GeoCoBox: Box-supervised 3D Tumor Segmentation via Geometric Co-embedding

Data economic efficiency (DE\textsuperscript{2}) drives AI by optimizing data usage, reducing costs, and enhancing efficiency. In 3D tumor segmentation, DE\textsuperscript{2} is crucial due to the high demand for labor-intensive manual annotations. Box-supervised segmentation offers a promising alternative but suffers from tumor morphology complexity and boundary ambiguity. In this paper, we propose a novel 3D tumor segmentation model that integrates both positional and embedding features to facilitate inter-task collaboration. We introduce an Anatomical-Driven Class Activation Map to predefine the complex tumor morphology prior, which is further refined by our Geometric Pixel Co-embedding Learner. This learner utilizes contrastive learning to encode semantic information between center and edge pixels, enhancing pixel clustering and progressively refining tumor boundary segmentation in a coarse-to-fine manner. Our approach outperforms existing box-supervised methods in segmentation performance, with extensive experiments on four tumor datasets demonstrating significant improvements in box-supervised image segmentation. This work provides a cost-effective and efficient solution for tumor segmentation, advancing the application of DE\textsuperscript{2} in medical imaging.