Estimate edge position accuracy from image sampling

A row of closely packed thin disks can look easy to measure until the apparent boundaries shift with illumination or focus. For this task, camera resolution is only the first sizing decision. You also need a visible boundary that consistently represents the physical position you care about.

Start by converting field of view into millimeters per pixel. Then test whether the complete setup can locate representative boundaries within your required error. This approach separates insufficient image sampling from problems that additional pixels cannot solve, including hidden contact interfaces, unstable reflections, and calibration bias.

Define the boundary and the permitted error

Before choosing hardware, define what an edge position means. Is it the left face of each disk, the center of a visible seam, or the intersection between a disk face and an outer surface? These positions may differ, especially with chamfers, rounded edges, or compressed contact surfaces.

Write the requirement as a position and a tolerance relative to a physical reference. For example: locate each specified boundary within ±0.020 mm across the complete measurement region. Also state whether measurements happen with the disks stationary or moving.

Three quantities must remain separate:

• Sampling: the object-space distance represented by adjacent pixels.
• Repeatability: the spread when measuring an unchanged boundary repeatedly.
• Accuracy: agreement with an independent physical reference, including systematic error.

A system can repeat to a small fraction of a pixel while consistently reporting the wrong physical position. Conversely, a correctly calibrated system can still have excessive frame-to-frame variation.

For moving parts, the related guide to camera resolution and measurement accuracy in motion explains why exposure and motion must join the sampling calculation.

Calculate sampling along the measurement axis

Use the number of delivered image pixels along the direction in which you measure position. Total megapixels alone do not answer this question. A wide image and a square image can have similar pixel totals but different horizontal sampling.

These relationships assume the field width and pixel count describe the same image region. Cropping, binning, resizing, and geometric correction can change that relationship. Establish the scale for the image actually supplied to the measurement algorithm.

The guide to calculating object-space pixel size from magnification develops the same relationship from the optical side. Use it when sensor dimensions and magnification are known before the final field width.

The following examples are hypothetical image configurations, not specifications of the products discussed later.

Doubling the field width without increasing pixel count halves the sampling density. Reducing the field can therefore be more effective than changing the camera, provided every required boundary remains visible.

Work through a closely spaced disk example

Suppose the required field width is 40 mm, each disk is approximately 0.60 mm thick, and a visible seam feature is approximately 0.030 mm wide. Assume an image containing 4000 horizontal pixels.

The disk thickness occupies many pixels, but that does not establish whether its boundary is measurable. The much narrower seam and its intensity profile may control detection reliability.

For an initial feasibility screen, suppose you allocate three pixels across that visible feature. The required horizontal count becomes:

Three pixels is a trial allocation, not a universal accuracy rule. An isolated, high-contrast edge can support position fitting without resembling a three-pixel-wide line. Two closely spaced transitions, however, become difficult to separate when optical blur merges their profiles.

The requested ±0.020 mm error corresponds to ±2 pixels in this example. That is an allowance for the complete measurement chain, not permission for the edge detector alone to vary by that amount.

Even if a fitted edge repeats within 0.2 pixel, the corresponding 0.002 mm spread does not establish absolute accuracy. Calibration, mechanical movement, and the relationship between the visible seam and the physical boundary still matter.

Make the boundary visible before adding pixels

First inspect representative disks under controlled illumination. A physical contact interface is not necessarily an optical edge. Identical surfaces pressed together may provide too little visible contrast, regardless of camera resolution.

For surface boundaries, test illumination direction as deliberately as camera sampling. Grazing illumination can emphasize a small groove or step. More diffuse illumination can reduce unstable reflections, but may also suppress the relief that made the seam visible.

Compare candidate arrangements at the same exposure, gain, and aperture. Examine an intensity profile across the boundary, rather than judging only the displayed image. Look for a repeatable transition that remains identifiable across representative finishes and assembly conditions.

A diffused illumination candidate is LS-BAR-1276. Its suitability depends on the required coverage, mounting geometry, and measured contrast.

Browse bar lights and use the lighting finder to compare candidate arrangements. The explanation of lighting angles for surfaces and silhouettes helps distinguish reflection-based boundary detection from outline measurement.

A shadow edge also may not coincide with the physical interface. If its position changes when the illumination angle changes, investigate the geometry before using it as a measurement datum.

Choose the camera and optics together

Select area scan cameras by delivered image dimensions, shutter behavior, acquisition requirements, and image format. Use the camera finder after defining the required field and sampling.

Two acquisition candidates are LS-CMR-0166 and LS-CMR-0053. Both are listed with rolling shutters, so assess movement during capture before treating either as suitable.

All 2 share: Sensor size 1/1.7". Values as printed in each product's data sheet; open a part for its drawing and full specifications.

Rolling-shutter capture deserves particular attention if the disks or camera move during image acquisition. A stationary fixture is a different application from continuous conveyor measurement. More pixels do not correct motion-dependent geometry.

For color acquisition, inspect the processing path as well as the nominal pixel count. Demosaicing and sharpening can affect narrow transitions. The guide to color-camera spatial resolution beyond pixel count explains this distinction.

Choose machine vision lenses for sensor coverage, mount compatibility, working distance, field width, and usable edge detail. The lens finder helps narrow those constraints, but representative images must confirm performance across the measurement region.

An optical candidate to evaluate is LS-FFL-0567. Confirm its field coverage and focus range against your actual camera and installation geometry.

Do not assume these catalog candidates form a validated assembly. Confirm mechanical clearance, image-circle coverage, focus travel, and the required working distance before ordering.

If disk positions vary toward or away from the camera, perspective can alter apparent spacing. Telecentric optics may reduce magnification sensitivity, but they do not eliminate focus or calibration limits. The guide to validating telecentric measurement through depth describes the necessary checks.

Fit the edge without confusing precision and accuracy

Start with an intensity profile perpendicular to the expected boundary. For a reasonably straight seam, combine information over a short region along its length. This can reduce random variation, provided the region does not mix curved sections or neighboring boundaries.

A fixed binary threshold is a useful baseline, but its crossing position can move when brightness changes. Gradient-based or fitted edge methods can reduce sensitivity to some intensity changes. They still depend on contrast, blur, saturation, and the assumed profile shape.

Subpixel coordinates come from estimating a position between sampled values. They are not additional physical sensor samples. Reporting several decimal places does not demonstrate that the corresponding physical accuracy exists.

Use these checks when selecting a measurement method:

• Plot profiles from several disks, not just the cleanest example.
• Check whether neighboring transitions merge after optical blur or filtering.
• Disable sharpening and automatic contrast adjustments during the baseline evaluation.
• Keep measurement settings fixed while comparing illumination arrangements.
• Reject ambiguous or clipped profiles rather than forcing a position from every image.

Fit confidence, contrast, and profile width can become useful rejection criteria. Set their acceptance limits from representative good and difficult samples, rather than from a single reference image.

Validate against an independent reference

Use a representative fixture, actual disks, and a reference whose uncertainty is suitable for the required tolerance. The reference must describe the same physical boundary that the vision system reports.

For a ±0.020 mm requirement, a reference uncertainty around 0.005 mm may be a useful planning target. The appropriate value depends on the uncertainty budget and acceptance method; it is not a universal ratio.

A practical initial validation sequence is:

1. Calibrate the measurement plane. Use a suitable reference across the field, not only at the center. The guide to length measurement from image markers explains the scale-setting approach.
2. Measure five field positions. Include the center and positions near the limits of the intended measurement region.
3. Capture 30 images per position. This produces 5 × 30 = 150 images for an initial repeatability assessment.
4. Repeat at three allowed depth positions. Minimum, nominal, and maximum depth expand that initial set to 450 images.
5. Move the reference through fractional-pixel positions. With 0.010 mm/pixel sampling, a 0.002 mm displacement corresponds to 0.2 pixel. Use only movements your reference can establish reliably.
6. Repeat representative operating conditions. Include expected finish variation, disk contact conditions, lighting changes, and movement where applicable.

Suppose a hypothetical test gives a mean error of +0.012 mm and a standard deviation of 0.002 mm. The screening quantity 0.012 + 3 × 0.002 equals 0.018 mm. That may look promising against a ±0.020 mm requirement, but it leaves little room for reference uncertainty or untested variation.

This screening calculation is not a complete uncertainty budget or proof of a particular confidence level. Inspect individual errors, missed detections, and variation between conditions before accepting the system.

Use adequate reference coverage. Calibration target coverage and margins explains why a center-only calibration does not establish performance at the field edges.

Recognize when more resolution is the wrong answer

Additional pixels help when the optical image contains useful detail that the current sampling cannot represent adequately. They help much less when the limiting factor is something else.

A smaller field with multiple measurements may outperform one wide image, but only if the additional positioning and coordinate transfer are controlled. Likewise, averaging many frames reduces some random noise but cannot correct a consistently displaced shadow boundary.

If no visible transition tracks the required interface, change the viewing geometry, presentation, or measurement principle. Do not specify a larger camera simply because the disks are thin.

Check the setup before ordering

Use this checklist to turn a feasibility image into a hardware specification:

• Physical datum: identify exactly which disk surface or interface defines position.
• Tolerance: state maximum permitted error separately from repeatability.
• Coverage: include every required boundary and the expected placement variation.
• Sampling: calculate millimeters per pixel from the delivered image dimensions.
• Visibility: demonstrate stable contrast on representative contact interfaces.
• Optics: verify coverage, working distance, focus, and field-edge performance.
• Acquisition: check shutter behavior, exposure, triggering, and processing changes.
• Validation: compare with an independent reference across field, depth, and operating conditions.

Start the camera configuration process once those requirements are defined. If the seam itself remains uncertain, use application support to discuss sample images, the required field width, and the physical tolerance before selecting more resolution.