How does an observer decide that a particular object viewed at one time is actually the "same" object as one viewed at a different time? We explored this question using an experimental task in which an observer views two objects as they simultaneously approach an occluder, disappear behind the occluder, and re-emerge from behind the occluder, having switched paths. In this situation the observer either sees both objects continue straight behind the occluder (called "streaming") or sees them collide with each other and switch directions ("bouncing"). This task has been studied in the literature on motion perception, where interest has centered on manipulating spatiotemporal aspects of the motion paths (e.g. velocity, acceleration). Here we instead focus on "featural" properties (size, luminance, and shape) of the objects. We studied the way degrees and types of featural dissimilarity between the two objects influence the percept of bouncing vs. streaming. When there is no featural difference, the preference for straight motion paths dominates, and streaming is usually seen. But when featural differences increase, the preponderance of bounce responses increases. That is, subjects prefer the motion trajectory in which each continuously existing individual object trajectory contains minimal featural change. Under this model, the data reveal in detail exactly what magnitudes of each type of featural change subjects implicitly regard as reasonably consistent with a continuously existing object. This suggests a simple mathematical definition of "individual object:" an object is a path through feature-trajectory space that minimizes feature change, or, more succinctly, an object is a "geodesic in Mahalanobis feature space."