# Singular Value Decomposition (SVD) Method for LiDAR and Camera Sensor Fusion and Pattern Matching Algorithm

## TL;DR

This paper introduces a new method using SVD and GD to align LiDAR and camera sensors in autonomous vehicles without manual calibration.

## Contribution

A targetless pattern matching algorithm using SVD and GD for sensor fusion without requiring manual calibration targets.

## Key findings

- The proposed method achieves up to 85% improvement in alignment accuracy.
- Projection error is reduced to less than 1 pixel in experiments.
- The framework maintains reliable sensor fusion under calibration drift.

## Abstract

LiDAR and camera sensors are widely utilized in autonomous vehicles (AVs) and robotics due to their complementary sensing capabilities—LiDAR provides precise depth information, while cameras capture rich visual context. However, effective multi-sensor fusion remains challenging due to discrepancies in resolution, data format, and viewpoint. In this paper, we propose a robust pattern matching algorithm that leverages singular value decomposition (SVD) and gradient descent (GD) to align geometric features—such as object contours and convex hulls—across LiDAR and camera modalities. Unlike traditional calibration methods that require manual targets, our approach is targetless, extracting matched patterns from projected LiDAR point clouds and 2D image segments. The algorithm computes the optimal transformation matrix between sensors, correcting misalignments in rotation, translation, and scale. Experimental results on a vehicle-mounted sensing platform demonstrate an alignment accuracy improvement of up to 85%, with the final projection error reduced to less than 1 pixel. This pattern-based SVD-GD framework offers a practical solution for maintaining reliable cross-sensor alignment under calibration drift, enabling real-time perception systems to operate robustly without recalibration. This method provides a practical solution for maintaining reliable sensor fusion in autonomous driving applications subject to long-term calibration drift.