# Globally-optimal greedy algorithms for tracking a variable number of objects

• 2011

#### Abstract

Problem input: • Detector scores for all space time windows in a video Problem output: • Number of objects (tracks) • Starting and ending frames for each track • Tracks themselves Our contributions: • Globally Optimal (for a common class of objective functions) • Locally Greedy (and hence straightforward to implement) • Scale linearly in the number of objects and (quasi)linearly with video-length A detection window A transition Has input flow of d Has output flow of d Equivalent graph problem: Min-cost flow Solutions: • Globally optimum • Push-relabel algorithm • Used in Zhang et al CVPR'08 • Solves for known d; Does binary search to find K=optimum d • Successive shortest path • Special structure in our graph (DAG, unit-capacity) • Is greedy • Approximate • Dynamic programming • Is greedy Successive shortest path: • At each iteration, find the shortest path and augment the graph by reversing edges along it. • Iterate as long as the cost of shortest path is positive. Dynamic programming: Sweep the graph and update paths to find the shortest one • Variable length DP because of " s " and " t " nodes • Is optimum for since the graph is DAG. • Is not optimum for next iterations • Ignore backward edges: works since the optimum solution rarely uses them. • 2-pass DP: Run one more DP along backward edges • Is not optimum because of very rare cases. • Can do multi-pass DP Caching: 1000X faster • Use shortest paths from previous iterations. Keep track of the origin for each path • After instancing a track, update only paths which share the same origin. • Non-max-suppression in the loop: • At each iteration, suppress all windows overlapping with the instanced track. • Handling occlusion: • Adding more than one-frame jumps to transition edges. • Markov model places geometric prior on track length (short tracks more likely). • Approximate DP algorithm tends to produce longer tracks which may be more accurate

DOI: 10.1109/CVPR.2011.5995604

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