Robotic manipulation is critical for admitting robotic agents to various application domains, like intelligent assistance. A major challenge therein is the effective 6DoF grasping of objects in cluttered environments from any viewpoint without requiring additional scene exploration. We introduce $\textit{NeuGraspNet}$, a novel method for 6DoF grasp detection that leverages recent advances in neural volumetric representations and surface rendering. Our approach learns both global (scene-level) and local (grasp-level) neural surface representations, enabling effective and fully implicit 6DoF grasp quality prediction, even in unseen parts of the scene. Further, we reinterpret grasping as a local neural surface rendering problem, allowing the model to encode the interaction between the robot's end-effector and the object's surface geometry. NeuGraspNet operates on single viewpoints and can sample grasp candidates in occluded scenes, outperforming existing implicit and semi-implicit baseline methods in the literature. We demonstrate the real-world applicability of NeuGraspNet with a mobile manipulator robot, grasping in open spaces with clutter by rendering the scene, reasoning about graspable areas of different objects, and selecting grasps likely to succeed without colliding with the environment. Visit our project website: https://sites.google.com/view/neugraspnet
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