3D Curve-to-Surface Registration Using Local Differential Features
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Solution Overview
Problem
Existing 3D registration methods face challenges in aligning diverse types of 3D models, particularly in Computer-Aided Orthopedic Surgery, such as aligning intra-operative curves with pre-operative surfaces, which is crucial for surgical guidance but often inefficient and inaccurate.
Innovation Solution
A method utilizing local differential information, such as normals and tangents, to establish correspondences between 3D models, reducing the complexity of matching and improving accuracy through a hypothesize-and-test strategy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional 3D registration methods are used to align curves and surfaces, then the registration can be performed, but the process is computationally expensive and time-consuming
Solution Approach 1:
The patent segments the 3D models into discrete 2-tuples of points with associated normal vectors, enabling independent processing and matching of local features rather than attempting to register entire surfaces simultaneously. This segmentation reduces computational complexity while maintaining registration accuracy through local feature correspondence.
Solution Approach 2:
The patent transforms the registration problem by changing parameters from full surface geometry to simplified 2-tuple representations consisting of point coordinates and normal vectors. This parameter reduction maintains essential geometric information while dramatically reducing computational burden and registration time.
2Reliability
If complex 3D models are registered using traditional methods, then complete alignment is achieved, but the device complexity and computational resources required increase significantly
Solution Approach 1:
The patent extracts only the essential elements needed for registration - specifically pairs of points with their normal vectors - from the complete 3D models. This extraction eliminates unnecessary geometric data while retaining sufficient information for accurate and robust alignment, thereby reducing system complexity.
Solution Approach 2:
The patent performs preliminary processing to identify and extract corresponding 2-tuples from the 3D models before the actual registration computation. This preliminary action organizes the data in advance, making the subsequent registration process simpler and more reliable without requiring complex real-time computations.
3Adaptability or versatility
If sparse 3D data such as curves are registered with dense surfaces, then the registration can be performed, but matching accuracy deteriorates due to data density differences
Solution Approach 1:
The patent creates a universal 2-tuple representation that works equally well for sparse curves and dense surfaces. By expressing both model types in terms of point-coordinate and normal-vector pairs, the system achieves model-type flexibility while maintaining matching accuracy through consistent feature correspondence rules applicable to any 3D geometry.
Solution Approach 2:
The patent applies local quality by focusing registration on local 2-tuple features rather than global model properties. Each 2-tuple captures local geometric characteristics (point position and surface orientation) that are independent of overall data density, enabling accurate matching between sparse and dense representations through local feature similarity.
Data Source
Figure 1A(a)~1A(c)
Figure 1B(a)~1B(f)
Figure 1C
AI summary
Systems and methods are provided for accomplishing fast and accurate 3D registration of curves and surfaces using local differential information, i.e., normals and tangents. In an embodiment, a method solves the curve-vs-surface alignment problem either by using a purely online search scheme, or by taking advantage of the availability of a pre-operative model, which often happens in medical procedures, to further speed-up the computational search by performing offline processing of the pre-operative bone model. The disclosed method is also extended to solve the curve-vs-curve and surface-vs-surface alignment problems, which also have important applications in medical procedures such as arthroscopy and arthroplasty.