Laboratory visualization of damage asymmetry formation of rock fracture via acoustic emission and digital imaging correlation

Rock fracture mechanics and accurate characterization of rock fracture are crucial for understanding a variety of phenomena interested in geological engineering and geoscience.These phenomena range from very large-scale asymmetrical fault structures to the scale of engineering projects and laboratory-scale rock fracture tests.Comprehensive study can involve mechanical modeling,site or post-mortem investigations,and inspection on the point cloud of the source locations in the form of earthquake,microseismicity,or acoustic emission.This study presents a comprehensive data analysis on characterizing the forming of the asymmetrical damage zone around a laboratory mixed-mode rock fracture.We substantiate the presence of asymmetrical damage through qualitative analysis and demonstrate that measurement uncertainties cannot solely explain the observed asymmetry.The implications of this demonstration can be manifold.On a larger scale,it solidifies a mechanical model used for explaining the contribution of aseismic mechanisms to asymmetrical fault structures.On a laboratory scale,it exemplifies an alternative approach to understanding the observational difference between the source location and the in situ or post-mortem inspection on the rock fracture path.The mechanical model and the data analysis can be informative to the interpretations of other engineering practices as well,but may face different types of challenges.

Tongue image feature correlation analysis in benign lung nodules and lung cancer

Objective To analyze the differences in the correlation of tongue image indicators among patients with benign lung nodules and lung cancer.Methods From July 1;2020 to March 31;2022;clinical information of lung cancer patients and benign lung nodules patients was collected at the Oncology Department of Longhua Hos-pital Affiliated to Shanghai University of Traditional Chinese Medicine and the Physical Ex-amination Center of Shuguang Hospital Affiliated to Shanghai University of Traditional Chi-nese Medicine;respectively.We obtained tongue images from patients with benign lung nod-ules and lung cancer using the TFDA-1 digital tongue diagnosis instrument;and analyzed these images with the TDAS V2.0 software.The extracted indicators included color space pa-rameters in the Lab system for both the tongue body(TB)and tongue coating(TC)(TB/TC-L;TB/TC-a;and TB/TC-b);textural parameters[TB/TC-contrast(CON);TB/TC-angular second moment(ASM);TB/TC-entropy(ENT);and TB/TC-MEAN];as well as TC parameters(perAll and perPart).The bivariate correlation of TB and TC features was analyzed using Pearson’s or Spearman’s correlation analysis;and the overall correlation was analyzed using canonical correlation analysis(CCA).Results Samples from 307 patients with benign lung nodules and 276 lung cancer patients were included after excluding outliers and extreme values.Simple correlation analysis indi-cated that the correlation of TB-L with TC-L;TB-b with TC-b;and TB-b with perAll in lung cancer group was higher than that in benign nodules group.Moreover;the correlation of TB-a with TC-a;TB-a with perAll;and the texture parameters of the TB(TB-CON;TB-ASM;TB-ENT;and TB-MEAN)with the texture parameters of the TC(TC-CON;TC-ASM;TC-ENT;and TC-MEAN)in benign nodules group was higher than lung cancer group.CCA further demon-strated a strong correlation between the TB and TC parameters in lung cancer group;with the first and second pairs of typical variables in benign nodules and lung cancer groups indicat-ing correlation coefficients of 0.918 and 0.817(P<0.05);and 0.940 and 0.822(P<0.05);re-spectively.Conclusion Benign lung nodules and lung cancer patients exhibited differences in correla-tion in the L;a;and b values of the TB and TC;as well as the perAll value of the TC;and the texture parameters(TB/TC-CON;TB/TC-ASM;TB/TC-ENT;and TB/TC-MEAN)between the TB and TC.Additionally;there were differences in the overall correlation of the TB and TC be-tween the two groups.Objective tongue diagnosis indicators can effectively assist in the diag-nosis of benign lung nodules and lung cancer;thereby providing a scientific basis for the ear-ly detection;diagnosis;and treatment of lung cancer.

Anisotropic creep behavior of soft-hard interbedded rock masses based on 3D printing and digital imaging correlation technology

Three-dimensional(3D)printing technology is increasingly used in experimental research of geotechnical engineering.Compared to other materials,3D layer-by-layer printing specimens are extremely similar to the inherent properties of natural layered rock masses.In this paper,soft-hard interbedded rock masses with different dip angles were prepared based on 3D printing(3DP)sand core technology.Uniaxial compression creep tests were conducted to investigate its anisotropic creep behavior based on digital imaging correlation(DIC)technology.The results show that the anisotropic creep behavior of the 3DP soft-hard interbedded rock mass is mainly affected by the dip angles of the weak interlayer when the stress is at low levels.As the stress level increases,the effect of creep stress on its creep anisotropy increases significantly,and the dip angle is no longer the main factor.The minimum value of the long-term strength and creep failure strength always appears in the weak interlayer within 30°–60°,which explains why the failure of the layered rock mass is controlled by the weak interlayer and generally emerges at 45°.The tests results are verified by comparing with theoretical and other published studies.The feasibility of the 3DP soft-hard interbedded rock mass provides broad prospects and application values for 3DP technology in future experimental research.

Diffusion tensor imaging and proton magnetic resonance spectroscopy in brain tumor Correlation between structure and metabolism

Proton magnetic resonance spectroscopy and diffusion tensor imaging are non-invasive techniques used to detect metabolites and water diffusion in vivo. Previous studies have confirmed a positive correlation of individual fractional anisotropy values with N-acetylaspartate/creatine and N-acetylaspartate/choline ratios in tumors, edema, and normal white matter. This study divided the brain parenchyma into tumor, pedtumoral edema, and normal-appearing white matter according to MRI data, and analyzed the correlation of metabolites with water molecular diffusion. Results demonstrated that in normal-appearing white matter, N-acetylaspartate/creatine ratios were positively correlated with fractional anisotropy values, negatively correlated with radial diffusivities, and positively correlated with maximum eigenvalues. Maximum eigenvalues and radial diffusivities in peritumoral edema showed a negative correlation with choline, N-acetylaspartate, and creatine. Radial diffusivities in tumor demonstrated a negative correlation with choline. These data suggest that the relationship between metabolism and structure is markedly changed from normal white matter to peritumoral edema and tumor. Neural metabolism in the peritumoral edema area decreased with expanding extracellular space. The normal relationship of neural function and microstructure disappeared in the tumor region.

Mesenchymal hamartoma of liver: Magnetic resonance imaging and histopathologic correlation

AIM： To describe the imaging features of hepatic mesenchymal hamartoma with emphasis on magnetic resonance imaging （MRI） compared to histopathologic results. METHODS： Spin-echo sequence（SE）,fast spin-echo sequence（FSE） were detected in 12 children （7 males,5 females） with mesenchymal hamartoma of the liver （IVlHL）, aged 1.2 months to 12 years,（ mean age, 6.3 years） by axial, saggital, coronary plain imaging with an Elscint 2.0T MR equipment. Their main symptoms were abdominal mass （5 cases）, enlarged liver （8 cases）, abdominal pain （1 case） and anemia （2 cases）, and negative alpha-fetoprotein. Dynamic enhancement examination was added in 2 cases. RESULTS： Six cases had single mass type of MHL, in which 3 cases had solid masses showing slight low- signal-intensity in TlWI, and irregular high-signal- intensity in T2WI, 1 case had a cystic-solid mixed mass showing several border-clear cysts in a solid mass, 2 cases had cystic masses with multi-septa. Five cases had diffuse and multifocal lesions type of MHL with its signal intensity being similar to that of the solid mass. One case had a combined diffuse and single cystic mass. In the early dynamic enhancement examination, the lesions were slightly circum-enhanced , and the center was enhanced in the later scan images. Inner hepatic vessels were compressed in 5 cases, vena cava and abdominal aortae were compressed in 3 cases. Pathological findings included fiber hyperplasia, hyaline degeneration, biliary duct hyperplasia, Iobule-like array. CONCLUSION： MR imaging is a better way to differentiate and diagnose MHL. MHL may be recognized by its characteristic occurrence in infancy and MR imaging features.

Probing granular inhomogeneity of a particle-emitting source by imaging two-pion Bose–Einstein correlations

Using the source imaging technique in two-pion interferometry,we study the image of the hydrodynamic particle-emitting source with the HIJING initial conditions for relativistic heavy-ion collisions on an event-by-event basis.It is shown that the initial-state fluctuations may give rise to bumpy structures of the medium during hydrodynamical evolution,which affects the two-pion emission space and leads to a visible two-tiered shape in the source function imaged using the two-pion Bose–Einstein correlations.This two-tiered shape can be understood within a similar but more analytic granular source model and is found to be closely related to the introduced quantity n,which characterizes the granular inhomogeneity of the source.By fitting the imaged source function with a granular source parametrization,we extract the granular inhomogeneity of the hydrodynamic source,which is found to be sensitive to both the Gaussian smearing width of the HIJING initial condition and the centrality of the collisions.

Is there a correlation between endoscopy and imaging findings in Crohn’s disease

Background and Aims: Crohn’s disease is a chronic inflammatory bowel disease (IBD). Endoscopy and radiology play an important role in the diagnosis and management of this specific disease. The ability of each of these two tests to detect the gastrointestinal involvement (ulceration, stenosis, fistula, polyp, mucosal thickening) varies according to the type of Crohn’s lesions. The purpose of our study was to evaluate the correlation between these two diagnostic methods in the detection of those specific lesions in 70 patients diagnosed with Crohn’s Disease (CD) during the period of 3 years. Methods: In this retrospective study, including 70 patients with Crohn’s disease, Four major characteristic lesions (ulceration, stenosis, fistula and polyps) were studied by endoscopy and radiological exams to evaluate the relationship between endoscopy and imaging findings in the detection of these lesions. The analysis of our results was made by statistical analysis system: EpiInfo and SPSS. Results: The concordance of each of these diagnostic modalities is average for stenosis and fistulas and low diagnostic significance for ulcers and polyps. However, the imaging features of mucosal thickening are sensitive but not specific.

3D prestack reverse time migration of ground penetrating radar data based on the normalized correlation imaging condition

The reverse time migration(RTM)of ground penetrating radar(GPR)is usually implemented in its two-dimensional(2D)form,due to huge computational cost.However,2D RTM algorithm is difficult to focus the scattering signal and produce a high precision subsurface image when the object is buried in a complicated subsurface environment.To better handle the multi-off set GPR data,we propose a three-dimensional(3D)prestack RTM algorithm.The high-order fi nite diff erence time domian(FDTD)method,with the accuracy of eighth-order in space and second-order in time,is applied to simulate the forward and backward extrapolation electromagnetic fi elds.In addition,we use the normalized correlation imaging condition to obtain pre-stack RTM result and the Laplace fi lter to suppress the low frequency noise generated during the correlation process.The numerical test of 3D simulated GPR data demonstrated that 3D RTM image shows excellent coincidence with the true model.Compared with 2D RTM image,the 3D RTM image can more clearly and accurately refl ect the 3D spatial distribution of the target,and the resolution of the imaging results is far better.Furthermore,the application of observed GPR data further validates the eff ectiveness of the proposed 3D GPR RTM algorithm,and its fi nal image can more reliably guide the subsequent interpretation.

Application value of four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging in screening fetal congenital heart disease

Objective:To explore the value of four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging in screening fetal congenital heart disease.Methods: A total of 671 pregnant women at 22-24 gestational weeks from January 2018 to December 2018 were examined by two-dimensional ultrasound and four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging to observe the development of fetal cardiovascular structure and to compare the two methods in terms of diagnostic accuracy, examination time, image quality and new physician training cycle.Results: Cardiac malformations were found in 12 of the 671 fetuses, among which 11 cases were detected by four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging and 1 case was missed. Postnatal echocardiographic reexamination and autopsy confirmed 12 cases of children with cardiac malformation, including 1 case of atrial septal defect (missed diagnosis by four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging), 4 cases of tetralogy of Fallot's disease, 1 case of right ventricular double outlet, 3 cases of left ventricular dysplasia, 2 cases of complete transposition of the great artery and 1 case of tricuspid valve descending malformation. There was no statistically significant difference between four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging and conventional two-dimensional color echocardiography or/and autopsy (P>0.05). In terms of examination time and new physician training, the four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging technique was superior to conventional color ultrasound screening. No statistically significant difference in image quality.Conclusions:The four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging can rapidly and accurately display fetal heart development, and can be used as the main screening method for fetal congenital heart disease in clinical practice.

Evaluation of fatigue property of asphalt mixtures based on digital image correlation method

In order to evaluate the accumulative of tensile strain in the process of fatigue failure, the digital image correlation（DIC） method was utilized to characterize the tensile strain development of asphalt mixtures in the indirect tensile（IDT）fatigue test. Three typical hot mix asphalt（HMA） mixtures with varying nominal maximum aggregate sizes were tested at four stress levels. During the tests, a digital camera was mounted to capture the displacement/strain fields on the surface of the specimen by recording the real-time change of speckle position. The results indicate that the vertical deformation curve can barely evaluate the fatigue performance accurately due to the non-negligible local deflection near the loading point. However, based on the analysis of strain fields,the optimal fatigue cracking zone is determined as a 40mm×40mm rectangle in the middle of the specimens. Also, a reasonable fatigue model based on the tensile strain curves calculated by DIC is proposed to predict the fatigue lives of asphalt mixtures.

Using shapes correlation for active contour segmentation of uterine fibroid ultrasound images in computer-aided therapy

Segmenting the lesion regions from the ultrasound （US） images is an important step in the intra-operative planning of some computer-aided therapies. High-Intensity Focused Ultrasound （HIFU）, as a popular computer-aided therapy, has been widely used in the treatment of uterine fibroids. However, such segmentation in HIFU remains challenge for two reasons： （1） the blurry or missing boundaries of lesion regions in the HIFU images and （2） the deformation of uterine fibroids caused by the patient＇s breathing or an external force during the US imaging process, which can lead to complex shapes of lesion regions. These factors have prevented classical active contour-based segmentation methods from yielding desired results for uterine fibroids in US images. In this paper, a novel active contour-based segmentation method is proposed, which utilizes the correlation information of target shapes among a sequence of images as prior knowledge to aid the existing active contour method. This prior knowledge can be interpreted as a unsupervised clustering of shapes prior modeling. Meanwhile, it is also proved that the shapes correlation has the low-rank property in a linear space, and the theory of matrix recovery is used as an effective tool to impose the proposed prior on an existing active contour model. Finally, an accurate method is developed to solve the proposed model by using the Augmented Lagrange Multiplier （ALM）. Experimental results from both synthetic and clinical uterine fibroids US image sequences demonstrate that the proposed method can consistently improve the performance of active contour models and increase the robustness against missing or misleading boundaries, and can greatly improve the efficiency of HIFU therapy.

Specimen aspect ratio and progressive field strain development of sandstone under uniaxial compression by three-dimensional digital image correlation

The complete stress-strain characteristics of sandstone specimens were investigated in a series of quasistatic monotonic uniaxial compression tests.Strain patterns development during pre-and post-peak behaviours in specimens with different aspect ratios was also examined.Peak stress,post-peak portion of stress-strain,brittleness,characteristics of progressive localisation and field strain patterns development were affected at different extents by specimen aspect ratio.Strain patterns of the rocks were obtained by applying three-dimensional(3D) digital image correlation(DIC) technique.Unlike conventional strain measurement using strain gauges attached to specimen,3D DIC allowed not only measuring large strains,but more importantly,mapping the development of field strain throughout the compression test,i.e.in pre-and post-peak regimes.Field strain development in the surface of rock specimen suggests that strain starts localising progressively and develops at a lower rate in pre-peak regime.However,in post-peak regime,strains increase at different rates as local deformations take place at different extents in the vicinity and outside the localised zone.The extent of localised strains together with the rate of strain localisation is associated with the increase in rate of strength degradation.Strain localisation and local inelastic unloading outside the localised zone both feature post-peak regime.

Uniaxial experimental study of the acoustic emission and deformation behavior of composite rock based on 3D digital image correlation(DIC)

In this paper, uniaxial compression tests were carried out on a series of composite rock specimens with different dip angles, which were made from two types of rock-like material with different strength. The acoustic emission technique was used to monitor the acoustic signal characteristics of composite rock specimens during the entire loading process. At the same time, an optical non-contact 3 D digital image correlation technique was used to study the evolution of axial strain field and the maximal strain field before and after the peak strength at different stress levels during the loading process. The effect of bedding plane inclination on the deformation and strength during uniaxial loading was analyzed. The methods of solving the elastic constants of hard and weak rock were described. The damage evolution process, deformation and failure mechanism, and failure mode during uniaxial loading were fully determined. The experimental results show that the θ = 0?–45?specimens had obvious plastic deformation during loading, and the brittleness of the θ = 60?–90?specimens gradually increased during the loading process. When the anisotropic angle θincreased from 0?to 90?, the peak strength, peak strain,and apparent elastic modulus all decreased initially and then increased. The failure mode of the composite rock specimen during uniaxial loading can be divided into three categories:tensile fracture across the discontinuities(θ = 0?–30?), slid-ing failure along the discontinuities(θ = 45?–75?), and tensile-split along the discontinuities(θ = 90?). The axial strain of the weak and hard rock layers in the composite rock specimen during the loading process was significantly different from that of the θ = 0?–45?specimens and was almost the same as that of the θ = 60?–90?specimens. As for the strain localization highlighted in the maximum principal strain field, the θ = 0?–30?specimens appeared in the rock matrix approximately parallel to the loading direction,while in the θ = 45?–90?specimens it appeared at the hard and weak rock layer interface.

Use of a Digital Image Correlation Technique for Measuring the Material Properties of Beetle Wing

Beetle wings are very specialized flight organs consisting of the veins and membranes.Therefore it is necessary from a bionic view to investigate the material properties of a beetle wing experimentally.In the present study,we have used a Digital Image Correlation (DIC) technique to measure the elastic modulus of a beetle wing membrane.Specimens were prepared by carefully cutting a beetle hind wing into 3.0 mm by 7.0 mm segments (the gage length was 5 mm).We used a scanning electron microscope for a precise measurement of the thickness of the beetle wing membrane.The specimen was attached to a designed fixture to induce a uniform displacement by means of a micromanipulator.We used an ARAMISTM system based on the digital image correlation technique to measure the corresponding displacement of a specimen.The thickness of the beetle wing varied at different points of the membrane.The elastic modulus differed in relation to the membrane arrangement showing a structural anisotropy;the elastic modulus in the chordwise direction is approximately 2.65 GPa,which is three times larger than the elastic modulus in the spanwise direction of 0.84 GPa.As a result,the digital image correlation-based ARAMIS system was suc- cessfully used to measure the elastic modulus of a beetle wing.In addition to membrane's elastic modulus,we considered the Poisson's ratio of the membrane and measured the elastic modulus of a vein using an Instron universal tensile machine.The result reveals the Poisson's ratio is nearly zero and the elastic modulus of a vein is about 11 GPa.

Convection and correlation of coherent structure in turbulent boundary layer using tomographic particle image velocimetry

The present experimental work focuses on a new model for space-time correlation and the scale-dependencies of convection velocity and sweep velocity in turbulent boundary layer over a flat wail. A turbulent boundary layer flow at Reo = 2460 is measured by tomographic particle image velocimetry （tomographic PIV）. It is demonstrated that arch, cane, and hairpin vortices are dominant in the logarithmic layer. Hairpins and hairpin packets are responsible for the elongated low-momentum zones observed in the instantaneous flow field. The conditionally-averaged coherent structures systemically illustrate the key roles of hairpin vortice in the turbulence dynamic events, such as ejection and sweep events and energy transport. The space-time correlations of instantaneous streamwise fluctuation velocity are calculated and confirm the new elliptic model for the space-time correlation instead of Taylor hypothesis. The convection velocities derived from the space-time correlation and conditionally-averaged method both suggest the scaling with the local mean velocity in the logarithmic layer. Convection velocity result based on Fourier decomposition （FD） shows stronger scale- dependency in the spanwise direction than in streamwise direction. Compared with FD, the proper orthogonal decomposition （POD） has a distinct distribution of convection velocity for the large- and small-scales which are separated in light of their contributions of turbulent kinetic energy.

Assessment of digital image correlation method in determining large scale cemented rockfill strains

A conventional contact method(using linear transducers)and a non-contact method are deployed to measure the axial and lateral deformations of large scale cylindrical cemented rockfill specimens.Experimental works incorporating two pinhole cameras to create one stereovision by digital image correlation shows that the non-contact method is as reliable for testing large cylindrical specimens as measurements done by using linear variable displacement transformer and string potentiometer.Considering this particular large specimen,the experiment resulted in the acceptable mean difference between lateral strain using both methods is 5.1 percent,and 14.5 percent for the axial strain.This occurrence is inevitable due to the heterogeneity of the concrete system and the placement of the monitoring point in digital image correlation method,although the comparison of stress-strain relationship in both methods still indicates a conformity.Based on the results of the present experiments,the authors recommend the noncontact method for a detailed investigation of the material behavior during the uniaxial compressive strength tests.Full field strain measurement enables this digital method to examine local strains near cracks at any point,a very useful tool for studying material deformation behavior.

Quasi-static tensile deformation and fracture behavior of a highly particle-filled composite using digital image correlation method

Polymer bonded explosives (PBXs) are highly particle-filled composite materials.This paper experimentally studies the tensile deformation and fracture behavior of a PBX simulation by using the semi-circular bending (SCB) test.The deformation and fracture process of a pre-notched SCB sample with a random speckle pattern is recorded by a charge coupled device camera.The displacement and strain fields on the observed surface during the loading process are obtained by using the digital image correlation method.The crack opening displacement is calculated from the displacement fields,the initiation and propagation of the crack are analyzed.In addition,the damage evolution and fracture mechanisms of the SCB sample are analyzed according to the strain fields and the correlation coefficient fields at different loading steps.

DAMAGE AND FRACTURE EVALUATION OF GRANULAR COMPOSITE MATERIALS BY DIGITAL IMAGE CORRELATION METHOD

This paper presents the applications of digital image correlation technique to the mesoscopic damage and fracture study of some granular based composite materials including steel- fiber reinforced concrete,sandstone and crystal-polymer composite.The deformation fields of the composite materials resulted from stress localization were obtained by the correlation computation of the surface images with loading steps and thus the related damage prediction and fracture parameters were evaluated.The correlation searching could be performed either directly based on the gray levels of the digital images or from the wavelet transform(WT)coefficients of the transform spectrum.The latter was developed by the authors and showed higher resolution and sensitivity to the singularity detection. Because the displacement components came from the rough surfaces of the composite materials without any coats of gratings or fringes of optical interferometry,both surface profiles and the deformation fields of the composites were visualized which was helpful to compare each other to analyze the damage of those heterogeneous materials.

Characterization for elastic constants of fused deposition modelling-fabricated materials based on the virtual fields method and digital image correlation

Fused deposition modelling(FDM), a widely used rapid prototyping process, is a promising technique in manufacturing engineering. In this work, a method for characterizing elastic constants of FDM-fabricated materials is proposed. First of all, according to the manufacturing process of FDM, orthotropic constitutive model is used to describe the mechanical behavior. Then the virtual fields method(VFM) is applied to characterize all the mechanical parameters(Q, Q, Q, Q) using the full-field strain,which is measured by digital image correlation(DIC). Since the principal axis of the FDM-fabricated structure is sometimes unknown due to the complexity of the manufacturing process, a disk in diametrical compression is used as the load configuration so that the loading angle can be changed conveniently. To verify the feasibility of the proposed method, finite element method(FEM) simulation is conducted to obtain the strain field of the disk. The simulation results show that higher accuracy can be achieved when the loading angle is close to 30?. Finally, a disk fabricated by FDM was used for the experiment. By rotating the disk, several tests with different loading angles were conducted. To determine the position of the principal axis in each test, two groups of parameters(Q, Q, Q, Q) are calculated by two different groups of virtual fields. Then the corresponding loading angle can be determined by minimizing the deviation between two groups of the parameters. After that, the four constants(Q, Q, Q, Q) were determined from the test with an angle of 27?.

Single foggy image restoration based on spatial correlation analysis of dark channel prior

Focusing on the degradation of foggy images, a restora- tion approach from a single image based on spatial correlation of dark channel prior is proposed. Firstly, the transmission of each pixel is estimated by the spatial correlation of dark channel prior. Secondly, a degradation model is utilized to restore the foggy image. Thirdly, the final recovered image, with enhanced contrast, is obtained by performing a post-processing technique based on just-noticeable difference. Experimental results demonstrate that the information of a foggy image can be recovered perfectly by the proposed method, even in the case of the abrupt depth changing scene.