  3D open-vocabulary scene understanding, crucial for advancing augmented
reality and robotic applications, involves interpreting and locating specific
regions within a 3D space as directed by natural language instructions. To this
end, we introduce GOI, a framework that integrates semantic features from 2D
vision-language foundation models into 3D Gaussian Splatting (3DGS) and
identifies 3D Gaussians of Interest using an Optimizable Semantic-space
Hyperplane. Our approach includes an efficient compression method that utilizes
scene priors to condense noisy high-dimensional semantic features into compact
low-dimensional vectors, which are subsequently embedded in 3DGS. During the
open-vocabulary querying process, we adopt a distinct approach compared to
existing methods, which depend on a manually set fixed empirical threshold to
select regions based on their semantic feature distance to the query text
embedding. This traditional approach often lacks universal accuracy, leading to
challenges in precisely identifying specific target areas. Instead, our method
treats the feature selection process as a hyperplane division within the
feature space, retaining only those features that are highly relevant to the
query. We leverage off-the-shelf 2D Referring Expression Segmentation (RES)
models to fine-tune the semantic-space hyperplane, enabling a more precise
distinction between target regions and others. This fine-tuning substantially
improves the accuracy of open-vocabulary queries, ensuring the precise
localization of pertinent 3D Gaussians. Extensive experiments demonstrate GOI's
superiority over previous state-of-the-art methods. Our project page is
available at https://quyans.github.io/GOI-Hyperplane/ .
