Robust and Real-Time Surface Normal Estimation from Stereo Disparities Using Affine Transformations
Muhammad Rafi Faisal, Csongor Csanád Karikó, Levente Hajder
AI summary
Problem
Current surface normal estimators face trade-offs between computational speed, noise sensitivity, and inaccurate border detection across multiple surfaces, limiting their use in real-time 3D reconstruction and robotics.
Approach
The authors derive a simplified geometric formula to compute normals from affine transformations in rectified stereo pairs, calculate these transformations efficiently via precomputed 2D convolutions on disparity maps, and introduce an adaptive star-shaped kernel that dynamically isolates flat surface regions at GPU cores.
Key results
- Derived a novel normal calculation formula for rectified stereo pairs
- Converted affine parameter estimation into fast 2D disparity convolutions
- Implemented an adaptive GPU-parallelized region detector that halts at depth edges
- Achieved sub-10ms real-time execution on GPU with high accuracy on synthetic and real datasets
Why it matters
Provides a fast, deterministic, and training-free alternative to machine learning for real-time 3D reconstruction, SLAM, and autonomous navigation.
Abstract
This work introduces a novel method for surface normal estimation from rectified stereo image pairs, leveraging affine transformations derived from disparity values to achieve fast and accurate results. We demonstrate how the rectification of stereo image pairs simplifies the process of surface normal estimation by reducing computational complexity. To address noise reduction, we develop a custom algorithm inspired by convolutional operations, tailored to process disparity data efficiently. We also introduce adaptive heuristic techniques for efficiently detecting connected surface components within the images, further improving the robustness of the method. By integrating these methods, we construct a surface normal estimator that is both fast and accurate, producing a dense, oriented point cloud as the final output. Our method is validated using both simulated environments and real-world stereo images from the Middlebury1 and Cityscapes datasets, demonstrating significant improvements in real-time perfor- mance and accuracy when implemented on a GPU. The source code is available at https://github.com/mrafifaisal/ Surface-Normal-Estimation/.