky Panoramic Image for Outdoor Illumination Estimation

Outdoor low dynamic range (LDR) panoramic images that contain the sun and sky are generally over-saturated because the sun is 10,000 times brighter than the regions that surround it. Because the luminance information in the region that contains the sun in these images is lost, it is difficult to identify the sun’s position and generate high dynamic range (HDR) environment maps that can be used to realistically relight virtual objects. Previous methods to reconstruct HDR maps did not consider that the sun covers a small area in an image but contains extremely high luminance values. These methods are therefore insufficient for estimating scene illumination. We propose a multi-faceted approach to reconstructing HDR maps from a single LDR sky panoramic image that considers the sun and sky regions separately. We encode an input image and transfer a multi-dimensional latent representation to two decoders, which reconstruct the luminance information in the sky and sun regions separately. To plausibly model sun illumination, we introduce two networks (Sunpose-net and Sunrad-net) that estimate the position and radiance of the sun. The generated sun radiance map is then merged with the output of the decoder that is responsible for sun regions. We demonstrated that the proposed method more plausibly reconstructs HDR maps than previous methods using the HDR-VDP-2.2 which measures the visual quality of reconstructed HDR maps against ground truth. The accuracy of the overall sun and sky illumination distribution in HDR maps reconstructed using the proposed method was evaluated using histogram distance measures.

Quantitative Spatial Characterization of Lymph Node Tumor for N Stage Improvement of Nasopharyngeal Carcinoma Patients.

This study aims to investigate the feasibility of improving the prognosis stratification of the N staging system of Nasopharyngeal Carcinoma (NPC) from quantitative spatial characterizations of metastatic lymph node (LN) for NPC in a multi-institutional setting. A total of 194 and 284 NPC patients were included from two local hospitals as the discovery and validation cohort. Spatial relationships between LN and the surrounding organs were quantified by both distance and angle histograms, followed by principal component analysis. Independent prognostic factors were identified and combined with the N stage into a new prognostic index by univariate and multivariate Cox regressions on disease-free survival (DFS). The new three-class risk stratification based on the constructed prognostic index demonstrated superior cross-institutional performance in DFS. The hazard ratios of the high-risk to low-risk group were 9.07 (p < 0.001) and 4.02 (p < 0.001) on training and validation, respectively, compared with 5.19 (p < 0.001) and 1.82 (p = 0.171) of N3 to N1. Our spatial characterizations of lymph node tumor anatomy improved the existing N-stage in NPC prognosis. Our quantitative approach may facilitate the discovery of new anatomical characteristics to improve patient staging in other diseases.

A connection between the density and temperature of the Lennard-Jones fluids at equilibrium and the first peak of the radial distribution function

A new method to obtain the density and temperature of the Lennard–Jones fluids at equilibrium from the height and the displacement of the first peak of the radial distribution function (RDF) is presented here. The density range and temperature range covered are 0.5≤ρ*≤1.2, 0.2≤β*≤2.0 with ρ*=ρσ3 andβ*=ϵ/kBT being the reduced density and temperature, respectively. Numerically, 152 state points (ρ*,β*) are obtained with Δρ*=0.1 and Δβ*=0.1 by molecular dynamics (MD) simulations. More than 10000 configurations are output for each state point. The RDFs are then obtained through classical distance histogram method. The stability of the RDF is found to be related to the number of configurations because of ensemble average. Two correlations establishing the relation of the height of the first peak of the RDF versus the density and temperature and the relation of the displacement of the first peak of the RDF versus the density and temperature are empirically constructed by fitting 40 state points out of 152. Other 112 state points are used to estimate the accuracy of the two correlations proposed. It is found that all of the 112 state points can be correctly predicted. These results indicate that the RDF can be conveniently used to assure the state point (ρ*,β*) of the Lennard–Jones fluids at equilibrium. The importance of the present work is that a clear connection between a special point of the RDF, i.e., its first peak, and the state point (ρ*,β*) is firstly empirically built up. Their one to one map is observed.

Contrast Enhancement of RGB Retinal Fundus Images for Improved Segmentation of Blood Vessels Using Convolutional Neural Networks.

Retinal fundus images are non-invasively acquired and faced with low contrast, noise, and uneven illumination. The low-contrast problem makes objects in the retinal fundus image indistinguishable and the segmentation of blood vessels very challenging. Retinal blood vessels are significant because of their diagnostic importance in ophthalmologic diseases. This paper proposes improved retinal fundus images for optimal segmentation of blood vessels using convolutional neural networks (CNNs). This study explores some robust contrast enhancement tools on the RGB and the green channel of the retinal fundus images. The improved images undergo quality evaluation using mean square error (MSE), peak signal to noise ratio (PSNR), Similar Structure Index Matrix (SSIM), histogram, correlation, and intersection distance measures for histogram comparison before segmentation in the CNN-based model. The simulation results analysis reveals that the improved RGB quality outperforms the improved green channel. This revelation implies that the choice of RGB to the green channel for contrast enhancement is adequate and effectively improves the quality of the fundus images. This improved contrast will, in turn, boost the predictive accuracy of the CNN-based model during the segmentation process. The evaluation of the proposed method on the DRIVE dataset achieves an accuracy of 94.47, sensitivity of 70.92, specificity of 98.20, and AUC (ROC) of 97.56.

Object Relocation Visual Tracking Based on Histogram Filter and Siamese Network in Intelligent Transportation.

Target detection and tracking algorithms are one of the key technologies in the field of autonomous driving in intelligent transportation, providing important sensing capabilities for vehicle localization and path planning. Siamese network-based trackers formulate the visual tracking mission as an image-matching process by regression and classification branches, which simplifies the network structure and improves the tracking accuracy. However, there remain many problems, as described below. (1) The lightweight neural networks decrease the feature representation ability. It is easy for the tracker to fail under the disturbing distractors (e.g., deformation and similar objects) or large changes in the viewing angle. (2) The tracker cannot adapt to variations of the object. (3) The tracker cannot reposition the object that has failed to track. To address these issues, we first propose a novel match filter arbiter based on the Euclidean distance histogram between the centers of multiple candidate objects to automatically determine whether the tracker fails. Secondly, the Hopcroft-Karp algorithm is introduced to select the winners from the dynamic template set through the backtracking process, and object relocation is achieved by comparing the Gradient Magnitude Similarity Deviation between the template and the winners. The experiments show that our method obtains better performance on several tracking benchmarks, i.e., OTB100, VOT2018, GOT-10k, and LaSOT, compared with state-of-the-art methods.

On the feasibility of cardiac substructure sparing in magnetic resonance imaging guided stereotactic lung radiotherapy.

Lung stereotactic body radiotherapy (SBRT) has proven an effective treatment for medically inoperable lung tumors, even for (ultra-)central tumors. Recently, there has been growing interest in radiation-induced cardiac toxicity in lung radiotherapy. More specifically, dose to cardiac (sub-)structures (CS) was found to correlate with survival afterradiotherapy. Our goal is first, to investigate the percentage of patients who require CS sparing in an magnetic resonance imaging guided lung SBRT workflow, and second, to quantify how successful implementation of cardiac sparing would be. The patient cohort consists of 34 patients with stage II-IV lung cancer who were treated with SBRT between 2017 and 2020. A mid-position computed tomography (CT) image was used to create treatment plans for the 1.5 T Unity MR-linac (Elekta AB, Stockholm, Sweden) following clinical templates. Under guidance of a cardio-thoracic radiologist, 11 CS were contoured manually for each patient. Dose constraints for five CS were extracted from the literature. Patients were stratified according to their need for cardiac sparing depending on the CS dose in their non-CS constrained MR-linac treatment plans. Cardiac sparing treatment plans (CSPs) were then created and dosimetrically compared with their non-CS constrained treatment plan counterparts. CSPs complied with the departmental constraints and were considered successful when fulfilling all CS constraints, and partially successful if some CS constraints could be fulfilled. Predictors for the need for and feasibility of cardiac sparing were explored, specifically planning target volume (PTV) size, cranio-caudal (CC) distance, 3D distance, and in-field overlap volume histograms (iOVH). 47% of the patients (16 out of 34) were in need of cardiac sparing. A successful CSP could be created for 62.5% (10 out of 16) of these patients. Partially successful CSPs still complied with two to four CS constraints. No significant difference in dose to organs at risk (OARs) or targets was identified between CSPs and the corresponding non-CS constrained MR-linac plans. The need for cardiac sparing was found to correlate with distance in the CC direction between target and all of the individual CS (Mann-Whitney U-test p-values <10-6 ). iOVHs revealed that complying with dose constraints for CS is primarily determined by in-plane distance and secondarily by PTVsize. We demonstrated that CS can be successfully spared in lung SBRT on the MR-linac for most of this patient cohort, without compromising doses to the tumor or to other OARs. CC distance between the target and CS can be used to predict the need for cardiac sparing. iOVHs, in combination with PTV size, can be used to predict if cardiac sparing will be successful for all constrained CS except the leftventricle.

Atmospheric light veil correction dehazing algorithm based on regional detection

To address the problems that the dehazing algorithm is prone to distortion, block artifacts, and edge pixel loss from the minimum filter in the highlighted area of an image, a dehazing algorithm with an atmospheric veil correction model under regional detection is proposed. First, the initial atmospheric light veil is obtained by using the improved dark channel, and the atmospheric light veil correction model is established for it. Then, the color distance and color distance histogram fitting curve of the haze image are used to accurately detect the region where the initial atmospheric light veil is corrected, and the correction term is established. Finally, the atmospheric light is estimated by combining the image information entropy with quad-tree subdivision algorithm. It is proved that the proposed method effectively solves the distorted problem in the highlighted region and the block artifacts produced by minimum filtering and can recover image with rich detailed information.

Distance distributions and inverse problems for metric measure spaces

AbstractApplications in data science, shape analysis, and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of metric measure spaces—that is, compact metric spaces endowed with probability measures. Such distances are typically defined as comparisons between metric measure space invariants, such as distance distributions (also referred to as shape distributions, distance histograms, or shape contexts in the literature). Generally, distances defined in terms of distance distributions are actually pseudometrics, in that they may vanish when comparing nonisomorphic spaces. The goal of this paper is to set up a formal framework for assessing the discrimininative power of distance distributions, that is, the extent to which these pseudometrics fail to define proper metrics. We formulate several precise inverse problems in terms of these invariants and answer them in several categories of metric measure spaces, including the category of plane curves, where we give a counterexample to the curve histogram conjecture of Brinkman and Olver, the categories of embedded and Riemannian manifolds, where we obtain sphere rigidity results, and the category of metric graphs, where we obtain a local injectivity result along the lines of classical work of Boutin and Kemper on point cloud configurations. The inverse problems are further contextualized by the introduction of a variant of the Gromov–Wasserstein distance on the space of metric measure spaces, which is inspired by the original Monge formulation of optimal transport.