We address the problem of localizing waste objects from a color image and an optional depth image, which is a key perception component for robotic interaction with such objects. Specifically, our method integrates the intensity and depth information at multiple levels of spatial granularity. Firstly, a scene-level deep network produces an initial coarse segmentation, based on which we select a few potential object regions to zoom in and perform fine segmentation. The results of the above steps are further integrated into a densely connected conditional random field that learns to respect the appearance, depth, and spatial affinities with pixel-level accuracy. In addition, we create a new RGBD waste object segmentation dataset, MJU-Waste, that is made public to facilitate future research in this area. The efficacy of our method is validated on both MJU-Waste and the Trash Annotation in Context (TACO) dataset.

Skowron's discernibility matrix plays a crucial role in the computation of all reducts of a decision table. In this paper, it is shown that the discernibility matrix must be modified in order to solve reduct computation problems in the presence of data inconsistency. Then an improved discernibility matrix is introduced and a discernibility function method based on the improved discernibility matrix is presented and proved to be correct for computation of all reducts of an inconsistent decision table