Accuracy, Precision, and Limitations

A map can be precise-looking and inaccurate.

That sentence should sound familiar by now. Week 6 taught the same problem with sensors. Photogrammetry is another measurement system, so the same discipline applies.

Precision is not accuracy

Precision describes repeatability or numerical detail.

Accuracy describes closeness to an accepted reference or true value.

A model can report the same wrong coordinate repeatedly with impressive decimal places.

The decimals are precision of representation. They are not proof of accuracy.

Checkpoints give you error evidence

Suppose a project holds out four independent checkpoints.

The important idea is not the exact formula yet.

It is that an independent reference gives you a measurable residual between known and reconstructed position.

Without that comparison, your confidence comes mostly from internal appearance.

Error varies across a project

One average accuracy number can hide local weakness.

A project may be strong near well-distributed control and weaker:

• near edges;
• in low-overlap areas;
• around tall structures;
• where scene texture is poor;
• where control geometry is weak.

That is why you should inspect the spatial pattern of errors, not only one summary statistic.

RMSE is a summary, not magic

Mapping workflows often summarize checkpoint error using metrics such as root mean square error (RMSE).

Conceptually, RMSE gives larger errors extra influence because errors are squared before averaging and taking the square root.

You do not need to perform a professional accuracy certification here.

The lesson is:

A summary metric is useful only when you know which independent points produced it and whether those points represent the area you are making claims about.

Four checkpoints in one corner do not validate an entire complex site equally well.

Horizontal and vertical accuracy are different

A dataset can perform differently in plan position and elevation.

Do not collapse every error into “the map accuracy.”

For 3D products, reviewers may need to consider:

• horizontal position;
• vertical/elevation position;
• local shape consistency;
• surface noise;
• systematic tilt or bowing.

A product good enough for plan-view visual annotation may not be good enough for precise elevation comparison.

GSD sets sampling scale, not final error

Suppose your images have a nominal GSD of 2 cm/pixel.

That means each pixel samples roughly a 2 cm ground dimension under the modeled geometry.

It does not mean:

horizontal accuracy = 2 cm
vertical accuracy = 2 cm
measurement uncertainty = ±2 cm

Those claims require validation evidence.

GSD is one input to expected detail. It is not a substitute for checkpoint testing.

Bias creates directional error

Imagine all checkpoints are shifted about 0.25 m east.

That pattern suggests a systematic bias rather than random scatter.

Possible causes could include:

• georeference bias;
• incorrect control coordinates;
• coordinate-system problems;
• consistent camera-position error;
• processing/configuration issues.

The pattern tells you more than the average magnitude alone.

Outliers need investigation

Suppose seven checkpoints are within the expected project tolerance and one is far outside it.

Do not automatically delete the outlier because it makes the statistics ugly.

Investigate:

• was the checkpoint measured incorrectly?
• was it marked on the wrong image location?
• is it in a weak reconstruction area?
• does it reveal a real local distortion?

An outlier is evidence until you have a defensible reason to classify it as bad reference data.

Worked claim: area measurement

A fictional project measures a roof-damage polygon as 18.4 m².

The stakeholder asks:

Is that exact?

A strong answer is not yes/no.

You examine:

• checkpoint errors near the roof;
• pixel/detail scale;
• annotation boundary uncertainty;
• reconstruction quality in that zone;
• whether the roof surface is represented correctly.

Then you state an appropriate confidence level or limitation.

The annotation itself may introduce uncertainty even if the map geometry is strong.

Uncertainty has sources

Build an uncertainty budget conceptually.

Possible contributors include:

• reference-coordinate uncertainty;
• image geolocation;
• camera calibration;
• tie-point geometry;
• image blur;
• surface reconstruction;
• checkpoint distribution;
• human annotation;
• coordinate transformation.

You do not need to combine these mathematically in this course.

You do need to stop pretending only one source exists.

Write a limitation that actually limits the claim

Weak limitation:

Results may vary.

Stronger:

Absolute positional accuracy was evaluated only at the supplied checkpoints, which are sparse near the northeast roof edge; measurements in that region should be treated as approximate rather than high-precision survey evidence.

The stronger statement tells the stakeholder where and why confidence changes.

Build an accuracy review card

For a supplied project, record:

1. intended use;
2. reference/control method;
3. independent checkpoint count/distribution;
4. horizontal error pattern;
5. vertical error pattern if available;
6. local weak areas;
7. appropriate measurement precision;
8. one unsupported precision claim to reject;
9. one limitation statement.

Misconception: accuracy is one number printed by software

Software can calculate a statistic from the inputs it has.

The engineer still has to ask whether:

• the reference data is trustworthy;
• the checkpoints are independent;
• the distribution is representative;
• the metric matches the stakeholder question;
• local defects invalidate specific claims.

The measurement standard

A defensible mapping claim connects:

independent reference → observed error → spatial pattern → intended use → reported precision → limitation.

If one of those pieces is missing, the polished output should not be allowed to fill in the gap with confidence.