Crack horizontal growth measurement from image sequences

A crack can curve substantially while making little progress along the axis you care about. Measuring its skeleton length, fitting a straight line, and tracking its tip therefore answer different questions. This procedure is for image-sequence measurements where horizontal advance matters more than vertical movement. You will define the measurement, restore crop coordinates, calibrate physical distances, and check that apparent growth is not specimen motion or endpoint noise.

Define the measurement before processing images

Choose a horizontal axis tied to the specimen or test fixture, rather than assuming the camera's pixel rows represent that direction. If the specimen appears tilted, transform its coordinates into an aligned measurement frame first.

Let the fixed initiation point be P₀ and the selected crack tip in frame t be Pₜ. In calibrated coordinates, horizontal extent is their signed horizontal separation. Growth over an interval is the change in that extent.

These quantities are not interchangeable:

For a crack advancing leftward, signed extent becomes negative when positive X points right. You can reverse the reporting axis for that branch, but document the choice. Do not switch between signed displacement and absolute distance during processing.

1. Establish one coordinate system and a fixed origin

Set up the coordinate bookkeeping before adjusting segmentation:

1. Record the initiation point in the reference image, preferably using a physical feature that remains identifiable.
2. Define the horizontal reporting axis and its positive direction.
3. Record each crop's actual first-pixel offset and indexing convention.
4. Map every detected tip into the full image, then into the common measurement frame.
5. Store the transformed tip, origin, timestamp, and validity flag for every frame.

For an unscaled, axis-aligned crop using zero-based pixel indices:

Here, the offsets identify the crop's first pixel in the full image. Confirm your software's indexing convention rather than copying a crop rectangle directly into this formula. A one-based local coordinate requires the corresponding indexing adjustment.

Never measure positions from a side-by-side display of separate crops. Display placement introduces an artificial offset unrelated to the specimen.

If you resize or rotate a crop, retain its inverse transform. Restore detections to full-image coordinates before applying calibration. The guide to coordinate matching across exposures explains why detections need a shared coordinate frame.

The initiation point is a material location, not necessarily the current image center. If the camera or specimen moves, use stable reference features to map each frame back to the reference coordinate system. Avoid registering on the growing crack itself.

2. Calibrate distances in the measurement plane

A single millimeters-per-pixel scale is suitable when the inspected surface is planar, perspective effects are negligible, and magnification stays constant. Measure a known reference distance near the crack and in the same plane.

For example, a 10.00 mm reference spanning 500 pixels gives:

Use the same distortion correction and image transformations for both calibration and crack measurement. Calibration performed on a full-resolution image does not automatically apply to resized coordinates.

If the surface is viewed obliquely, transform image points into calibrated planar coordinates instead of applying one global scale. Compute horizontal separation after that transformation. The image-marker length calibration procedure covers establishing a physical measurement frame.

Check the calibration at several positions across the measurement region. Agreement near the origin does not establish accuracy near the final tip position. Out-of-plane specimen motion changes apparent magnification and can invalidate a planar measurement.

3. Isolate the connected crack without changing its tip

Segmentation should support a defined endpoint measurement, not merely produce a visually clean binary image. First check whether the crack appears darker or brighter than its surroundings. Select foreground polarity accordingly.

Restrict processing to a region that includes the expected path and enough margin for genuine movement. Use a seed region near the known initiation point to identify the relevant connected structure. A component selected only because it is largest may instead represent a scratch, boundary, or shadow.

Aggressive dilation can join unrelated marks or move the apparent terminal boundary. Removing all small components can also erase a faint, disconnected tip. Inspect the original grayscale image beside the mask before accepting either operation.

The crack segmentation guide addresses mask construction. For endpoint localization, use the edge endpoint detection procedure. Keep those operations separate from the growth calculation so you can test each independently.

A straight-line detector can help estimate orientation when the crack is nearly straight. It does not necessarily identify the physical tip, and its fitted line length should not replace horizontal displacement.

4. Calculate horizontal growth with a worked example

Assume the following coordinates already belong to a distortion-corrected, axis-aligned image frame. The scale is 0.0200 mm/pixel, and the fixed initiation point is at x = 1600 pixels, y = 900 pixels.

In the first measured frame, the crop starts at x = 1400 pixels. The local tip coordinate is x = 260 pixels:

In a later frame, the crop has moved. Its horizontal offset is 1500 pixels, and the local tip coordinate is 310 pixels:

Subtracting local crop coordinates alone would give 50 pixels, or 1.00 mm. That answer is wrong because it ignores the changed crop position.

Suppose the later tip is also at y = 970 pixels. Its displacement from the initiation point is 210 pixels horizontally and 70 pixels vertically:

The angle calculation reproduces the horizontal projection, but subtracting horizontal coordinates is simpler. A curved crack connecting the same endpoints would have a path length at least as large as the straight-line distance.

5. Track the same physical tip across frames

Sort images by acquisition order or recorded timestamps, not an unverified filename order. Keep the elapsed time with each measurement, especially when frames can be dropped.

Use the previous accepted tip as a prediction, not as an instruction to select whichever point lies farthest right. That extreme point could be noise, a secondary branch, or a neighboring defect. Associate candidates using connectivity to the tracked crack, local appearance, and a physically plausible displacement range.

For an illustrative tracking gate, suppose expected maximum horizontal tip speed is 2 mm/s, frame spacing is 0.05 s, and scale is 0.020 mm/pixel:

Add allowances for localization and registration uncertainty. Treat the gate as a review trigger rather than a way to force a desired growth rate. Sudden fracture may exceed the assumed speed.

Define branch handling in advance: follow a designated branch, follow a specified connected main path, or report branches separately. Do not silently change tip identity when a branch becomes longer.

When no credible tip is visible, mark the frame invalid. Do not report the crop boundary as an endpoint or hold the previous value without identifying it as missing data. The image-sequence tracking workflow covers maintaining associations across changing images.

6. Verify accuracy and reject false growth

Begin with a stationary specimen. Process repeated images through the complete pipeline, including registration and segmentation. Their spread estimates repeatability under those conditions, not absolute accuracy.

Check these failure modes separately:

• Origin drift: Overlay the reference origin after registration. Movement of a stationary reference should remain within your error allowance.
• Crop mistakes: Process the same image with two overlapping crops. Restored endpoint coordinates should agree within localization uncertainty.
• Threshold sensitivity: Vary segmentation settings over a reasonable range. Large tip shifts indicate unstable contrast or an ambiguous endpoint.
• Boundary clipping: Flag tips touching the processing boundary. Expand the region before accepting a terminal location.
• Focus changes: Check whether the endpoint moves as sharpness changes. Use the focus-metric guide to monitor image quality consistently.
• Incorrect physical scale: Measure independent known distances that were not used to establish calibration.

For a simple uncertainty estimate, assume independent horizontal tip and origin localization uncertainties of 0.8 pixels and 0.5 pixels:

This excludes scale error, residual distortion, registration error, and endpoint-definition bias. A shared fixed-origin error cancels when subtracting two extents in the same reference frame, but frame-specific registration errors do not necessarily cancel.

Avoid forcing a nondecreasing curve. Small negative changes can reveal noise; larger reversals can indicate tip reassignment, specimen movement, or loss of visibility.

7. Choose acquisition hardware around the error budget

Choose area scan cameras using required image width, exposure time, acquisition timing, and shutter behavior. Use the camera finder to narrow candidates after defining those requirements.

For example, a 40 mm horizontal field spanning 2000 pixels gives 40 / 2000 = 0.020 mm/pixel. A 0.06 mm feature then spans 3 pixels. That is a sampling check, not proof of reliable segmentation or tip localization. The dimensional-inspection resolution guide explains the distinction.

Select machine vision lenses to cover the required specimen region at the available working distance. Leave margin for movement and the final crack position, rather than filling the image with only the initial crack.

The LS-CMR-0053 is a rolling-shutter GigE area scan camera. Consider this type of acquisition for a stationary specimen or a test with controlled holds. For continuous motion, evaluate global-shutter alternatives and exposure duration rather than assuming all pixels represent the same instant.

The LS-FFL-0567 is a C-mount lens with a 16 mm focal length. It is a candidate to evaluate, not a guarantee of the required field coverage or measurement accuracy.

Check sensor coverage, mount compatibility, working distance, focus, and usable field sharpness before selecting a pair. Compare alternatives in the lens finder or begin with the lens configurator.

Checks before accepting the measurement

Use this release checklist before analyzing an entire sequence:

• The reporting axis, positive direction, and initiation point are documented.
• Horizontal extent and interval growth are stored as separate quantities.
• Crop offsets, resizing, and registration transforms are retained.
• Calibration applies to the actual measurement plane and processed coordinates.
• The chosen endpoint belongs to the intended crack branch.
• Missing tips and clipped regions generate explicit validity flags.
• Stationary-repeatability and independent-distance checks meet the error allowance.
• Original images and endpoint overlays remain available for review.

This method is not sufficient when a crack leaves the calibrated plane, becomes hidden, or develops branches without a defined selection rule. A sharper mask cannot resolve those measurement-definition problems.

For help choosing acquisition hardware, send your field of view, smallest relevant feature, expected tip speed, working distance, and allowable measurement error through applications support.