# T-Spline Based Unifying Registration Procedure for Free-Form Surface Workpieces in Intelligent CMM
## 4 Experiments  
### Workpiece Recognition  
The human knee bone model, Chinese lion head model and girl's face model are used in the following experiments, as shown in Figure 6. The physical equipment is designed as shown in Figure 6, where (a) is the overall physical Figure and (b) is the Figure partially enlarged. The Ximea MU9 PM-MH camera (Ximea, Munster, Germany) used in our experiment has a resolution of 2592 \(\times\) 1944 and a pixel size of 2.2 \(\upmu\)m \(\times\) 2.2 \(\upmu\)m. The focal length of the lens is 6 mm. The CMM adopted in this paper is Global classic SR 07. 10. 07 CMM (Hexagon, Qingdao, China).The maximum error of CMM is less 3 \(\upmu\)m. The error of the visual inspection system includes a camera and a laser is less 1 mm. The initial state of the system is camera has a certain distance to platform, and parts are photographed and detected roughly the size of the outline. And then according to the part of the outline size CMM move from a side of the workpiece to the other side in a certain interval. The interval size is generally 2-5 mm, and then if the workpiece is large enough to properly enlarge the scanning interval. In this paper,through the point cloud registration the workpiece and rough position and orientation are recognized. The application condition of the system is that the point cloud collected by the visual system is enough to represent the general shape of the workpiece. It is difficult to achieve accurate identification if the interval size is too large or only part of the workpiece is collected. Figures 7a and 8a are the human knee bone model and Chinese lion head model, respectively. Figures 7b and 8b show the results of the quad-tree division of the parameter field, where the red grid corresponds to the pre-image of the T-mesh and the point cloud in blue corresponds to the vertex of the triangular mesh. The T-meshes obtained by fitting the T-spline surface are shown in Figures 7c and 8c. The point in light blue is the control point of the T-spline surface. Part of the control point is in the shape, which results in an intermittent display. This is a reasonable distribution of control points. Figures 9a and 10a show the point clouds generated by the T-spline surface formula. Figures 9b and 10b show the partial magnification. Here, the adjacent distance to the nearest point is no more than 2 mm, as this department is only involved in the workpiece position recognition and initial registration, within the error no more than 2 mm can meet the actual needs, it can also be specified as some other value. This generated point cloud and that extracted by the visual system are then registered. Figures 11 and 12 show the registration results of the point cloud collected by the visual system and the point cloud generated by the T-spline surface formula. In this paper, the free-form surface workpiece, position and orientation are recognized via point cloud registration. In the experiment, the point clouds of the knee bone model, Chinese lion head model and girl's face model are collected by the visual system. Then, the collected point cloud and generated point cloud are registered one by one. The results of the registration are shown in Table 1. When the \(D_{max}\) between the corresponding points after the registration is greater than a certain threshold, it is not considered to be the same free-form surface workpiece. Table 1 shows that for the same workpiece, the \(D_{max}\) is less than 1 mm. The registration results between the different workpieces are considerably larger than this threshold. Figure 6: The actual experiment equipment includes coordinate measuring machine, measured workpiece and visual system, (**a**) the overall physical diagram, (**b**) the partial magnification of probe and visual system. Figure 8: Chinese lion head model as an example of fitting T-splines, (**a**) the original lion head model, (**b**) the pre-image of T-meshes and triangle mesh vertexes, (**c**) the spatial distribution of control points and T-meshes.