Anomaly detection is important in many real-life applications. Recently, self-supervised learning has greatly helped deep anomaly detection by recognizing several geometric transformations. However these methods lack finer features, usually highly depend on the anomaly type, and do not perform well on fine-grained problems. To address these issues, we first introduce in this work three novel and efficient discriminative and generative tasks which have complementary strength: (i) a piece-wise jigsaw puzzle task focuses on structure cues; (ii) a tint rotation recognition is used within each piece, taking into account the colorimetry information; (iii) and a partial re-colorization task considers the image texture. In order to make the re-colorization task more object-oriented than background-oriented, we propose to include the contextual color information of the image border via an attention mechanism.We then present a new out-of-distribution detection function and highlight its better stability compared to existing methods. Along with it, we also experiment different score fusion functions. Finally, we evaluate our method on an extensive protocol composed of various anomaly types, from object anomalies, style anomalies with fine-grained classification to local anomalies with face anti-spoofing datasets. Our model significantly outperforms state-of-the-art with up to 36% relative error improvement on object anomalies and 40% on face anti-spoofing problems.