Abstract: 3D hand pose estimation approaches can be divided into two categories, including regression-based methods and detection-based methods. Detection-based methods utilize fully convolutional networks to obtain hand-crafted coordinate representations like heatmaps and then use a coordinate decoding function like soft-argmax to decode coordinates. In contrast, regression-based methods employ low-dimension features from convolutional networks as unconstrained coordinate representations and then use fully-connected layers to decode coordinates. This way allows the network to learn the coordinate representations and the corresponding coordinate decoding function automatically. However, it causes either weak coordinate representational power or decoding's optimization difficulty. These drawbacks cause regression-based methods far less accurate than detection-based methods. However, detection-based methods require many computations for deconvolution, and their hand-crafted coordinate representations may not be optimal. This paper proposes a novel framework for regression-based methods that can preserve the strength of representations and avoid severe optimization difficulty while remaining flexible, lightweight, and efficient. More specifically, we use joint-specific feature maps as coordinate representations and the joint-shared coordinate decoding module. Moreover, we apply a multi-head mechanism to exploit different coordinate representations and design a learnable re-parameterization method to do multi-stage refinement better. Our approach outperforms state-of-the-art methods on four public benchmarks, including FreiHAND, HO-3D, RHD, and STB.