Creating high-fidelity 3D head avatars has always been a research hotspot, but it remains a great challenge under lightweight sparse view setups. In this paper, we propose HHAvatar represented by controllable 3D Gaussians for high-fidelity head avatar with dynamic hair modeling. We first use 3D Gaussians to represent the appearance of the head, and then jointly optimize neutral 3D Gaussians and a fully learned MLP-based deformation field to capture complex expressions. The two parts benefit each other, thereby our method can model fine-grained dynamic details while ensuring expression accuracy. Furthermore, we devise a well-designed geometry-guided initialization strategy based on implicit SDF and Deep Marching Tetrahedra for the stability and convergence of the training procedure. To address the problem of dynamic hair modeling, we introduce a hybrid head model into our avatar representation based Gaussian Head Avatar and a training method that considers timing information and an occlusion perception module to model the non-rigid motion of hair. Experiments show that our approach outperforms other state-of-the-art sparse-view methods, achieving ultra high-fidelity rendering quality at 2K resolution even under exaggerated expressions and driving hairs reasonably with the motion of the head
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