Results and Discussions To begin with, a cubic dataset with no noise is utilized and reconstructed using the MC algorithm and the approach proposed in this study, as shown in Fig. 7. Sharp features including angles are lost by the MC algorithm [Fig. 7(a)]. The approach in this article not only generates the cube's edges but also a smaller triangular mesh to represent sharper features such as angles [Fig. 7(b)]. Next, in order to demonstrate the algorithm's simplification effect in this paper, an experiment is performed utilizing a set of real scanned gear CT sequence image data. This study's algorithm generates an unsimplified mesh model [Fig. 8(a)], which is then processed using vertex clustering and edge-shrinking algorithms. The vertex clustering approach results in the loss of the model's detailed features after simplification [Fig. 8(b)], whereas the edge-shrinking algorithm saves the details but generates a large number of long-narrow triangles with poor mesh quality [Fig. 8(c)]. The method used in this study efficiently prevents the formation of long-narrow triangles while preserving the model's detailed features and guaranteeing the quality of the model [Fig. 8(d)]. Besides, in order to further validate the effectiveness of the algorithm presented in this study, a set of engine CT sequence image data with a complicated internal cavity structure is applied. The mesh models shown in Fig. 9 are reconstructed by varying the simplified parameters. Different simplification effects can be obtained by changing the simplified parameters (Fig. 9). The method used in this study can adaptively extract the isosurface in voxels of different sizes according to the local characteristics of the object and achieve the reconstruction of an adaptive 3D mesh model under the given simplified parameters. The experimental results demonstrate that the method presented in this study can preserve object sharpness while simplifying the mesh, reducing the number of long-narrow triangles, and improving the quality of the triangular mesh model reconstructed from industrial CT images. In this study, the simplification rate of the triangular mesh model generated by the algorithm can achieve 90%, with an average proportion of mesh quality greater than 0.3 after simplification of 99% (Table 2).

As a typical numerical representation of geometric models, the triangular mesh is widely used in additive manufacturing, inverse design, and finite element analysis. The triangular mesh model is directly reconstructed based on industrial CT images, which allows for the reconstruction of 3D representations of parts with complicated internal cavity structures. However, current algorithms for reconstructing triangular mesh models based on industrial CT images, for example, marching cube (MC) algorithm, have problems such as loss of sharp features, many long-narrow triangles, and a large number of triangular surfaces. In this paper, we propose an adaptive 3D mesh model reconstruction method to simultaneously address these issues while improving the quality of the reconstructed triangular mesh model from industrial CT images.

First, a bilateral filter and an OTSU algorithm are utilized to preprocess industrial CT images, so as to denoise and determine the value of the isosurface. Second, an octree structure is used to confirm the voxels; the octree is created top-down recursively, while non-boundary voxels are deleted to save storage space. The quadratic error function (QEF) is then applied to each boundary voxel of the octree to produce a feature point, and the octree is simplified by merging the feature points from the bottom up. Third, a quadrilateral formed by four adjacent feature points is divided into two triangular meshes. In order to validate the performance of the proposed algorithm, experiments are performed using a cubic dataset and two groups of real industrial CT images.

This paper proposes an adaptive 3D mesh model reconstruction algorithm to deal with the problems of sharp feature loss, many long-narrow triangles, and a large number of triangular surfaces in the reconstructed triangular mesh model of industrial CT images obtained from X-rays. Firstly, the image is denoised by the bilateral filter, and the value of the isosurface is determined using the OTSU algorithm. Then, voxels are organized by an octree structure, and the octree is generated top-down; feature points are generated by minimizing a quadratic error function (QEF), and an adaptive octree is constructed by merging feature points bottom-up. Finally, triangular meshes are generated by dividing the quadrilateral formed by four adjacent feature points. The algorithm in this paper checks its ability to keep sharp features compared with the MC algorithm. Compared with vertex clustering and edge-shrinking mesh simplification algorithms, the algorithm in the present paper can keep features and guarantee the quality of simplified meshes. Under the given simplified parameters, the method used in this research can adaptively extract the isosurface in voxels of different sizes based on the local characteristics of the object and achieve the reconstruction of an adaptive 3D mesh model. From the experimental results, it is found that the simplification rate of the triangular mesh model generated by the algorithm in this paper can be as high as 90%, and the average proportion of mesh quality higher than 0.3 after simplification reaches 99%. Compared with the conventional mesh method, the proposed method can maintain the sharp features of the model while simplifying the mesh, reducing the number of long-narrow triangles, and improving the quality of the reconstructed triangular mesh model from industrial CT images.