Registration of Structured Square-Cell Grids

Relief models, also known as digital elevation model (DEMs) or grids, are comprised of cells, each of which has a value representative of the average elevation over the cell's footprint. Most grids are structured, in that all cells have exactly the same dimensions (regularly repeating structure), though some grids are unstructured (cells have varying size and/or shape). These unstructured grids are typically dense (have small cell sizes) where there are many data points contributing to the grid (e.g., shallow water), and sparse (large cell sizes) where there is less data (e.g., deep water). Structured grids, which typically have square cells but may have other regular shapes, require interpolation between sparse data points to determine the value of cells without data.

Structured square-cell grids have either of two registrations: grid- or node-registration and cell- or pixel-registration. Figure 1 illustrates the differences between these two registrations. An individual grid cell in either registration has one elevation value that represents the average elevation over the extent of that cell. This value can alternatively be represented as a point at the center of the cell. The difference between the two registrations is in how the grid ranges are defined (red lines in Fig. 1). Ranges for grid- or node-registered grids refer to the centers of the cells that lie along the boundaries of the grid (Panel A), and the footprints of the cells extend 1/2 cell width outside the range. Ranges for cell- or pixel-registered grids refer to the outside edges of the boundaries of the grid (Panel B). This means that for two grids with the same range, the grid-registered grid will have one more row and one more column than the cell-registered version. For global grids, a grid-registered grid has cells along the northern boundary that sit atop the North Pole, and similarly for the South Pole. Cell-registered grids have cells along the northern boundary that just touch the North Pole.

Cell-registered grids are more typically used in images (to prevent edge pixels from being cut in half along the boundaries), while grid-registered grids are more commonly used for representing discrete point data.

Figure 1. Difference between grid-registration and cell-registration for structured grids. Panel A is a grid-registered grid with cells centered on the gridlines. Panel B is the corresponding cell-registered grid with cells lying between the gridlines. Note that each cell in one registration overlaps quadrants of four cells in the other registration.

Grids can be converted between the two registration types, though this results in some degree of flattening of relief. Figure 2 illustrates how this happens in a very simple case. Each cell in one registration type overlies the corners of four cells in the opposing type. The cell value in the new grid will be an average of the four overlapped cells in the initial grid. Local highs, such as the 90 in the center of Panel A, are reduced in the new grid (Panel B), whose central cell values are lower due to averaging. Repeating the conversion, to return to a grid-registered grid, does not produce the original relief (Panel C). There are ways to reduce this registration-conversion effect, but converting between registration types is one-way and should be minimized.

Figure 2. Flattening of relief due to conversion between registrations. Local high ('90') in Panel A, is reduced in Panel B ('60') following registration conversion. Repeating the conversion does not reproduce the original elevation (Panel C), though the overall morphology (a hill) remains. This same flattening effect occurs with local deeps as well.

A note of caution: a grid of one type that is mistakenly identified as the other type can produce a shift in the cell locations (and thus a shift of the data where it to be converted to points lying at the centers of the cells). In other words, does the location of a cell refer to its center or to its lowermost left corner? Most grid applications recognize both types and avoid this problem but care should be taken.

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