Gradient of B-splines in volume rendering

This paper deals with surface reconstruction and the gradient reconstruction in the volume rendering. In the volume rendering procedure, reconstruction according to the discrete set of samples is required. Due to the reconstruction procedure alias artifacts in the final image, it could not be neglected. In this paper, we focus our attention on the gradient reconstruction based on the surface reconstruction. For the surface reconstruction we use the cubic B-splines and for the gradient reconstruction corresponding derivative. If the noise is present in the input data, the approximation of B-spline is used, and the interpolation B-spline is used for the input signal without the noise. The shading procedure requires normal estimation. Two approaches are used for normal estimation. The classic approach for normal estimation is central difference calculation, and we propose derivative calculation of the reconstruction B-spline function. We show that the calculation of the normal vector has important influence on the alias artifacts in the result.