This paper proposes a novel approach, the sinogram polygonizer, for directly reconstructing 3D shapes from sinograms (i.e., the primary output from X-ray computed tomography (CT) scanners consisting of projection image sequences of an object shown from different viewing angles). To obtain a polygon mesh approximating the surface of a scanned object, a grid-based isosurface polygonizer, such as Marching Cubes, has been conventionally applied to the CT volume reconstructed from a sinogram. In contrast, the proposed method treats CT values as a continuous function and directly extracts a triangle mesh based on tetrahedral mesh deformation. This deformation involves quadratic error metric minimization and optimal Delaunay triangulation for the generation of accurate, high-quality meshes. Thanks to the analytical gradient estimation of CT values, sharp features are well approximated, even though the generated mesh is very coarse. Moreover, this approach eliminates aliasing artifacts on triangle meshes.