Shape Template Matching: Rotation-Invariant Localisation Without Retraining

Template matching is the workhorse of industrial vision localisation. You have a reference image of a part; you want to find that part in a scene image, even if it has rotated or shifted. The classic approach — normalised cross-correlation (NCC) — breaks down the moment the part rotates more than a few degrees. VisionLab's shape-based matcher handles arbitrary rotation without any retraining.

Why NCC Fails Under Rotation

NCC computes pixel-by-pixel intensity similarity between template and scene patch. Rotation changes pixel intensities at every position, so a 30° rotation can drop NCC score from 0.95 to below threshold even on a perfect match.

The fix: match on gradient orientation rather than pixel intensity.

Gradient Orientation: What It Is

For each pixel in the template, compute the image gradient $(G_x, G_y)$ using Sobel filters. The orientation of that gradient:

\theta = \text{atan2}(G_y, G_x)

is a direction, not a magnitude. Crucially:

It is invariant to uniform illumination changes (brightness shift does not change gradient direction)
It rotates rigidly with the object — if the part rotates by $\alpha$ , every gradient orientation shifts by exactly $\alpha$

The Matching Score

At each candidate position and rotation hypothesis $(\Delta x, \Delta y, \alpha)$ , the matching score is:

S = \frac{1}{N} \sum_{i=1}^{N} \cos\bigl(\theta_i^{\text{scene}} - \theta_i^{\text{template}} - \alpha\bigr)

$\cos = 1$ when orientations align perfectly; $\cos = -1$ when they are anti-parallel. Summing over all $N$ template edge pixels gives a robust score in $[-1, 1]$ .

This is evaluated on a coarse rotation grid (e.g., every 1°) over the search range. The candidate with the highest score becomes the initial hypothesis.

Hierarchical Search (Image Pyramid)

Exhaustive search over all positions × all rotations is slow on full-resolution images. VisionLab uses a Gaussian image pyramid:

Level 2 (1/4 res): coarse search, large step → top-K candidates
Level 1 (1/2 res): refine top-K at finer step
Level 0 (full res): sub-pixel refinement of top-1

Typical speedup: 10–30× over brute-force full-resolution search.

Upstream for Defect Detection

Shape matching is not just a standalone tool — it is the upstream localization stage in VisionLab's Golden Template defect detection pipeline:

Scene image
    ↓
FitTemplateMatch → centre (x, y), angle θ, bounding rect
    ↓
warpAffine crop → aligned_crop (same pose as golden template)
    ↓
ECC sub-pixel alignment → pixel-level difference → defect regions

Without accurate localisation, the pixel-level diff would contain large alignment residuals that look like defects. Shape matching eliminates position and rotation error before the sensitive diff stage runs.

Practical Parameters

Parameter	Effect	Recommendation
`angle_range`	± search range (degrees)	Set to expected max rotation
`angle_step`	Rotation grid step	1° for precision; 3° for speed
`min_score`	Match threshold	0.7–0.85 for industrial parts
`pyramid_levels`	Search speed vs coverage	3 levels for large scenes

Robustness Comparison

Condition	NCC	Gradient Orientation
Illumination change	✗ Fails	✅ Robust
Rotation > 10°	✗ Fails	✅ Handles ±180°
Partial occlusion	Partial	✅ Score degrades gracefully
Texture-less metal	✅ OK	✅ OK (uses edges)