Image Hashing by Minimizing Discrete Component-wise Wasserstein Distance

Abstract

Image hashing is a fundamental problem in the computer vision domain with various challenges, primarily, in terms of efficiency and effectiveness. Existing hashing methods lack a principled characterization of the goodness of the hash codes and a principled approach to learn the discrete hash functions that are being optimized in the continuous space. Adversarial autoencoders are shown to be able to implicitly learn a robust hash function that generates hash codes which are balanced and have low-quantization error. However, the existing adversarial autoencoders for hashing are too inefficient to be employed for large-scale image retrieval applications because of the minmax optimization procedure. In this paper, we propose an Independent Relaxed Wasserstein Autoencoder, which presents a novel, efficient hashing method that can implicitly learn the optimal hash function by directly training the adversarial autoencoder without any discriminator/critic. Our method is an orderof-magnitude more efficient and has a much lower sample complexity than the Optimal Transport formulation of the Wasserstein distance. The proposed method outperforms the current state-of-the-art image hashing methods for the retrieval task on several prominent image collections.

Image Generation Via Minimizing Fréchet Distance in Discriminator Feature Space

“…As shown in Figure 1, the models generate CIFAR-10 images (higher-dimensional) with significant mode collapse or white noise than the generated MNIST images (low-dimensional). Minimizing OT on the original input space only works in domains where the input data is already low-dimensional and the Frobenius distance is suitable [20,9]. Another challenge of using OT is its high computational cost.…”

“…Solving the linear-sum assignment program has a complexity of O(N 2.5 log N ) where N is the number of samples [5]. Reducing OT's computational cost is necessary to utilize it in practice [9].…”