SO and O Equivariance in Image Recognition with Bessel-Convolutional Neural Networks

For many years, it has been shown how much exploiting equivariances can be beneficial when solving image analysis tasks. For example, the superiority of convolutional neural networks (CNNs) compared to dense networks mainly comes from an elegant exploitation of the translation equivariance. Patterns can appear at arbitrary positions and convolutions take this into account to achieve translation invariant operations through weight sharing. Nevertheless, images often involve other symmetries that can also be exploited. It is the case of rotations and reflections that have drawn particular attention and led to the development of multiple equivariant CNN architectures. Among all these methods, Bessel-convolutional neural networks (B-CNNs) exploit a particular decomposition based on Bessel functions to modify the key operation between images and filters and make it by design equivariant to all the continuous set of planar rotations. In this work, the mathematical developments of B-CNNs are presented along with several improvements, including the incorporation of reflection and multi-scale equivariances. Extensive study is carried out to assess the performances of B-CNNs compared to other methods. Finally, we emphasize the theoretical advantages of B-CNNs by giving more insights and in-depth mathematical details.

Industrial and Medical Anomaly Detection Through Cycle-Consistent Adversarial Networks

In this study, a new Anomaly Detection (AD) approach for real-world images is proposed. This method leverages the theoretical strengths of unsupervised learning and the data availability of both normal and abnormal classes. The AD is often formulated as an unsupervised task motivated by the frequent imbalanced nature of the datasets, as well as the challenge of capturing the entirety of the abnormal class. Such methods only rely on normal images during training, which are devoted to be reconstructed through an autoencoder architecture for instance. However, the information contained in the abnormal data is also valuable for this reconstruction. Indeed, the model would be able to identify its weaknesses by better learning how to transform an abnormal (or normal) image into a normal (or abnormal) image. Each of these tasks could help the entire model to learn with higher precision than a single normal to normal reconstruction. To address this challenge, the proposed method utilizes Cycle-Generative Adversarial Networks (Cycle-GANs) for abnormal-to-normal translation. To the best of our knowledge, this is the first time that Cycle-GANs have been studied for this purpose. After an input image has been reconstructed by the normal generator, an anomaly score describes the differences between the input and reconstructed images. Based on a threshold set with a business quality constraint, the input image is then flagged as normal or not. The proposed method is evaluated on industrial and medical images, including cases with balanced datasets and others with as few as 30 abnormal images. The results demonstrate accurate performance and good generalization for all kinds of anomalies, specifically for texture-shaped images where the method reaches an average accuracy of 97.2% (85.4% with an additional zero false negative constraint).