To address the problem that vehicle tracking accuracy is limited by sparse and unevenly distributed millimeter-wave radar point clouds in roadside perception, a radar-vision fusion extended object tracking method is proposed. First, a radar-vision joint observation model based on error-state is constructed to realize the collaborative representation of heterogeneous data. Second, aiming at the non-uniform generation characteristics of roadside radar, a Soft-Gated Visibility Gaussian Mixture Model (SGV-GMM) is proposed. By explicitly modeling the visibility of reffection points and updating parameters online within a variational Bayesian framework, the generation mechanism of sparse point clouds is effectively characterized. Third, to address the instability of shape estimation under sparse conditions, a Responsibility-Aware Adaptive Elastic Skeleton (RA-ES) model is constructed, which utilizes responsibility to quantify structural consistency and adaptively adjusts skeleton stiffness to enhance the robustness of contour estimation. Finally, the collaborative recursive estimation of vehicle motion and shape is implemented within the variational Bayesian framework. Experiments based on CARLA demonstrate that the proposed method signiffcantly improves contour estimation and state tracking accuracy in scenarios with vehicle maneuvering and sparse point clouds. Keywords: roadside perception; millimeter-wave radar; radar-vision fusion; extended object tracking; variational Bayesian; Gaussian mixture model; vehicle contour estimation