[Paper Review] A Fast Method For Computing Principal Curvatures From Range Images

Andrew Spek, Wai Ho Li+1 more|arXiv (Cornell University)|Jul 3, 2017

Robotics and Sensor-Based Localization6 references3 citations

TL;DR

This paper proposes a real-time, GPU-accelerated method for computing accurate metric principal curvatures from noisy range images using iterative parabolic quadric surface patch fitting. Unlike conventional methods that amplify noise through double differentiation, this approach directly fits quadric surfaces to local point clouds, achieving superior curvature estimates on low-cost RGB-D data such as from the Microsoft Kinect, with frame-rate performance and improved robustness to noise.

ABSTRACT

Estimation of surface curvature from range data is important for a range of tasks in computer vision and robotics, object segmentation, object recognition and robotic grasping estimation. This work presents a fast method of robustly computing accurate metric principal curvature values from noisy point clouds which was implemented on GPU. In contrast to existing readily available solutions which first differentiate the surface to estimate surface normals and then differentiate these to obtain curvature, amplifying noise, our method iteratively fits parabolic quadric surface patches to the data. Additionally previous methods with a similar formulation use less robust techniques less applicable to a high noise sensor. We demonstrate that our method is fast and provides better curvature estimates than existing techniques. In particular we compare our method to several alternatives to demonstrate the improvement.

Motivation & Objective

• To address the challenge of accurate principal curvature estimation from noisy, real-world range data generated by low-cost RGB-D sensors like the Microsoft Kinect.
• To overcome the noise amplification inherent in traditional double-differentiation methods that rely on surface normal differentiation.
• To develop a real-time curvature estimation system suitable for robotics and computer vision applications requiring viewpoint-invariant geometric features.
• To improve the accuracy and consistency of curvature-based object correspondence estimation across multiple viewpoints.
• To provide a robust, open-source GPU implementation for high-performance curvature computation on dense point clouds.

Proposed method

• The method iteratively fits a parabolic quadric surface to local 3D point cloud patches using a least-squares optimization to estimate principal curvatures directly.
• It avoids surface normal differentiation by modeling curvature estimation as a direct geometric fitting problem, reducing noise amplification.
• The algorithm is implemented on the GPU to enable real-time processing at frame rate for dense RGB-D data.
• A patch size of 37×37 is used for local surface fitting, with sparse sampling to maintain performance.
• The curvature estimation is based on the eigenvalues of the Hessian matrix derived from the fitted quadric, providing metric principal curvature values.
• The method is compared against PCL’s PCA-based curvature estimation and other baseline techniques using real-world and synthetic datasets.

Experimental results

Research questions

• RQ1 Can a direct quadric fitting approach outperform conventional double-differentiation methods in estimating principal curvatures from noisy range data?
• RQ2 How does the proposed method perform in terms of accuracy and robustness compared to PCL’s PCA-based curvature estimation on real-world RGB-D scans?
• RQ3 To what extent does the method maintain consistent curvature estimates across different viewpoints, enabling reliable correspondence estimation?
• RQ4 Can the method achieve real-time performance on GPU for dense, noisy range images from consumer-grade sensors?
• RQ5 Does the method improve the discriminative power of curvature for object segmentation and recognition tasks?

Key findings

• The proposed method achieves significantly more accurate metric curvature estimates than PCL’s PCA-based approach, especially on noisy data from low-cost RGB-D sensors.
• The method produces smoother and more reliable surface normal estimates compared to PCA-based differentiation, reducing noise-induced artifacts.
• The system runs at frame rate on GPU, enabling real-time curvature estimation for dynamic applications such as robotic grasping and scene understanding.
• Curvature-based correspondence estimation using the proposed method shows high consistency across multiple viewpoints, with confusion matrices indicating strong object-specific matching.
• In contrast, PCL’s method exhibits poor correspondence consistency, frequently matching points to background or incorrect objects due to noise sensitivity.
• The method demonstrates superior performance on high-curvature objects like stress balls and similarly curved objects (e.g., chocA and badminton), though these remain challenging due to similar curvature profiles.