3D reconstruction from serial 2D microscopy images depends on non-linear alignment of serial sections. For some structures, such as the neuronal circuitry of the brain, very large images at very high resolution are necessary to permit reconstruction. These very large images prevent the direct use of classical registration methods. We propose in this work a method to deal with the non-linear ali...

The Body Centered Cubic (BCe) and Face Centered Cubic (FCC) lattices along with a set of box splines for sampling and reconstruction of trivariate functions are proposed. The BCC lattice is demonstrated to be the optimal choice of a pattern for generic sampling purposes. While the FCC lattice is the second best choice for this purpose, both FCC and BCC lattices significantly outperform the accu...

where MiðxÞ and NjðyÞ denote normalised cubic B-splines, the former defined on the knots i to iþ4 and the latter on the knots j to jþ4. For further details, see Hayes and Halliday (1974) for bicubic splines and de Boor (1972) for normalised B-splines. The total numbers nx and ny of these knots and their values 1; . . . ; nx and 1; . . . ; ny are chosen automatically by the routine. The knots 5;...

where Mi x ð Þ and Nj y ð Þ denote normalized cubic B-splines, the former defined on the knots i to iþ4 and the latter on the knots j to jþ4. For further details, see Hayes and Halliday (1974) for bicubic splines and De Boor (1972) for normalized B-splines. The total numbers nx and ny of these knots and their values 1; . . . ; nx and 1; . . . ; ny are chosen automatically by the routine. The kn...

We show that the geometric Hermite interpolant can be easily calculated without solving a system of nonlinear equations. In addition we give geometric conditions for the existence and uniqueness of a solution to the interpolation problem. Finally we compare geometric Hermite interpolation with standard cubic Hermite interpolation. x1 Introduction Since parametric representations of curves are n...

A spline function is a curve constructed from polynomial segments that are subject to conditions or continuity at their joints. In this paper, we shall present the algorithm of the cubic smoothing spline and we shall justify its use in estimating trends in time series. Considerable effort has been devoted over several decades to developing the mathematics of spline functions. Much of the intere...