GeoTIFF Cells and Point Samples Give Extent Different Meanings

Start with the spatial meaning of each value

PixelIsArea associates a value with a finite raster cell. PixelIsPoint places a value at a discrete location, also called a posting. The distinction gives a buyer a useful question to settle before comparing two geospatial AI deliveries: what does the offered extent actually bound?

This explanation uses OGC GeoTIFF 1.1, document 19-008r4, published September 14, 2019. Section 7.2.1 specifies GTRasterTypeGeoKey ID 1025, type SHORT; value 1 denotes PixelIsArea and value 2 PixelIsPoint. Annex B.2.2 explains their geometry informatively. Section 6 confirms that Annex B adds no requirements.

An offer described only as three columns, two rows and a 10-unit step leaves room for different spatial requests. A cell-coverage request needs the outer cell boundaries. A point-location request needs the extreme posting coordinates. A display request needs its stated footprint convention. Each can be useful when it answers the intended question.

References: [GT1]

GT-48: six area cells cover 30u by 20u

GT-48 is an original fictional grid with three columns, two rows and six unspecified numeric values. Both alternatives use the expressly stipulated raster-to-model mapping X = 100 + 10I and Y = 200 - 10J. I increases along columns and J along rows. X and Y use invented model units u; each index step changes the corresponding model coordinate by 10u in magnitude.

The grid is axis-aligned, with no rotation or skew. This numerical illustration supplies no real dataset, actual coordinate reference system, reader behavior or file-conformance result. Both raster types are explicitly declared.

For the area alternative, the first cell occupies raster coordinates I = 0 to 1 and J = 0 to 1. Its model-coordinate bounds are X = 100 to 110u and Y = 190 to 200u. Its geometric center is at raster position (0.5,0.5), which maps to (105,195)u.

Three cells extend across raster coordinates I = 0 to 3. Two rows extend through J = 0 to 2. The complete outer bounds are therefore X = 100 to 130u and Y = 180 to 200u. Width is 130 - 100 = 30u; height is 200 - 180 = 20u.

The center calculation identifies a geometric position within the first cell. It supplies no assumption about averaging the six values or how they were produced.

References: [GT1]

The same six point locations span 20u by 10u

Keep GT-48's dimensions and equations, and consider the point alternative. Its column locations are I = 0, 1 and 2; its row locations are J = 0 and 1. The first posting at (0,0) maps to (100,200)u.

The top row has locations (100,200), (110,200) and (120,200)u. The second row has locations (100,190), (110,190) and (120,190)u. All six array positions have a location.

Their extreme coordinates are X = 100 to 120u and Y = 190 to 200u. The horizontal span is 120 - 100 = 20u; the vertical span is 200 - 190 = 10u. These bounds enclose the posting locations without assigning a finite coverage area to each posting.

The interval count explains the result. Three cell widths add to 3 x 10 = 30u. Three posting locations have two intervening steps, adding to (3 - 1) x 10 = 20u. Two rows similarly give two cell heights or one interval between posting rows.

The first area cell's center, (105,195)u, also differs from the first posting, (100,200)u, under the same equations. The alternatives describe different spatial associations. Their legitimate uses do not depend on making those coordinates agree.

References: [GT1]

A 30u by 20u point display can have shifted bounds

Now invent a display convention for GT-48: draw a 10u by 10u square centered on each posting. This optional convention defines only the display footprint.

The first square extends 5u to either side of (100,200)u. Across all six squares, X extends from 95 to 125u and Y from 185 to 205u. The footprint measures 125 - 95 = 30u by 205 - 185 = 20u.

Those dimensions equal the area alternative's dimensions, but the bounds differ. The area cells occupy X = 100 to 130u and Y = 180 to 200u. Matching the displayed width and height has therefore concealed a positional difference.

The six postings still lie at their original locations. Drawing surrounding squares creates neither additional observations nor evidence that the values describe those squares. A provider reporting this footprint needs to name the display convention so the buyer can distinguish it from the 20u by 10u sample-location span.

References: [GT1]

Reaching both area boundaries needs twelve postings

Consider a different request: supply regularly spaced point locations that reach both outer boundaries of the area alternative, X = 100 and 130u, Y = 180 and 200u, with 10u separation.

The required X locations are 100, 110, 120 and 130u. The required Y locations are 200, 190 and 180u. Four columns and three rows give 4 x 3 = 12 postings. Equivalently, a 30u span contains three 10u intervals and therefore four endpoints; a 20u span contains two intervals and three endpoints.

This is a new sampling request. The arithmetic counts twelve required locations; it does not transform six area values into twelve point values or establish a method for obtaining them.

For this axis-aligned example, N columns and M rows of cells cover N x 10u by M x 10u. The corresponding N by M posting locations span (N - 1) x 10u by (M - 1) x 10u. The buyer's boundary requirement determines which count is relevant.

Compare each extent declaration with the required input

A useful cell-delivery statement for GT-48 would identify three columns and two rows of area cells, the stipulated mapping and units, and outer bounds X = 100 to 130u, Y = 180 to 200u. A useful point-delivery statement would identify the same dimensions and mapping, then give sample-location bounds X = 100 to 120u, Y = 190 to 200u. A display footprint would be a separately named quantity.

If the required input is the six area cells, the six postings have not established that deliverable merely by matching its array shape. If the task requires those six posting locations, the point alternative answers that spatial request. If the task requires postings across the full original outer bounds, the twelve-location request identifies the additional population needed. Choose against the stated consumer requirement.

For an actual offer, have the data provider identify the delivered raster, array-axis meanings, declared raster type, coordinate reference system, units and raster-to-model relationship together with the extent definition. Ask for the relevant boundary coordinates or extreme sample locations. A label such as origin or extent needs enough context to identify which spatial quantity it describes. Other grid geometries need their own stated boundary geometry; GT-48's simple width and height arithmetic depends on its axis-aligned premises.

Keep the values' meaning alongside that geometry: the selected band, value units, missing-value convention and how the delivered values were obtained may matter to the intended input. A spatial declaration alone establishes neither value provenance nor spatial accuracy or AI performance. The appointed data and application owners need evidence that the proposed delivery and the receiving interpretation answer the same request.

The related COG article addresses resolution levels and storage tiles. The DICOM and NIfTI articles address coordinate mappings. Those remain separate decisions from choosing which boundary a cell or posting extent reports.

References: [GT1]

If the surrounding equipment needs physical connections

For an independently needed equipment-cabling project, Leviathan's Structured Cabling & Fiber Installation service covers agreed physical routing, dressing, endpoint labels and connection records. Use the related project inquiry with a nonconfidential equipment and site outline, approved endpoints, material responsibilities and the required physical handoff to discuss scope and availability. Raster interpretation and geospatial AI input preparation remain with the appointed data and software providers.

References: [L1]