Chronic wound monitoring and management require accurate and efficient wound measurement methods. This paper presents a fast, non-invasive 3D wound measurement algorithm based on RGB-D imaging. The method combines RGB-D odometry with B-spline surface reconstruction to generate detailed 3D wound meshes, enabling automatic computation of clinically relevant wound measurements such as perimeter, surface area, and dimensions. We evaluated our system on realistic silicone wound phantoms and measured sub-millimetre 3D reconstruction accuracy compared with high-resolution ground-truth scans. The extracted measurements demonstrated low variability across repeated captures and strong agreement with manual assessments. The proposed pipeline also outperformed a state-of-the-art object-centric RGB-D reconstruction method while maintaining runtimes suitable for real-time clinical deployment. Our approach offers a promising tool for automated wound assessment in both clinical and remote healthcare settings.