Robust and accurate tracking of multiple objects is a key challenge in video surveillance. Tracking algorithms generally suffer from either one or more of the following problems, excluding detection errors. First, objects can be incorrectly interpreted as one of the other objects in the scene. Second, interactions between objects, such as occlusions, may cause tracking errors. Third, globally-optimum tracking is hard to achieve since the combinatorial assignment problem is NP-Complete. We present a modified Multiple-Hypothesis Tracking algorithm, MHT, for globally optimum tracking of moving objects. The system defines five states for tracked objects: appear, disappear, track, split, and merge, and these states cover all the interactions of object pairs. After the detection of objects in the current frame, a resemblance matrix is computed for every object pair. We convert the two-dimensional resemblance matrix into a three-dimensional state-likelihood structure and use a MHT technique to solve the state-assignment problem in 3D. This prevents incorrect assignments due to local minima in the assignment process. Moreover, the method models occlusion cases with the split and merge states. Finally, this method approximates a globally optimum state assignment in polynomial time complexity.