Does “Feret” always mean maximum diameter?

Not in every context. Some tools use it that way, while the general concept includes widths at specified orientations. Check the definition.

Is the maximum Feret diameter rotation-invariant?

For an ideal unchanged planar outline measured over all orientations, yes. Rasterization and segmentation can introduce practical differences.

Can it measure a concave shape?

Yes. Supporting-line measurements effectively reflect its convex hull, so they do not describe every indentation.

AI Glossary / Computer vision and multimodal AI / Beginner

Feret's diameter

Definition

Feret's diameter is a size measurement obtained from the separation of parallel lines that enclose an object's outline, like the jaws of a caliper. The separation depends on orientation. Maximum and minimum Feret diameters report the largest and smallest such widths across orientations.

What it means

An irregular particle does not have one obvious diameter in the way a perfect circle does. Feret measurements provide defined ways to describe its extent. They are useful for shapes such as grains, fragments and segmented objects in an image.

Terminology needs care. Some software uses “Feret's diameter” specifically for the maximum caliper diameter. Other descriptions discuss a Feret diameter at a specified angle. A measurement report should state which version it means.

These are measurements of the selected outline. A two-dimensional photograph usually provides a projected shape, not the object's complete three-dimensional dimensions. Its outline also depends on segmentation accuracy, image resolution and viewing direction.

How it works

Imagine placing two parallel supporting lines on opposite sides of an outline so that they just enclose it. Their perpendicular separation is the caliper width for that orientation. Rotate the pair to obtain widths in other directions.

The maximum over all orientations is the maximum Feret diameter. For a planar shape it corresponds to the greatest distance between points in its extent. The minimum is the narrowest enclosing strip width.

Algorithms commonly work with the shape's convex hull because indentations do not change these supporting-line widths. Pixel-based outlines introduce discretization choices, and physical-unit measurements require spatial calibration. The measurement method should also handle any unequal horizontal and vertical pixel scales appropriately.

Three practical examples

1. Particle analysis: A materials team compares maximum Feret diameters of segmented fragments to describe their projected size distribution.

2. Seed inspection: An image-analysis workflow records minimum and maximum caliper dimensions alongside area. These complementary measurements describe different aspects of the outline.

3. Quality monitoring: A manufacturer measures the extent of visible surface marks. The reported Feret diameter describes each selected mark's geometry, not automatically its depth, severity or cause.

Think of it this way

Think of sliding a pair of caliper jaws around a flat paper cutout while changing their angle. Different angles produce different readings, even though the cutout has not changed.

The analogy is close to the geometric definition, but an image-based measurement does not physically touch an object. It relies on the projected outline and calibration, so an inaccurate mask can give a precise-looking but inaccurate result.

Worked example

Take an ideal rectangular outline 4 millimeters wide and 3 millimeters high. Its horizontal extent is 4 millimeters and its vertical extent is 3 millimeters. The maximum Feret diameter is the corner-to-corner diagonal: the square root of 4² + 3², which is 5 millimeters.

The minimum Feret diameter is 3 millimeters, the separation of the closer pair of parallel sides. Therefore the maximum is not simply the longer side of this rectangle.

If the same outline was represented with a scale of 20 pixels per millimeter in both directions, its ideal dimensions would be 80 by 60 pixels and its diagonal 100 pixels. Real raster boundaries may produce slightly different estimates depending on how the outline is defined. Calibration should be checked before interpreting those pixel measurements physically.

Illustrative case study

Fictional case: Elm Materials compares fragments from two preparation methods. Its analyst initially labels a spreadsheet column “diameter” without identifying the measurement. A colleague assumes that it means the diameter of a circle with the same area, while the software actually reports maximum Feret diameter.

The team renames the column, records minimum Feret diameter separately and keeps the segmented outlines for inspection. It checks a calibration target and reviews touching particles that were accidentally merged. The resulting report is clearer about what has been measured. This is a teaching scenario, not evidence that one preparation method produces better fragments.

Common misconceptions and mistakes

Maximum Feret diameter is not generally the same as an equivalent-circle diameter, fitted-ellipse major axis or an image-axis bounding-box width. These measurements answer different geometric questions.

Minimum Feret diameter is not necessarily the width perpendicular to the maximum Feret direction. Its own orientation must be determined.

A long Feret measurement does not reveal internal shape details. Two outlines with different indentations can share the same convex hull and caliper widths.

The measurement is only as meaningful as the selected outline and calibration. Merged particles, cropped objects and perspective effects can change the interpretation even when the software calculation is correct.

Business use

Feret measurements help businesses compare irregular objects using reproducible geometric definitions. They are particularly useful when a simple width at a fixed image angle would change as objects rotate.

Reports should name the measurement variant, units, calibration and segmentation procedure. Include complementary statistics such as area or shape descriptors when the decision depends on more than overall extent. Avoid treating a two-dimensional projected measurement as a full three-dimensional specification without an appropriate measurement model.

Check your understanding

A 4-by-3 rectangle has a maximum Feret diameter of 5. Why is it not 4?

Answer: The maximum searches over orientations and corresponds to the largest separation of points on the outline. Opposite corners are 5 units apart, exceeding either side length. A fixed horizontal width would answer a different question.

Related terms

Convex hull
Image segmentation
Bounding box
caliper diameter
shape descriptor
equivalent diameter
spatial calibration

Learn next

Draw a rectangle and an irregular polygon, then estimate their caliper widths at several angles. Compare maximum Feret diameter with bounding-box width and equivalent-circle diameter. Finally, measure a calibrated sample image and inspect the outline that produced each reported number.

Bounding box

Sources

Primary documentation: ImageJ, Analyze menu and Set Measurements, https://imagej.net/ij/docs/menus/analyze.html . Its definitions of Feret, MinFeret and spatial calibration were reviewed. The rectangle calculation is an original geometric illustration; it does not specify every raster-boundary convention used by image-analysis software.

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