Noisy estimations of shape can be partially resolved by incorporating relevant information from the context. The effect of surround stimuli on shape perception becomes clear in illusions of shape contrast and assimilation. In this study, we answer the question how a surround-induced bias depends on the reliability of shape signals. This way, we assess the processes by which an observer incorporates relevant data from the context into the shape estimate. We selectively added visual noise to the center and surround and compared a bias in shape perception with a control condition where no noise was added. In the conditions where shape and surround stimuli were well defined, we found a shape-contrast bias. When the surround stimuli were degraded, this contrast bias decreased. Most interestingly, when the central shape was degraded, an assimilation bias was observed. This bias was larger when the entire stimulus was degraded compared to when only the central shape was degraded. This suggests that shape contrast is the result of inference processes relying on local representations in early visual areas whereas assimilation is related to inference processes by global representations in higher visual areas.