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The reconstruction of graph representations from Images (Image-to-graph) is a frequent task, especially vessel graph extraction from biomedical images. Traditionally, this problem is tackled by a two-stage process: segmentation followed by skeletonization. However, the ambiguity in the heuristic-based pruning of the centerline graph from the skeleta makes it hard to achieve a compact yet faithful graph representation. Recently, \textit{Relationformer} proposed an end-to-end solution to extract graphs directly from images. However, it does not consider edge features, particularly radius information, which is crucial in many applications such as flow simulation. Further, Relationformer predicts only patch-based graphs. In this work, we address these two shortcomings. We propose a task-specific token, namely radius-token, which explicitly focuses on capturing radius information between two nodes. Second, we propose an efficient algorithm to infer a large 3D graph from patch inference. Finally, we show experimental results on a synthetic vessel dataset and achieve the first 3D complete graph prediction. Code is available at \url{https://github.com/****}.
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