Choose your reading route
Choose a route or read from the beginning. All twelve chapters are open; the expandable index below groups navigation links only.
Find the distinction
Chapters 1–2. Find the difference between changed ground and shifted pixels.
State the model
Chapters 3–5. Define a fixed boundary, pixel footprints and an offset.
Calculate and check
Chapters 6–7. Calculate a false difference and test a reporting threshold.
Change the conditions
Chapters 8–10. Transfer the check to multispectral analysis and real movement.
Practise and continue
Chapters 11–12. Audit evidence, answer FAQs and explore the remote-sensing root.
Two satellite images of the same street, field or forest edge can disagree even when nothing on the ground changed. Before calling that disagreement a new event, check whether the pixels looked at the same place.
We use a transparent one-dimensional boundary example to isolate registration error from real spectral change. The simplification is deliberate: actual sensors also have point-spread functions, atmosphere, resampling and changing illumination.
Chapter index
Find the distinction · Chapters 1–2
1. The convincing change that never happened
2. Start with a precise reflectance model
State the model · Chapters 3–5
3. What co-registration must align
4. Read the two pixel footprints
5. Derive the false signal
Calculate and check · Chapters 6–7
6. A threshold cannot correct bad geometry
7. Vary the offset with the same unchanged ground
Change the conditions · Chapters 8–10
8. Carry the problem into NDVI and multispectral analysis
9. Build a trustworthy change-detection workflow
10. What if the boundary really moved?
Practise and continue · Chapters 11–12
11. Practical tests and frequent questions
12. Read outward from the example
CHAPTER 1 OF 12 · Find the distinction
1. The convincing change that never happened
Imagine a dark field immediately beside a bright paved area. On Monday a border pixel looks dark. On Friday it looks brighter. A change map may claim that pavement has invaded the field.
But a positional shift in the Friday image could move a portion of the bright paving into the same pixel index. The land remained fixed: the measurement footprint moved.
This is the difference between actual temporal change and apparent change caused by geometric misregistration. A neat map is not proof that two dates refer to the same ground footprint.
Place the stationary boundary at x=0. For x less than zero, surface reflectance is 0.20; at x equal to or greater than zero, reflectance is 0.80. These are illustrative dimensionless reflectance values at one wavelength.
Let pixels cover one unit of horizontal distance, with no atmosphere, noise, sensor drift or point-spread blur. Approximate a pixel as the area-weighted mean reflectance of its footprint.
At the first date, the left pixel covers [−1,0] and the next pixel covers [0,1]. Their measurements are 0.20 and 0.80. This is not an NDVI calculation; it is a single-band demonstration of footprint mixing.
Co-registration means placing two acquisitions into a common spatial reference so the pixels compared across dates correspond to the same ground area. It includes coordinate systems, geometric transforms and choices about resampling.
An offset of 0.20 pixel is small on a map overview but is one fifth of the footprint width. At a sharp edge, a fifth of a pixel can carry a great deal of contrast.
Our sign convention is explicit: a positive offset δ moves the second-date sampling footprint to the right relative to the first-date footprint; the underlying field-to-paving boundary stays at x=0.
With δ=+0.20, the original left pixel [−1,0] has second-date footprint [−0.8,+0.2]. Eight tenths now sample the dark side and two tenths the bright side.
The second-date left measurement is 0.8×0.20 + 0.2×0.80 = 0.32. A naïve index-to-index comparison reports +0.12 even though the surface reflectance function itself has not changed.
| Pixel index | Date 1 footprint | Date 2 footprint | Date 1 | Date 2 |
|---|---|---|---|---|
| Left | [−1,0] | [−0.8,+0.2] | 0.20 | 0.32 |
| Right | [0,1] | [+0.2,+1.2] | 0.80 | 0.80 |
For a rightward shift δ between zero and one pixel, the left pixel at the boundary contains fraction 1−δ of the dark side and fraction δ of the bright side.
Its second-date reflectance is R₂=(1−δ)×0.20+δ×0.80=0.20+0.60δ. Because the first-date value was 0.20, the apparent difference is ΔR=0.60δ.
At δ=0.20 the difference is 0.12. With a leftward shift, it is the right neighbour that acquires a dark fraction and shows a negative change. The sign and location of the artefact depend on which way the footprints move.
Suppose a change detector flags pixels whose absolute reflectance difference exceeds 0.10. Our unchanged land at δ=0.20 produces |ΔR|=0.12, so it becomes a false change report.
If someone raises the threshold to 0.20 to hide this one case, they may also erase small real changes elsewhere. Threshold adjustment is not a substitute for correcting and validating the geometry.
Look for edge-aligned positive or negative bands and test whether known stable features still match in the two images. The correct response begins with evidence about alignment.
CHAPTER 7 OF 12 · Calculate and check
7. Vary the offset with the same unchanged ground
Keep the reflectance contrast fixed at 0.60. Change only the offset δ. The false change scales linearly with the fraction of the bright side moved into the originally dark pixel in this simple model.
At δ=0.05, the apparent difference is 0.03. At δ=0.40 it is 0.24. Neither requires a bulldozer, fire or new crop; the underlying map of reflectance has been unchanged throughout.
| Positive offset δ (pixels) | Apparent ΔR | Flagged at |ΔR| > 0.10? |
|---|---|---|
| 0.00 | 0.00 | No |
| 0.05 | 0.03 | No |
| 0.20 | 0.12 | Yes — false change |
| 0.40 | 0.24 | Yes — false change |
CHAPTER 8 OF 12 · Change the conditions
8. Carry the problem into NDVI and multispectral analysis
Actual vegetation studies often compare red and near-infrared reflectance, or combine them into an index such as NDVI. Image registration must be checked for both bands and both dates, not just for the final colour rendering.
The index is nonlinear: an average of NDVI values generally differs from NDVI calculated from averaged red and near-infrared signals. Registration and spectral mixing can interact, so correcting geometry after making indices may not undo every artefact.
Read Why Averaging NDVI Differs from Averaging Reflectance for the separate averaging question. Do not treat that sibling example as the same error as positional misregistration.
CHAPTER 9 OF 12 · Change the conditions
9. Build a trustworthy change-detection workflow
Begin with compatible datasets: inspect sensor, acquisition geometry, georeferencing, acquisition dates, seasonal conditions, cloud and shadow masks, resolution and resampling history.
Select stable reference features or independent control points, estimate the transform, co-register or orthorectify as required, and quantify residual offsets. Report the registration error relative to pixel size and the landscape gradients that matter for this question.
Then compare radiometrically consistent inputs, test unchanged control areas and verify suspected changes with independent imagery, field records or higher-resolution evidence where possible. One global alignment statistic does not reveal every local deformation.
A genuine shoreline movement, flood front, harvest edge or building change can also look like an edge difference. Forcing both dates to have the same semantic boundary would risk erasing the real signal.
Registration uses stable coordinate evidence and sufficiently unchanged features, rather than assuming that all land-cover patterns must match. Keep the control transform and the actual change target conceptually separate.
Our area-average equation also ignores sensor point-spread blur, orthorectification error, terrain and viewpoint, spectral calibration and imperfect subpixel mixtures. Real operational methods must assess those effects.
CHAPTER 11 OF 12 · Practise and continue
11. Practical tests and frequent questions
Exercise: keep the dark and bright reflectances at 0.20 and 0.80, but reduce the offset from 0.20 to 0.05 pixel. The false difference becomes 0.60×0.05=0.03. Verify why a threshold of 0.10 no longer flags it, without assuming the imagery is now perfectly aligned.
FAQ: Does subpixel error mean harmless error? No, not at a sharp high-contrast boundary. Can an NDVI trend fix a positional problem? No, the index needs spatially comparable inputs. Does a sharp red-blue edge always mean misregistration? No, actual changes and other artefacts need investigation.
An audit-ready report documents the units, registration method, control points, residual statistics, radiometric consistency, decision threshold, false-positive checks and independent validation.
The Remote Sensing subject root connects satellites, sensors, spatial and spectral resolution, processing, field validation and map interpretation. Visit Cartography for a related discussion of what a map represents.
For methodology, consult Virginia Tech’s Landsat change-detection teaching chapter and the USGS Landsat documentation on terrain and geometric error. Published remote-sensing literature also documents spurious change caused by image misregistration.
The useful habit is not merely to compare values in two data files. First establish that they are measurements of the same place, scale and physical quantity.
Continue with the Remote Sensing root, The Gold Standard of Education and How X Works.
Sources checked 22 October 2026. Original numerical and abstract examples are teaching models with assumptions stated above.