## 1 Introduction  
As an important non-destructive testing technique, X-ray computed tomography (CT) imaging has evolved beyond medical applications in the past two decades. Based on CT imaging, recent applications include virtual unwrapping of ancient scrolls to decipher text [1], reconstruction of ancient artifact structures [2] and biological morphology [3], characterization of polymer porosity in 3D-printed materials [4], and studying corrosion kinetics in metal additive manufacturing [5]. Advances in micro-CT and nano-CT technologies enabled imaging of three-dimensional material compositional distributions at voxel sizes ranging from micrometers to tens of nanometers, presenting new opportunities for quantitative characterization of the microscopic structures of materials. Particularly in the characterization of energy reservoir samples, CT imaging has been employed for in situ dynamic studies of methane hydrate formation and dissociation in sandstone [6], quantifying pore morphology and structure in oil and gas reservoir rocks [7; 8; 9], and establishing physical property numerical simulations such as fluid flow [10], thermal conduction [11], and diffusion [12]. X-rays attenuate as they pass through material samples due to interactions with the material, resulting in intensity attenuation recorded on the detector, forming a projection image. By imaging a material sample from various angles and employing sophisticated mathematical inversion algorithms, the cross-section images of the sample can be reconstructed. The intensity values of each pixel in the reconstructed cross-section images are proportional to the sum of the X-ray linear attenuation coefficients of the compositions contained in those pixels. The X-ray linear attenuation coefficient primarily depends on the X-ray beam energy, material density, and elemental composition. Establishing the correlation between the X-ray linear attenuation coefficients of the CT slice and the physical compositions of the material is crucial for image recognition and quantitative analysis. The image threshold segmentation algorithm is currently the mainstream method for processing CT images. It determines the image segmentation thresholds for different compositions based on the pixel intensity distribution of the CT image. This method assigns voxels to specific compositions based on predefined intensity thresholds, facilitating image recognition and quantitative analysis. However, practical CT applications often encounter reconstructed voxels containing multiple physical compositions smaller than the voxel size, leading to a weighted average of X-ray linear attenuation coefficients within each voxel. This is the so-called partial volume effect. When using image threshold segmentation algorithms for image recognition, the presence of voxels occupied partially by multiple compositions introduces biases regardless of the classification of these voxels into specific compositions. Studies by [PERSON] et al. [13] and [PERSON] et al. [14] have highlighted that the partial volume effect significantly affects the evaluation of tooth morphology volumes in dental CT imaging. In recent years, various methods have been proposed to avoid the partial volume effect. [PERSON] et al. [15] proposed a dual-projection scanning method where slight detector movements were employed at each angle during scanning to collect two projection images. This method decreased the effective imaging pixel size and reduced the averaging effect of the partial volume effect on material composition densities. [PERSON] et al. [16] developed a new partial volume effect correction method based on the imaging system's point spread function. To address the issue of blurred edges of image compositions due to the partial volume effect, a smoothing-based approach [17] is proposed to improve edge detection accuracy. Machine learning and deep learning methods have also been applied by researchers for the precise segmentation of medical CT images [18; 19; 20]. [PERSON] et al.