  Current massive datasets demand light-weight access for analysis. Discrete
hashing methods are thus beneficial because they map high-dimensional data to
compact binary codes that are efficient to store and process, while preserving
semantic similarity. To optimize powerful deep learning methods for image
hashing, gradient-based methods are required. Binary codes, however, are
discrete and thus have no continuous derivatives. Relaxing the problem by
solving it in a continuous space and then quantizing the solution is not
guaranteed to yield separable binary codes. The quantization needs to be
included in the optimization. In this paper we push for quantization: We
optimize maximum class separability in the binary space. We introduce a margin
on distances between dissimilar image pairs as measured in the binary space. In
addition to pair-wise distances, we draw inspiration from Fisher's Linear
Discriminant Analysis (Fisher LDA) to maximize the binary distances between
classes and at the same time minimize the binary distance of images within the
same class. Experiments on CIFAR-10, NUS-WIDE and ImageNet100 demonstrate
compact codes comparing favorably to the current state of the art.
