Digital Images with 3D Geometry from Data Compression by Multi-scale Representations of B-Spline Surfaces

To build up a 3D (three-dimensional) model of the surface of an object, the heights of points on the surface are measured, for instance, by a laser scanner. The intensities of the reflected laser beam of the points can be used to visualize the 3D model as range image. It is proposed here to fit a two-dimensional B-spline surface to the measured heights and intensities by the lofting method. To fully use the geometric information of the laser scanning, points on the fitted surface with their intensities are computed with a density higher than that of the measurements. This gives a 3D model of high resolution which is visualized by the intensities of the points on the B-spline surface. For a realistic view of the 3D model, the coordinates of a digital photo of the object are transformed to the coordinate system of the 3D model so that the points get the colors of the digital image. To efficiently compute and store the 3D model, data compression is applied. It is derived from the multi-scale representation of the dense grid of points on the B-spline surface. The proposed method is demonstrated for an example.