# Fiber Orientation Reconstruction from SEM Images of Fiber-Reinforced Composites
## 1 Introduction  
In recent decades, the rapid advancement of science and technology has made it challenging for single materials to satisfy the material performance indicators of new products. As a result, composite material technologies have been investigated. Since 1940, spearheaded by the aerospace and military industries, composite materials have been widely exploited in many facets of the national economy, bringing immense convenience to human life while supporting modern science and social economics [1]. Fiber-reinforced composites are the most popular and flexible composite materials because of their high specific strength and modulus, fatigue resistance, and versatility [2; 3]. During the molding process of short fiber reinforced composites, the short fibers present different orientations under the action of external force fields [4]. When loads are applied to fiber-reinforced composites, the mechanical characteristics of the material in each direction are directly proportional to the fiber volume fraction in that direction [5]. It is vital to evaluate fiber orientation to comprehend the macroscopic mechanical properties of short-fiber-reinforced composites. [PERSON] et al. [6] studied the tensile strength and modulus of short glass fibers (SGF)/polyppropylene (PP) and short carbon fibers(SCF)/PP composites taking into account the combined effect of fiber volume fraction and mean fiber length. [PERSON] et al. [7] employed the Morie-Tanaka theory to relate the tensile modulusof the composites to fiber morphology determined by TEM and SEM. For visually examining the correlation between composite fiber morphology and mechanical performance, obtaining the orientation distribution of fibers in fiber-reinforced composites and products is particularly relevant. Due to its low cost, simple principle, high spatial resolution, and simple computer processing and analysis, two-dimensional cross-sectional microscopic image processing is the conventional direct fiber orientation measurement method, which relies primarily on X-ray diffraction and microscopic measurement [8]. The microscopic fiber orientation measuring technique is based on the hypothesis that the horizontal plane intercepts a cylinder in any orientation as an ellipse, and the cylinder axis may be inferred from the elliptical shape parameter of the cross-section. Typical methods involve fitting an ellipse to the fiber on a microscopic image of a smooth piece of material and deriving fiber orientation information from the fitted cylinder parameters [9; 10]. Several efficient approaches exist for fitting cylindrical parameters to point clouds of cylindrical surface measurements [11; 12]. [PERSON] et al. [13] applied microscopic measurements to measure fiber orientation in glass fiber/polypropylene composites. [PERSON] et al. [14] measured glass fiber orientation in glass fiber/polyamide composites based on microscopic measurements and verified the correctness of the fiber orientation results from computer simulations. [PERSON] et al. [15] used the modified method of ellipses (MoE) to determine the fiber orientation in a center-gated disk mold filled with a short glass fiber suspension. With an optical microscope, researchers may obtain images of fibers' elliptical footprints. The MoE is used to estimate the orientation angles for each individual fiber and to calculate the volumetric average of orientation represented through a second-order tensor [16]. Nevertheless, the microscope measuring technique requires preliminary preparation of a smooth specimen cross-section. The quality of the captured material cross-section pictures is readily impacted by processing markings, which reduces the fiber cross-section cylinder fitting accuracy. To reflect the real 3D structure inside the material, 3D reconstruction techniques based on 2D image processing of the material to obtain the internal structure of the material have become a hot research topic in recent years [17]. [PERSON] et al. [18] successfully applied a C.T.