This article proposes a generative adversarial network called explicit affine disentangled generative adversarial network (EAD-GAN), which explicitly disentangles affine transform in a self-supervised manner. We propose an affine transform regularizer to force the InfoGAN to have explicit properties of affine transform. To facilitate training an affine transform encoder, we decompose the affine matrix into two separate matrices and infer the explicit transform parameters by the least-squares method. Unlike the existing approaches, representations learned by the proposed EAD-GAN have clear physical meaning, where transforms, such as rotation, horizontal and vertical zooms, skews, and translations, are explicitly learned from training data. Thus, we set different values of each transform parameter individually to generate specifically affine transformed data by the learned network. We show that the proposed EAD-GAN successfully disentangles these attributes on the MNIST, CelebA, and dSprites datasets. EAD-GAN achieves higher disentanglement scores with a large margin compared to the state-of-the-art methods on the dSprites dataset. For example, on the dSprites dataset, EAD-GAN achieves the MIG and DCI score of 0.59 and 0.96 respectively, compared to 0.37 and 0.71, respectively, for the state-of-the-art methods.

This paper proposes a Recurrent Affine Transform Encoder (RATE) that can be used for image representation learning. We propose a learning architecture that enables a CNN encoder to learn the affine transform parameter of images. The proposed learning architecture decomposes an affine transform matrix into two transform matrices and learns them jointly in a self-supervised manner. The proposed RATE is trained by unlabeled image data without any ground truth and infers the affine transform parameter of input images recurrently. The inferred affine transform parameter can be used to represent images in canonical form to greatly reduce the image variations in affine transforms such as rotation, scaling, and translation. Different from the spatial transformer network, the proposed RATE does not need to be embedded into other networks for training with the aid of other learning objectives. We show that the proposed RATE learns the affine transform parameter of images and achieves impressive image representation results in terms of invariance to translation, scaling, and rotation. We also show that the classification performance is enhanced and is more robust against distortion by incorporating the RATE into the existing classification model.