Fast, Accurate and Memory-Efficient Partial Permutation Synchronization
This work addresses a bottleneck in structure-from-motion and multi-object matching for computer vision researchers, offering a more scalable solution, though it is incremental as it builds on the CEMP framework.
The paper tackles the problem of partial permutation synchronization for multi-object matching, which is computationally intensive and memory-demanding for large datasets, by proposing MatchFAME, a new algorithm that achieves state-of-the-art accuracy, speed, and memory efficiency through sparse matrix operations.
Previous partial permutation synchronization (PPS) algorithms, which are commonly used for multi-object matching, often involve computation-intensive and memory-demanding matrix operations. These operations become intractable for large scale structure-from-motion datasets. For pure permutation synchronization, the recent Cycle-Edge Message Passing (CEMP) framework suggests a memory-efficient and fast solution. Here we overcome the restriction of CEMP to compact groups and propose an improved algorithm, CEMP-Partial, for estimating the corruption levels of the observed partial permutations. It allows us to subsequently implement a nonconvex weighted projected power method without the need of spectral initialization. The resulting new PPS algorithm, MatchFAME (Fast, Accurate and Memory-Efficient Matching), only involves sparse matrix operations, and thus enjoys lower time and space complexities in comparison to previous PPS algorithms. We prove that under adversarial corruption, though without additive noise and with certain assumptions, CEMP-Partial is able to exactly classify corrupted and clean partial permutations. We demonstrate the state-of-the-art accuracy, speed and memory efficiency of our method on both synthetic and real datasets.