Motion estimation is a fundamental step in dynamic medical image processing for the assessment of target organ anatomy and function. However, existing image-based motion estimation methods, which optimize the motion field by evaluating the local image similarity, are prone to produce implausible estimation, especially in the presence of large motion. In addition, the correct anatomical topology is difficult to be preserved as the image global context is not well incorporated into motion estimation. In this study, we provide a novel motion estimation framework of dense-sparse-dense (DSD), which comprises two stages. In the first stage, we process the raw dense image to extract sparse landmarks to represent the target organ's anatomical topology, and discard the redundant information that is unnecessary for motion estimation. For this purpose, we introduce an unsupervised 3-D landmark detection network to extract spatially sparse but representative landmarks for the target organ's motion estimation. In the second stage, we derive the sparse motion displacement from the extracted sparse landmarks of two images of different time points. Then, we present a motion reconstruction network to construct the motion field by projecting the sparse landmarks' displacement back into the dense image domain. Furthermore, we employ the estimated motion field from our two-stage DSD framework as initialization and boost the motion estimation quality in light-weight yet effective iterative optimization. We evaluate our method on two dynamic medical imaging tasks to model cardiac motion and lung respiratory motion, respectively. Our method has produced superior motion estimation accuracy compared to the existing comparative methods. Besides, the extensive experimental results demonstrate that our solution can extract well-representative anatomical landmarks without any requirement of manual annotation. Our code is publicly available online: https://github.com/yyguo-sjtu/DSD-3D-Unsupervised-Landmark-Detection-Based-Motion-Estimation.