This paper introduces Quaternion Approximate Networks (QUAN), a novel deep learning framework that leverages quaternion algebra for rotation equivariant image classification and object detection. Unlike conventional quaternion neural networks attempting to operate entirely in the quaternion domain, QUAN approximates quaternion convolution through Hamilton product decomposition using real-valued operations. This approach preserves geometric properties while enabling efficient implementation with custom CUDA kernels. We introduce Independent Quaternion Batch Normalization (IQBN) for training stability and extend quaternion operations to spatial attention mechanisms. QUAN is evaluated on image classification (CIFAR-10/100, ImageNet), object detection (COCO, DOTA), and robotic perception tasks. In classification tasks, QUAN achieves higher accuracy with fewer parameters and faster convergence compared to existing convolution and quaternion-based models. For objection detection, QUAN demonstrates improved parameter efficiency and rotation handling over standard Convolutional Neural Networks (CNNs) while establishing the SOTA for quaternion CNNs in this downstream task. These results highlight its potential for deployment in resource-constrained robotic systems requiring rotation-aware perception and application in other domains. Code: https://cwru-aism.github.io/ QUANpaper/
Video stylization typically transforms entire scenes, while local artistic editing requires precise region--style association, spatial control, and temporal consistency. We introduce LociArt, a unified paradigm for free-style local video stylization that explicitly specifies where to stylize and what style to apply while preserving non-target content. At its core, GRNStyle builds on Generative Refinement Networks (GRN) and introduces a polar style-aware mask that embeds style identities as equal-norm directions within selected regions. Complementary representation--geometry conditioning combines encoded mask features with raw-mask spatial support, integrating spatiotemporal context with geometric control. To provide paired supervision, we develop an automated pipeline combining global stylization, video object removal, matting, and compositing, and construct the LociArt-100K Dataset with 100K local stylization pairs. We further establish the LociArt Benchmark, comprising 80 source videos and 84 target masks covering 168 foreground/background stylization cases, with a Style Prototype Similarity (SPS) evaluation scheme for regional style quality and complementary measures of non-target preservation and temporal consistency. Experiments show that GRNStyle outperforms existing methods in regional style quality and spatial control while maintaining strong temporal consistency. Qualitative examples further illustrate joint stylization of multiple regions with the same or different learned styles, despite training only on single-region, single-style pairs. Together, these components provide a unified foundation for learning and evaluating controllable local video stylization. Project page: https://higherhu.github.io/lociart/.