The objects we perceive guide our eye movements when observing real-world dynamic scenes. Yet, gaze shifts and selective attention are critical for perceiving details and refining object boundaries. Object segmentation and gaze behavior are, however, typically treated as two independent processes. Here, we present a computational model that simulates these processes in an interconnected manner and allows for hypothesis-driven investigations of distinct attentional mechanisms. Drawing on an information processing pattern from robotics, we use a Bayesian filter to recursively segment the scene, which also provides an uncertainty estimate for the object boundaries that we use to guide active scene exploration. We demonstrate that this model closely resembles observers' free viewing behavior on a dataset of dynamic real-world scenes, measured by scanpath statistics, including foveation duration and saccade amplitude distributions used for parameter fitting and higher-level statistics not used for fitting. These include how object detections, inspections, and returns are balanced and a delay of returning saccades without an explicit implementation of such temporal inhibition of return. Extensive simulations and ablation studies show that uncertainty promotes balanced exploration and that semantic object cues are crucial to forming the perceptual units used in object-based attention. Moreover, we show how our model's modular design allows for extensions, such as incorporating saccadic momentum or presaccadic attention, to further align its output with human scanpaths.