  In this paper, we present a novel model for simultaneous stable co-saliency
detection (CoSOD) and object co-segmentation (CoSEG). To detect co-saliency
(segmentation) accurately, the core problem is to well model inter-image
relations between an image group. Some methods design sophisticated modules,
such as recurrent neural network (RNN), to address this problem. However,
order-sensitive problem is the major drawback of RNN, which heavily affects the
stability of proposed CoSOD (CoSEG) model. In this paper, inspired by RNN-based
model, we first propose a multi-path stable recurrent unit (MSRU), containing
dummy orders mechanisms (DOM) and recurrent unit (RU). Our proposed MSRU not
only helps CoSOD (CoSEG) model captures robust inter-image relations, but also
reduces order-sensitivity, resulting in a more stable inference and training
process. { Moreover, we design a cross-order contrastive loss (COCL) that can
further address order-sensitive problem by pulling close the feature embedding
generated from different input orders.} We validate our model on five widely
used CoSOD datasets (CoCA, CoSOD3k, Cosal2015, iCoseg and MSRC), and three
widely used datasets (Internet, iCoseg and PASCAL-VOC) for object
co-segmentation, the performance demonstrates the superiority of the proposed
approach as compared to the state-of-the-art (SOTA) methods.
