Attention operators based on 2D image cues (such as color, texture) are well known and discussed extensively in the vision literature but are not ideally suited for robotic applications. In such contexts it is the 3D structure of scene elements that makes them interesting or not. We show how a bottom-up exploration mechanism that fuses 2D saliency-based conspicuity with spatial abstraction resulting from the coherent plane estimation and stereo line detection is well suited for typical indoor robotics tasks. This spatial abstraction is performed by a joint probabilistic model which takes the interaction of stereo line detection and 3D supporting plane estimation into consideration. By maximizing the probability of the joint model, our method facilitates reduction of false-positive stereo line detection and refines the estimation of supporting surface simultaneously. Experiments demonstrate that our approach provides more accurate and plausible attention.