Computer-Aided Detection of Exact Reflection and Axisymmetry in B-rep CAD Models

Abstract

Spinal deformity is a disease that causes a three-dimensional deformation of the spinal column. When it worsens, surgery is required to screw correction rods to the spinal column. However, the surgery requires intraoperative rod bending work, which burdens the patients and causes unexpected rod breakage inside the body. Therefore, "pre-bent" rods comprising several rods with standardized shapes have been proposed to solve these problems. When designing pre-bent rods, knowing the number of rods to be prepared and the kinds of shapes required is essential. In this paper, we propose a geometric processing technique to identify an optimal set of these standardized pre-bent rod shapes for surgeries on adult spinal deformity and describe the similarity evaluation among existing rod shapes using CT scan, medial axis extraction, and iterative closest point algorithm. Moreover, we present the derivation of standardized rod shapes using hierarchical cluster analysis and the best fit of the B-spline curve to each cluster. Finally, we discuss the effectiveness of prebent rod shapes derived from CT scans of 26 existing rods of 13 patients.

A Framework for Detection of Exact Global and Partial Symmetry in 3D CAD Models

“…CASD has been the subject in different research fields, such as mathematics [17], mechanical engineering [8], computer engineering [18], civil engineering [19], medicine [20], etc. When it comes to mechanical engineering, CASD has been explored for retrieval [21], The most common way to retrieve symmetry information in mechanical parts is through visual recognition by engineers [14,15]. As the number of 3D CAD models increases, the ability of engineers to visually recognize symmetry decreases.…”

“…The common strategy for many CASD techniques [3,8,11,12,14,15,[29][30][31]33,34] is to first generate a set of candidates for the planes of symmetry and/or the axis of symmetry from the given input model. The candidates are, for instance, obtained by principal component analysis [14,15,27], pair matching [8,11,35], incremental rotations around the centroid/center of mass [12,30], from the intrinsic surface properties [3,36], etc.…”

“…The common strategy for many CASD techniques [3,8,11,12,14,15,[29][30][31]33,34] is to first generate a set of candidates for the planes of symmetry and/or the axis of symmetry from the given input model. The candidates are, for instance, obtained by principal component analysis [14,15,27], pair matching [8,11,35], incremental rotations around the centroid/center of mass [12,30], from the intrinsic surface properties [3,36], etc. Some of the proposed techniques [12,14,30] are constrained to only detect candidates that pass through a reference point (e.g., origin, centroid, or center of mass), which is, however, only suitable for objects exhibiting exact symmetry [11].…”

“…In the second step, the generated candidates are assessed to identify the possible existence of the actual planes and/or axes of symmetry among them. The assessment of the candidates includes searching for the optimal among them [3,8,11] or evaluating each candidate with respect to the input model's geometry [12,14,15,30]. A large number of planes and axes of symmetry candidates can lead to a time-consuming computation [29], limiting them in practical application.…”

“…For instance, a mechanical part can be simultaneously reflectional and cyclic symmetric (Figure 1c). The most common way to retrieve symmetry information in mechanical parts is through visual recognition by engineers [14,15]. As the number of 3D CAD models increases, the ability of engineers to visually recognize symmetry decreases.…”