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Theory

For simplicity, throughout this section we refer to a two-dimensional sampled image, ${\bf b}$; however, the beauty of the helical coordinate system is that everything can be trivially extended to an arbitrary number of dimensions.

We employ two equivalent subscripting schemes for referring to an element of the two-dimensional image, ${\bf b}$. Firstly, with two subscripts, bpx,py refers to the element that lies px increments along the x-axis, and py increments along the y-axis. Ranges of pxand py are given by $0 \leq p_x < N_x$, and $0 \leq p_y < N_y$ respectively. Helical coordinates suggest an alternative subscripting scheme: We can use a single subscript, ph=px + py Nx, such that bpx,py = bph and the range of ph is given by $0 \leq p_h < N_x N_y$.Moreover, if we impose helical boundary conditions, we can treat ${\bf b}$ as a one-dimensional function of subscript ph.


 
next up previous print clean
Next: Linking 1-D and 2-D Up: Rickett & Guitton: Helical Previous: Introduction
Stanford Exploration Project
9/5/2000