Index CRSs

This page describes how to use and interpret Index Coordinate Reference Systems (CRSs), and how they differs from other linear coordinate systems and especially how it differs from the internal grid CRS, known as CRS:1.

GML definitions for ​Index1D, ​Index2D and ​Index3D are already embedded in our [SecoreDevGuide SECORE] resolver and their official acknowledgment is on OGC table.

Definition

As you can verify by looking at the "extra" (non-EPSG) CRS definitions ​provided by SECORE, among others there are three new Index CRSs, namely ​1D, ​2D and ​3D reference systems.

The index prefix refers to the fact that integral coordinates shall be used in the geometric (cartesian) space. The n-dimensional Coordinate System (CS) is supposed to be bound to an multidimensional array (marray) of cells: the origin of the CS is placed in the centre of the 0-cell. This represents the datum and completes the picture to define the CRS.

Using index CRSs can be useful especially when using rasdaman for applications not related to the geo-referenced world of satellite products, or more generally to remote-sensing imagery. For instance, rasdaman could be used to process ​large bio-medical images, which do not need a geo-reference.

The previous case is out of scope in the OGC services, and it is probably better handled via direct rasql requests (also via [PetascopeUserGuide Petascope] rasql web interface). However, more interestingly, index CRSs could also be used to access "pixel" coordinates from an image, or to access layers of height/time via their ordinal position in the stack (this requires CRS extensions [Features available]).

Index CRSs exploit indexed cartesian CSs by defining the Unit of Measure (Uom) of each of its axes to be an integral. The specific terminology that is used is ​GridSpacing, defined by OGC in the context of the ​deprecated (2D) Image CRS. Indeed index CRSs are considered the n-dimensional extension/generalization of the previously defined ​Image CRSs: this means replacing the typically-2D terminology of pixels, rows and columns with the more general cells and axis.

The following picture clarifies what is the space of coordinates covered by a standard 2D (linear) cartesian CS, and an indexed one:

The 2D space is fully covered on a geometric space with no additional constraints, whereas limiting the coordinates to integrals confines the address space to a grid of 0D points. While this is easily understandable, it has some important consequences: sample sizes (footprints) of coverages' points are confined to be 0D on an index CRSs since the areas between CRS points is not reachable and hence loses its meaning.

In the regular 2D case, usually a pixel represents its extent/area (though ​not always of course), while a coverage point is always a 0D point: on an index CRS the point is on integral coordinates, and the footprint would be half-pixel away from it, over unreachable spaces 0.5 GridSpacing away from it. Truncating this footprint to the legal index space, the footprints/pixels reduce to the point itself.

Grid origin and offset vectors

TBD

Change label of the axes

TBD Parametrized