  A fundamental problem in robotic perception is matching identical objects or
data, with applications such as loop closure detection, place recognition,
object tracking, and map fusion. While the problem becomes considerably more
challenging when matching should be done jointly across multiple, multimodal
sets of data, the robustness and accuracy of matching in the presence of noise
and outliers can be greatly improved in this setting. At present, multimodal
techniques do not leverage multiway information, and multiway techniques do not
incorporate different modalities, leading to inferior results. In contrast, we
present a principled mixed-integer quadratic framework to address this issue.
We use a novel continuous relaxation in a projected gradient descent algorithm
that guarantees feasible solutions of the integer program are obtained
efficiently. We demonstrate experimentally that correspondences obtained from
our approach are more stable to noise and errors than state-of-the-art
techniques. Tested on a robotics dataset, our algorithm resulted in a 35%
increase in F1 score when compared to the best alternative.
