Co-transduction for shape retrieval

In this paper, we propose a new shape/object retrieval algorithm, namely, co-transduction. The performance of a retrieval system is critically decided by the accuracy of adopted similarity measures (distances or metrics). In shape/object retrieval, ideally, intraclass objects should have smaller distances than interclass objects. However, it is a difficult task to design an ideal metric to account for the large intraclass variation. Different types of measures may focus on different aspects of the objects: for example, measures computed based on contours and skeletons are often complementary to each other. Our goal is to develop an algorithm to fuse different similarity measures for robust shape retrieval through a semisupervised learning framework. We name our method co-transduction, which is inspired by the co-training algorithm. Given two similarity measures and a query shape, the algorithm iteratively retrieves the most similar shapes using one measure and assigns them to a pool for the other measure to do a re-ranking, and vice versa. Using co-transduction, we achieved an improved result of 97.72% (bull's-eye measure) on the MPEG-7 data set over the state-of-the-art performance. We also present an algorithm called tri-transduction to fuse multiple-input similarities, and it achieved 99.06% on the MPEG-7 data set. Our algorithm is general, and it can be directly applied on input similarity measures/metrics; it is not limited to object shape retrieval and can be applied to other tasks for ranking/retrieval.