  This paper proposes a novel ternary hash encoding for learning to hash
methods, which provides a principled more efficient coding scheme with
performances better than those of the state-of-the-art binary hashing
counterparts. Two kinds of axiomatic ternary logic, Kleene logic and
{\L}ukasiewicz logic are adopted to calculate the Ternary Hamming Distance
(THD) for both the learning/encoding and testing/querying phases. Our work
demonstrates that, with an efficient implementation of ternary logic on
standard binary machines, the proposed ternary hashing is compared favorably to
the binary hashing methods with consistent improvements of retrieval mean
average precision (mAP) ranging from 1\% to 5.9\% as shown in CIFAR10, NUS-WIDE
and ImageNet100 datasets.
