3-D range data interpolation using B-Spline surface fitting

Many optical range sensors use an Equal Angle Increment (EAI) sampling. This type of sensors uses rotating mirrors with a constant angular velocity using radar and triangulation techniques, where the sensor sends and receives the modulated coherent light through the mirror. Such an EAI model generates data for surface geometrical description that has to be converted, in many applications, into data which meet the desired Equal Distance Increment (EDI) orthographic projection model. For an accurate analysis in three-dimensional (3-D) images, a 3-D interpolation scheme is needed to resample the range data into spatially equally-distance sampling data that emulate the Cartesian orthographic projection model. In this paper, a resampling approach using a B-Spline surface fitting is proposed. The first step is to select a new scale for all X, Y, Z directions based on the 3-D Cartesian coordinates of range data obtained from the sensor parameters. The size of the new range image and the new coordinates of each point are then computed according to the actual references of (X, Y, Z) coordinates and the new scale. The new range data are interpolated using a B-Spline surface fitting based on the new Cartesian coordinates. The experiments show that this 3-D interpolation approach provides a geometrically accurate solution for many industrial applications which deploy the EAI sampling sensors.