1. A shape-extraction method comprising: (1) a step of receiving image data of a projective image that has been acquired by radiation projection to an object; (2) a step of using a predetermined mesh structure to acquire a cross-sectional image of the object from the image data of the projective image by reconstruction using tomography; (3) a step of causing a lattice point that forms the mesh structure to move in conformity with the surface shape of the object based on the cross-sectional image that has been acquired by the reconstruction; and (4) a step of carrying out step (2) using a mesh that has had the position of the lattice point corrected using step (3), and then repeatedly executing step (3) and step (2) as many times as required; wherein the mesh structure is a tetrahedral mesh for producing a three-dimensional shape, and wherein the processing for causing the lattice point to move in conformity with the surface shape of the object, in step (3), comprises: (3p) a step of obtaining barycentric positions for two adjacent tetrahedron meshes that also include a boundary surface; (3q) a step of obtaining a point constituting a predetermined CT value, between the barycentric positions of two tetrahedron meshes, as a barycenter of a triangle constituting a boundary mesh; (3r) a step of obtaining orientation of the boundary mesh such that a normal direction of a triangle constituting the boundary mesh conforms to a gradient direction of the CT values of the two adjacent tetrahedron meshes; and (3s) a step of moving the lattice point using an apex position of the triangle constituting the boundary mesh that was obtained in steps 3q and 3r.