Four neighbouring land-cover cells are labelled Forest, Forest, Water and Urban. Their stored class codes are 1, 1, 5 and 9. Bilinear interpolation at the exact centre of all four returns 4—an invented intermediate number, not a measured land-cover category. The map may look smoother while its meaning has been damaged.
Remote sensing rasters can store continuous measurements, such as reflectance, or discrete thematic labels, such as land cover. They may look like similar grids but their values mean different things. This guide compares interpolation methods, explains why class numbers cannot be averaged safely, and gives practical checks for reprojection, resampling and area summaries.
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Choose a route or read all twelve open teaching chapters. The chapter index is grouped by the decision you need to make.
Identify the data type: chapters 1–2. Start this route.
Calculate three resampling choices: chapters 3–5. Start this route.
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Chapter index
Identify the data type · Chapters 1–2
Calculate three resampling choices · Chapters 3–5
Separate labels from quantities · Chapters 6–7
Audit boundaries and metadata · Chapters 8–10
Practise and continue · Chapters 11–12
A satellite reflectance raster stores a measured or calibrated numeric quantity representing a spectral observation. Two reflectance values have an ordered quantitative meaning within their defined band and processing system. Depending on the scientific purpose, numerical interpolation may be a useful approximation when moving reflectance to a different grid.
A classified land-cover raster is different. A code such as 1 = forest, 5 = water or 9 = urban is a label. The numbers are identifiers chosen by a codebook; their arithmetic differences and averages do not represent distances between landscapes.
Before a reprojection, aggregation or raster overlay, ask whether each pixel is a physical quantity, a probability, a class label or a special NoData code. That answer determines which resampling methods preserve meaning.
Imagine four equal-area source cells in a two-by-two block. The upper row contains Forest (code 1) and Forest (code 1). The lower row contains Water (code 5) and Urban (code 9). The input contains three kinds of landscape, but no category code 4.
The four cells are deliberately constructed as a small, clear test of how resampling algorithms operate. Real mapped boundaries can be more complicated, with mixed-pixel classifications, uncertain labels and geolocation errors already present before any software changes the grid.
An output cell near their meeting point has to be assigned or summarised somehow. Whether it should copy one label, represent the most common area class, or store fractional cover depends on the intended product.
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Bilinear interpolation treats neighbouring pixel values as numbers and takes a weighted combination determined by output position. At the exact midpoint between four equally spaced cell centres, each corner contributes one-quarter of the result.
Our invented values give (1 + 1 + 5 + 9)/4 = 4. No source cell carries class 4. If the land-cover codebook does not define 4, the result is invalid. If class 4 happens to mean wetland somewhere in the codebook, the interpolation can falsely claim wetland even though none of the four source cells is wetland.
The problem is not insufficient decimal precision. It is applying arithmetic to nominal labels. Reassigning the same three categories to different integer codes changes the bilinear result without changing the actual landscape.
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Nearest-neighbour resampling identifies the input pixel centre closest to the output location and copies its category code unchanged. If an output point lies just closer to the upper-left forest cell than to the other three centres, the output is forest, code 1. It never becomes code 4 through numerical averaging.
At the exact symmetric centre of all four cells, several neighbours are equally close. The result can depend on the software’s tie-breaking or coordinate convention, so avoid relying on that single ambiguous location to demonstrate a unique nearest-neighbour answer.
Nearest neighbour protects the set of class codes from new numerical combinations. It does not guarantee perfect spatial alignment or preservation of every tiny feature after changing scale; it answers a different question from bilinear interpolation.
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Suppose one output cell intentionally aggregates exactly these four equal-area source cells. Forest appears twice, water once and urban once. A majority-or-mode calculation can choose forest because it is the most frequent class in the represented group. It returns a real source class, but loses the minority categories.
If the task is calculating land-cover composition, a fractional summary is more informative: 50% forest, 25% water and 25% urban for this idealised aggregation. These numbers describe area fractions, not land-cover codes to be treated as colours or categories.
Nearest neighbour, mode and fractional aggregation answer different questions: which local label is nearest, which category dominates an area, and what mixture of categories occupies the area. Choose by purpose rather than by which image looks smoothest.
| Resampling question | Result | Interpretation |
|---|---|---|
| Bilinear at exact centre | 4 | Mathematical code average, not a valid observed class |
| Nearest to upper-left cell | 1 = Forest | Copies an existing label |
| Mode over four equal cells | 1 = Forest | Most common class, discards minority classes |
| Fractional area | 50% forest, 25% water, 25% urban | Preserves mixture, not one class label |
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Replace the example codebook with Forest = 8, Water = 3 and Urban = 2. The physical cells are unchanged: forest, forest, water and urban. Yet the bilinear midpoint becomes (8 + 8 + 3 + 2)/4 = 5.25, entirely different from the previous 4.
A scientifically meaningful interpolation of a physical quantity should not change merely because a database administrator renamed category identifiers. The dependence on arbitrary numbering is a simple proof that linear interpolation has no general categorical interpretation.
Good workflows preserve the category label as a nominal variable. If algorithms need a continuous quantity, consider appropriate physically meaningful measurements or class probabilities instead of pretending the integer label is that quantity.
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For continuous values such as a reflectance band, elevation surface or estimated temperature field, nearest, bilinear and cubic methods make different numerical and spatial assumptions. Bilinear interpolation can provide a smooth estimate at new sample locations, though it may smooth narrow features and alter pixel-level statistics.
For a class-probability raster, interpolating probability estimates can be meaningful if their interpretation, spatial support and normalisation are addressed. Interpolating the final class label is not the same operation as interpolating a probability for each class and then choosing a class under a documented rule.
Land-cover products often combine multiple bands, classifiers and postprocessing. If preservation of original measurements matters, the order of resampling and classification can change the result. Keep the original inputs and describe the pipeline.
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A crisp-looking raster created with nearest neighbour may preserve valid codes and still alter class areas, particularly when a small output grid poorly represents narrow rivers, field boundaries or fragmented habitat. Pixels can be gained or lost as output cell centres move.
If accurate change in area is the scientific objective, record pixel area in a suitable equal-area framework or use robust polygon/fractional-area methods appropriate to the product. Counting cells in geographic degrees as though each occupied equal square metres can add a second, unrelated error.
The resampling method is therefore a necessary but insufficient quality decision. Valid classes, positional alignment, scale and area interpretation all require checks.
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NoData is not an ordinary land-cover class. If a missing-data flag is encoded as 0, −9999 or another number, interpolating it as a physical value can create extreme artefacts or spurious intermediate class codes. Some tools handle masks specially, but the behaviour needs verification.
Likewise, class code 0 may be legitimate in one product and missing in another. Never assume its meaning from appearance alone. Preserve the documented class legend and the mask indicating missing or unreliable observations.
After resampling, compare unique class IDs against the authorised legend, inspect NoData edges, verify data type and check whether fractional values appeared in what should be an integer-labelled product.
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Suppose one classified map is reprojected using nearest neighbour while another is shifted half a pixel or resampled bilinearly and then rounded. The difference map may show changes generated by processing instead of genuine land conversion.
Before reporting forest loss or urban expansion, align coordinate reference systems, pixel grids, geographic footprints, class definitions, resampling methods and validation procedures. Even perfectly matched grids do not eliminate classifier uncertainty or true mixed-pixel ambiguity.
The related co-registration and false boundary change guide addresses the separate spatial-offset problem. Combining its checks with the correct categorical resampling rule prevents two common kinds of artificial change.
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Practice A: source codes are 1, 1, 5 and 9 at four symmetric corners. What does bilinear interpolation at the centre return? It gives 4, not an observed source class. Why is that unacceptable as a categorical result? Because category numbers do not encode a measurable continuum.
Practice B: an output location lies closest to the first forest cell. What does nearest neighbour produce? It copies 1 = Forest. Does that guarantee the entire output cell is forest? No; nearest neighbour samples a local label, not an area-fraction analysis.
Practice C: an output cell intentionally covers the four equal-area source cells. If asked for land-cover proportions, report 50% Forest, 25% Water, 25% Urban. If asked for one modal class, report Forest but explicitly acknowledge what the simplification discards.
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First inspect metadata and the class codebook. Define whether the raster is categorical, continuous or probabilistic. Preserve an untouched original and record the intended output grid, coordinate system, cell support and transformation. Choose nearest neighbour for ordinary categorical reprojection; choose a justified modal or area-fraction aggregation when deliberately changing support.
Second check the saved result rather than trusting visual appearance: list unique IDs, compare to the class legend, examine NoData, inspect class boundaries and quantify relevant area differences. Third verify alignment with any second-date raster before calculating change statistics.
The wider Gold Standard of Remote Sensing connects this category problem to image formation, resolution and interpretation. Its companion NDVI averaging example addresses a different mathematical trap: even continuous reflectance transformations cannot always be interchanged with spatial averaging.
Sources and connected reading
Class-coded examples are constructed for explanation. A real land-cover map must be interpreted using its own legend, pixel geometry, accuracy assessment and NoData conventions.