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Automated extraction of plant morphological traits is crucial for supporting crop breeding and agricultural management through high-throughput field phenotyping (HTFP). Solutions based on multi-view RGB images are attractive due to their scalability and affordability, enabling volumetric measurements that 2D approaches cannot directly capture. While advanced methods like Neural Radiance Fields (NeRFs) have shown promise, their application has been limited to counting or extracting traits from only a few plants or organs. Furthermore, accurately measuring complex structures like individual wheat heads-essential for studying crop yields-remains particularly challenging due to occlusions and the dense arrangement of crop canopies in field conditions. The recent development of 3D Gaussian Splatting (3DGS) offers a promising alternative for HTFP due to its high-quality reconstructions and explicit point-based representation. In this paper, we present Wheat3DGS, a novel approach that leverages 3DGS and the Segment Anything Model (SAM) for precise 3D instance segmentation and morphological measurement of hundreds of wheat heads automatically, representing the first application of 3DGS to HTFP. We validate the accuracy of wheat head extraction against high-resolution laser scan data, obtaining per-instance mean absolute percentage errors of 15.1%, 18.3%, and 40.2 % for length, width, and volume. We provide additional comparisons to NeRF-based approaches and traditional Muti-View Stereo (MVS), demonstrating superior results. Our approach enables rapid, non-destructive measurements of key yieldrelated traits at scale, with significant implications for accelerating crop breeding and improving our understanding of wheat development.