ABSTRACT
X-ray imaging is broadly applied for defect detection in industry and research. However, traditional X-ray imaging methods struggle to achieve high sensitivity for pixel-level defects (1–3 pixels) in noisy or scattering-dominated environments, such as metal workpieces or thick low-Z materials. To address this, we introduce move contrast X-ray imaging (MCXI), which leverages relative motion between the sample and imaging system to suppress noise and enhance the sensitivity of weak signal detection in complex backgrounds. MCXI has been successfully applied in fields such as biomedical imaging and high-resolution material studies, demonstrating significant noise resistance and sensitivity improvements. This paper extends MCXI to the testing of defects in static samples, aiming to solve the challenges of detecting pixel-level in high-noise and complex backgrounds. Numerical simulations demonstrate MCXI’s capability for single-pixel defect detection. Synchrotron radiation experiments validate this technique through quantitative characterization of 1.54-pixel defects (1-μm polystyrene spheres) in low-contrast polyvinyl chloride (PVC) samples, achieving a CNR of 26.12 - representing a 14.04 × improvement over direct projection imaging. The method’s industrial applicability is demonstrated through alloy steel pipe testing with 81.2 μm defects (8.12 pixels), where MCXI achieves a CNR of 15.16 (8.1 × enhancement) using laboratory-based X-ray systems. MCXI’s seamless integration with both synchrotron facilities and industrial X-ray machines, combined with its noise-resistant characteristics, establishes a universal solution for high-sensitivity nondestructive testing in challenging environments with strong scattering and complex backgrounds.
1. Introduction
Early-stage defects—physical discontinuities in materials or structures [1]—pose significant risks across industries, potentially leading to catastrophic failures, reduced lifespan, and increased maintenance costs [2,3]. For example, sub-10 μm cracks in wind turbine blades caused by cyclic loading can severely compromise structural integrity [4,5]. Detecting such defects at the near-pixel in X-ray imaging is critical for timely intervention through repair techniques like localized heat treatment or ultrasonic processing [6–9].
Nondestructive testing (NDT) plays a vital role in defect characterization, yet existing methods face inherent limitations. Conventional X-ray imaging, while versatile for complex materials, often fails to resolve defects approaching the detector’s pixel size, particularly in noisy or scattering-dominated environments such as thick low-Z materials or metal workpieces [10]. Advanced techniques like computed tomography (CT) and computed laminography (CL) are constrained by resolution limits (e.g., minimum detectable defects ≥3–4 pixels [11,12]), reconstruction artifacts, and impracticality for large-scale industrial applications [11–19]. Even phase-contrast imaging (PCI), which enhances sensitivity for low-density materials, struggles when defect and matrix densities are comparable or defect sizes near the pixel size [20–25].
A central challenge lies in overcoming the pixel-size barrier—detecting defects near to the imaging system’s nominal pixel size. Recent advances in X-ray physics and instrumentation provide potential pathways. For instance, dark-field imaging exploits scattered X-rays to detect sub-pixel microstructures like microcracks or porosity [26,27], while coded-aperture masks inspired by X-ray astronomy enable sub-pixel resolution through geometric signal modulation [28,29]. Mechanical super-resolution methods, such as grating displacement or X-ray spot scanning, synthesize high-resolution images by combining multiple shifted exposures [30,31]. However, these approaches often require specialized hardware (e.g., synchrotron sources [14]), suffer from compatibility issues with conventional NDT setups, or lack robustness in high-noise environments. Dark-field imaging, for example, performs poorly in strongly absorbing materials due to signal attenuation [32], and mask-based techniques demand precise alignment incompatible with industrial workflows [29]. Thus, a lab-compatible, noise-resistant method for pixel-level defect detection remains an unmet need. To address these gaps, we propose Move Contrast X-ray Imaging (MCXI), a motion-based technique initially developed for dynamic systems [33–40], for sensitive detection of defects with sizes at the pixel level. Unlike conventional absorption or phase-contrast imaging, MCXI exploits relative motion between the sample and imaging system to isolate defect signals from static background noises. For defects in a relatively uniform medium, the motion of the defects can be realized by simply scanning the sample taking advantage of movement relativity. This motion-induced signal modulation enhances sensitivity to the detection of defects at the pixel level even in scattering-heavy or low-contrast scenarios.
This paper intends to introduce X-ray move contrast imaging into NDT for sensitive detection of defects at the pixel level. Firstly, the principle of the MCXI method is briefly introduced. The digital simulation is used to study the feasibility of pixel-level resolution defect testing and the effect of noise on the NDT sensitivity. Then, experiments with the standard samples and alloy steel pipe samples are carried out to evaluate the proposed NDT method. Except for synchrotron radiation, an X-ray tube-based imaging system is also employed to verify the proposed method for defect testing in a conventional laboratory. Finally, the conclusion is given.
2. Principle and method
X-ray move contrast imaging (MCXI) leverages the time-domain frequency properties of moving targets to suppress, complex backgrounds, motion artifacts, and high-frequency noise. By projecting the frequency-domain signal of the target back into real space, MCXI achieves highly sensitive imaging of weak signals that are difficult to resolve using conventional methods. When applied to non-destructive testing (NDT), MCXI significantly enhances the detection sensitivity for pixel-level defects while effectively eliminating the influence of scattering and other complex backgrounds.
2.1. Principle of move contrast X-ray imaging
Based on the Fourier transform move contrast imaging, our research group has further developed wavelet transform move contrast imaging, Hilbert-Huang transform move contrast imaging, and has extended the technique to the visible light domain [38]. Fourier transform integrates across the entire time domain, and its spectrum does not contain time variables, making it suitable for frequency analysis of stationary signals. Here, Fourier transform move contrast imaging is used for defect detection.
Assuming that the grayscale value at each point in the projection image is represented as g(x,y). The detector collects a sequence of projection images over a period T (seconds) with a frame rate of fs (frames per second). The grayscale value at a specific point at time t is expressed as g(x,y,t), and this value changes over time, containing information about motion and noise. By applying a discrete Fourier transform to the grayscale value g(x,y,t) at point (x,y), the frequency spectrum information at that point can be obtained, and different motion signals can be distinguished through frequency domain expansion and analysis, the formula is as follows:
G(x,y,k) represents the frequency information of g(x,y,t), where N is the length of the sequence. As long as a certain frame rate is used to record a sequence of images, the spatial distribution of move-contrast amplitude and phase at specific frequencies can be obtained, resulting in amplitude and phase contrast images. By expanding Equation (1) using Euler’s formula, the amplitude and phase can be derived:
The amplitude reflects the coherence between the motion of the sample and the target, which corresponds to the motion trajectory, while the phase indicates the time evolution of the motion signal which can be used to calculate the velocity of the target. Finally, through image fusion, a move contrast image containing motion trajectory, direction, and velocity information is obtained. To filter out the motion information of the target, the amplitude information can be decomposed into a sum of different frequencies, where each frequency represents the motion information of different components. The formula is as follows:
The first term A(x,y,0) represents the average signal intensity, which corresponds to the Direct Current component of the amplitude and de scribes the trend of the signal at different frequencies. The second, third and fourth terms represent the low-frequency component, bandpass and high-frequency components of the signal, respectively. kLP and kHP are the spectral ranges of the band-pass filter. By selecting an appropriate frequency range, the target’s motion can be separated from the complex background and high-frequency noise, achieving high-sensitivity imaging of weak signals of the target, referring to the defect in the proposed method.
2.2. Defect testing based on relative movement
Usually, move contrast imaging is used for high-sensitivity tracking of moving targets, and it should be impossible to form imaging contrast for stationary targets. Since motion is relative, when scanning a relatively uniform matrix with defects, the defects exhibit relative motion with respect to the uniform matrix, which can generate motion contrast and enable high-sensitivity defect detection. Based on this principle, a method of continuous sample scanning at a constant speed is adopted to obtain projection images that contain move contrast information. As shown in Fig. 1, the sample is scanned horizontally while the detector synchronously acquires the projection image information of the sample.
Sample scanning speed and detector sampling frequency are crucial for the image reconstruction of MCXI, which depends on sample material and defect characteristics. For fine detection, the scanning step of one pixel size of the detector is recommended. After collecting a set of images in time sequence which contains defect motion information, the defect image is reconstructed by MCXI and then distribution map of defects is obtained through the fusion of move contrast signal and projection image. In this way, the MCXI method is implemented.
Fig. 1. (a) Schematic diagram of image data acquisition by scanning the sample horizontally and taking the projection images synchronously. Fig. 1(b) illustrates the signal processing workflow of MCXI: (1) acquisition of time-series projection data; (2) Fourier transform to the frequency domain; (3) band-pass filtering to isolate defect motion signals; (4) inverse Fourier transform for image reconstruction. The selected frequency band [kLP,kHP] effectively suppresses noise and enhances defect contrast.
3. Results and analysis
Digital simulations were carried out to verify the feasibility of applying move contrast X-ray imaging for defect detection in samples. Simulation was conducted under ideal noise-free conditions, followed by the introduction of noise and variation of defect size to test the imaging performance under various conditions. Standard samples were then tested using synchrotron radiation to verify the feasibility of the method experimentally. Finally, the NDT method of MCXI was extended to an X-ray tube and a sample of special steel tube is tested to verify its feasibility for a laboratory X-ray imaging system.
Fig. 2. Simulated pipe samples and pore defects (a) sample of pipe, front view; (b) sample, side view; (c) image of defects; (d) 5th image of direct projections; (e) image of the time-domain differential imaging (result by subtracting the 6th with 5th projection); (f) MCXI image.
Fig. 3. Simulation results of noisy defect detection (a) 5th image of direct projections; (b)image of time domain differential imaging (result by subtracting the 6th with 5th projection); (c) MCXI image.
3.1. Digital simulation
3.1.1. Noise-free NDT of MCXI
To verify the feasibility of our method, the simulation is conducted out in the ideal situation without noise, and the simulated sample is a carbon steel pipe, as shown in Fig. 2(a)(b). The outside and inside radius of the pipe is 200 μm and 125 μm respectively, the length is 1200 μm, and the linear absorption coefficient is about 0.2 cm− 1 at X-ray energy of 15 keV, the absorption coefficient of the defective area is 0.1 cm− 1. The pixel size of the detector is 1 μm. As shown in Fig. 2(c), spherical defects are observed in the tube, including one defect at the one-pixel scale (marked by the green arrow) and two larger defects with diameters of 2 μm and 3 μm (indicated by the yellow and blue arrows, respectively). The sample is scanned with a step of 1 μm/s to capture 32 projections. The X-ray absorption through the pipe follows the Lambert-Beer law [41]. The gray value in the projection image depends on X-ray absorption while penetrating through the pipe. The lower absorption at the optical path with defect results in gray difference, which is taken as tracking signal for MCXI.
To benchmark the performance of MCXI, we implemented a conventional time-domain differential imaging (TDDI) method [42], which calculates defect signals by subtracting consecutive projection images:
Simulation results are shown in Fig. 2(d), (e), (f) respectively. One of the projection images obtained from the simulation is given in Fig. 2(d), where the defects are completely indistinguishable due to their small size and weak signal within the strong absorption background. Fig. 2(e) depicts an image reconstructed using time-domain differential imaging [42], which distinguishes defects with diameter of 3 μm (blue arrow) and 2 μm (yellow arrow). However, the resolution for pixel-level (green arrow) is insufficient for visual identification. This implies that traditional methods struggle to detect such tiny defects. In contrast, Fig. 2(f) displays the image reconstructed by MCXI, in which all three defects with a size of 1, 2, and 3 pixels respectively are all definitely revealed. This indicates that the MCXI method has the capability to detect subtle one-pixel-level defects.
3.1.2. Effect of noise on MCXI
In X-ray imaging, noises are mainly introduced by the detectors due to photon count fluctuations, thermal noise, dark current, pixel response inconsistency, and photoelectric conversion errors. These noises typically fluctuate within a certain range. When the signal strength significantly exceeds the noise, the noise influence can be ignored. However, when the signal becomes weaker, approaching or even falling below the noise’s average intensity, it becomes difficult for direct projection imaging to capture effective defect information. Conditions such as small defect sizes or defects composed of low-Z materials can weaken the defect signal, rendering existing detection methods ineffective. To simulate the real imaging process, we add random Gaussian noise that masks the defect signal in the projected image. We then investigate the effect of this noise on MCXl non-destructive testing.
The results of the noise simulation are shown in Fig. 3. The simulated projection image is shown in Fig. 3(a), where the defects are completely indistinguishable due to the small size against the strong absorption background, the weak signal, and the influence of noise. Fig. 3(b) shows the image reconstructed using the time-domain difference mode. While TDDI can amplify temporal variations caused by defect motion, it suffers from a critical limitation: Noise amplification, Stochastic noise in adjacent frames is uncorrelated, leading to a √2-fold increase in noise variance after subtraction [43]. Since this, the image cannot distinguish the defective signal. This means that it is difficult for traditional methods to detect such tiny defects in the projection image under the influence of noise. In contrast, MCXI’s frequency-domain filtering (Eq. (4)) selectively enhances defect motion signals while suppressing noise. Fig. 3(c) shows the image reconstructed with MCXI, which clearly distinguishes between defects with a diameter of 3 μm (blue) and 2 μm (yellow) respectively. However, due to the effect of noises, the defect with a diameter of 1 μm is not revealed in the reconstructed move contrast image. This simulation results shows that the MCXI method for NDT has excellent anti-noise ability and can detect defective signals with a size of 2 pixels in the case of strong noises. Because of noises, the signal of the defect with a size of 1 pixel is not efficiently detected.
Here, to quantitatively assess the effectiveness of the MCXI method, we introduce the Contrast-to-Noise Ratio (CNR), which is an important metric for evaluating the contrast between the signal and the noise background in an image. CNR reflects the difference between the region of interest (ROI) and the background. A higher CNR typically indicates better defect inspection quality, making it easier to distinguish the target region from the background. The formula for calculating the CNR is given in Eq. (6), where St represents the mean signal intensity of the target region, Sb denotes the mean signal intensity of the background region, σ b is the standard deviation of the background noise.
Taking the 2 μm defect (marked by the orange arrow) as an example, the CNR of the defect in the direct projection image is 1.73, while in the time-domain differential imaging, it is 2.16. In contrast, the MCXI method achieves a CNR of 74.60, representing a 43.12 × improvement over direct projection imaging and a 34.54 × enhancement compared to time-domain differential imaging. This significant improvement demonstrates that motion contrast not only enables the detection of defects that are undetectable by traditional methods but also exhibits excellent noise resistance, making it highly suitable for challenging detection scenarios with weak signals and complex backgrounds.
3.1.3. Parametric study of MCXI performance
To optimize MCXI for industrial NDT, we simulated defects undervarying step sizes and density contrasts (Table 1). In the simulations, random Gaussian noise with a mean of 0 and a variance of 0.01 was added. The absorption coefficient of the pipe is set to 1, and Δμ represents the density difference between the defect and the pipe.
3.2. Evaluation experiments with synchrotron radiation X-rays
To address the challenge of controlling small defects in real samples, this study employs 1 μm polystyrene particles [44] as standardized defects, enabling systematic validation of detection methods under controlled conditions. These particles were randomly dispersed on a 2 mm-thick polyvinyl chloride (PVC) plate, selected for its density matching that of polystyrene to minimize contrast between defects and the background. The 1 μm diameter corresponds to 1.54 pixels in the imaging system, providing a rigorous test case for evaluating the MCXI method’s capability in detecting pixel-level defects.
The experiments were conducted at the X-ray dynamic imaging beamline BL16U2 of the Shanghai Synchrotron Radiation Facility (SSRF), a third-generation synchrotron radiation source. Monochromatic mode was used for imaging. The experimental setup is illustrated in Fig. 4(a)(b). The X-ray beam passing through the sample was converted into visible light by a scintillator (LuAG:Ce,100 μm) and then magnified using a 10 × optical microscope. The resulting image was recorded by a CMOS fast imaging detector. The CMOS detector has a basic pixel size of 6.5 μm, which, after 10 × optical magnification, results in an effective pixel size of 0.65 μm. During the moving scan, a total of 36 projections were collected. To balance image quality and time efficiency, the exposure time was set to 100 ms, and the energy was set to 13 keV.
Fig. 4. (a) Diagram of the experimental setup for synchrotron X-ray imaging detection of polystyrene spheres; (b) picuture of experimental facilities; (c) 13th image of direct projections; (d) image of the time domain differential imaging (result by subtracting the 36th with 35th projections); MCXI image with halo artifacts; (f) MCXI image with noise suppressing.
Fig. 4(c) is a direct projection image, due to the weak absorption of the polystyrene microsphere and low contrast, combined with the influence of stray noise, the spheres are hard to be distinguished. The arrows in the image indicate the locations of the simulated defects. When their positions are known, a certain grayscale difference between the defects and the background can be observed. However, when the positions are unknown, the defects lack clear boundaries and sufficient grayscale contrast with the background, making them indistinguishable. Fig. 4(d) is an image of time-domain differential imaging, and the defect cannot be detected at the corresponding positions; Fig. 4(f) shows the MCXI results, which successfully detected all seven defects marked by arrows and demonstrated high image quality. The experimental results indicate that the MCXI method has high sensitivity for detecting small and weak defects. Experimental results indicate that the proposed MCXl method can detect weak absorption defects as small as a single pixel, even in a simple background. The method clearly identifies the defects marked by the arrows. The move contrast defect detection imaging method demonstrates high sensitivity and successfully detects small defects with a weak signal, such as a 1.54-pixel defect in the actual sample.
Taking the left defect as an example, the CNR of the defect in the direct projection image is 1.86, while in the time-domain differential imaging, it is 1.48. The MCXI method achieves a CNR of 26.12, representing a 14.04 × improvement over direct projection imaging and a 17.65 × enhancement compared to time domain differential imaging. While the experimental CNR gains (14–18 × ) are slightly lower than those observed in simulations (34–43 × for a 2 μm defect), this discrepancy stems from the experimental defect size (1.54-pixel) is smaller than the simulated defect (2 μm). Nevertheless, both experimental and simulated results consistently demonstrate that MCXI significantly outperforms conventional methods, validating its robustness in practical scenarios with challenging detection conditions.
Due to the pixel-level size and low X-ray absorption of the polystyrene microspheres, the defect signals are extremely weak, and noise dominates the projection images. To enhance sensitivity in such noisy environments, the MCXI reconstruction algorithm selectively amplifies high-frequency boundary signals. While this improves defect contrast, it may also introduce a “halo” effect, causing perceived rounding or edge blurring in the reconstructed images. To further suppress noise and mitigate these artifacts, we applied a post-processing denoising algorithm based on the noise2noise framework [45]. The MCXI image with halo artifacts and MCXI image with noise suppressing are shown in Fig. 4 (e) and (f), respectively, demonstrating improved defect clarity and reduced halo effects.
3.3. MCXI with laboratory X-ray imaging system
3.3.1. Sample preparation
The alloy steel tube material features excellent mechanical performance, corrosion resistance, and radiation resistance, allowing it to operate stably in high-temperature, high-pressure, and complex environments. Ensuring the integrity of both the inner and outer surfaces of the tube is critical for maintaining the structural reliability and sealing performance in industries such as aerospace, energy, chemical processing, and fluid transportation. Even minor defects, such as micro-cracks, pores, or inclusions, can compromise the tube’s mechanical strength or lead to leaks, reducing its overall service life and increasing maintenance costs. The sample selected for the experiments is a piece of alloy steel tube used in industry, with a length of 110 ± 1.00 mm, an outer profile diameter of 13.44 ± 0.06 mm, an outer circle diameter of 12 ± 0.05 mm, and an inner circle diameter of 11 ± 0.04 mm. The sample diagram is shown in Fig. 5(a).
Its strong scattering and absorption to X-rays, complex geometry and stringent defect detection requirements provide a benchmark to validate the pixel-level sensitivity and accuracy of the MCXI method. In this study, the steel tube serves as the final test sample to demonstrate the feasibility and effectiveness of the proposed MCXI technique in practical defect detection scenarios.
3.3.2. MCXI test results
A laboratory X-ray imaging system was used for the experiments, to verify the applicability of the proposed NDT method of MCXI for conventional test. The imaging system consists mainly of a micro-focus X-ray tube, sample stage with lateral scanning function and a large-area CMOS flat-panel X-ray detector. The geometrical magnification of the projection imaging with a conical X-ray beam allows for flexible adjustment of the magnification by varying the relative distance between the sample, detector, and X-ray source. This not only meets the imaging requirements of samples of different sizes but also reduces the need for detector pixel size in high-resolution imaging. The imaging system uses a large-area flat-panel X-ray detector with a single pixel size of 49.5 μm. The experimental optical path diagram is shown in Fig. 5(b). The energy used for the experiments was 120 kV, the current was set to 100 μA, and the exposure time was 0.5 s. The magnification was 4.95× , and the effective pixel size was 10 μm. During data acquisition, the sample’s movement step size was 10 μm, which corresponds to 1pixels. In each set of experiments, the sample was continuously scanned for 40 steps. The experimental setup is shown in Fig. 5(c).
Fig. 5(d) is a direct projection image of the sample, where the small defects are drowned by severe X-ray scattering from the high-density metal background. Quantitative analysis of the defect marked by the orange circle (diameter: 81.2 μm, 8.12 pixels) reveals a CNR of 1.88, insufficient for reliable detection. In contrast, Fig. 5(e) demonstrates the MCXI reconstruction, where multiple defects (like orange marker) and welds circled in red are clearly identified. For this defect, MCXI achieves a CNR of 15.16—a 8.1 × improvement over direct projection imaging. Independent validation through classical CT (Fig. 5(f)) confirms that while conventional CT reliably identifies weld seams marked in red, it fails to resolve isolated shallow micro-defects due to scattering interference. In contrast, MCXI successfully detects both types of flaws with precise spatial alignment, demonstrating its compatibility with laboratory X-ray systems. Under the same resolution conditions, MCXI achieves significantly higher sensitivity and defect contrast compared to conventional CT. This capability to reveal defects undetectable by conventional imaging underscores MCXI’s superior performance in industrial NDT applications, particularly under challenging conditions with strong noise and scattering backgrounds.
Unlike conventional CT, which requires hundreds of projections for full-volume reconstruction, MCXI enables a two-step screening strategy: Rapid full-length scanning to localize potential defects. Targeted high-sensitivity scanning to resolve pixel-level features with minimal radiation dose.
This approach significantly reduces inspection time while maintaining high sensitivity, making it ideal for large-scale industrial applications such as pipeline monitoring and turbine blade inspection. While the 81.2-μm defect (8.12-pixels) in the alloy steel pipe exceeds the nominal pixel-level range (1–3 pixels), its successful detection by MCXI under laboratory X-ray systems validates the method’s compatibility with conventional industrial equipment. This case demonstrates MCXI’s adaptability to varying defect scales, complementing its core capability of pixel-level defect detection in high-noise environments. The synergy between high sensitivity for sub-3-pixel defects and robustness in industrial-scale applications positions MCXI as a versatile solution for comprehensive NDT workflows.
4. Conclusion
This paper proposes and develops a pixel-level defect testing method based on move contrast X-ray imaging to meet the non-destructive and high sensitivity defect testing needs of various material samples. Through digital simulations, synchrotron radiation experiments, and experiments with laboratory X-ray imaging system, we demonstrate that the MCXI method can successfully detect defects even when traditional NDT method fails. The study highlights the following key features and advantages of the method.
- High Sensitivity Detection. We significantly enhance the ability to detect weak signals in complex backgrounds, achieving pixel-level defect recognition. And we demonstrate that the MCXI method can successfully detect defects even when traditional NDT method fails.
- Strong Noise Resistance. We effectively suppress noise and scattering effects, improving imaging contrast and detection accuracy.
- Broad Applicability. We demonstrate MCXI works well with X-rays from both synchrotron radiation and laboratory X-ray tube, making it applicable for both scientific research and industry in sensitive defect detecting.
While the method shows remarkable advantages in sensitivity, challenges remain in the ‘precise characterization of defect sizes and shapes’, particularly for defects at pixel-level where spatial information is inherently limited. Future research will focus on optimizing image reconstruction algorithms and exploring applications in three-dimensional detection. By integrating advanced technologies such as deep learning, automated defect detection and classification, we can further improve the testing efficiency and accuracy of the proposed method.
In summary, the MCXI NDT method proposed in this paper offers an innovative and highly sensitive solution for non-destructive defect detection across various materials. In the future, this method is expected find broad applications in high-sensitivity non-destructive defect testing.
CRediT authorship contribution statement
Zenghao Song: Writing – original draft, Visualization, Validation, Software, Resources, Methodology, Investigation, Formal analysis. Kang Du: Data curation. Ke Li: Investigation. Feixiang Wang: Formal analysis. Mingwei Xu: Software, Investigation. Chengcong Ma: Datacuration. Tiqiao Xiao: Writing –review & editing, Visualization, Validation, Supervision, Funding acquisition, Conceptualization.
