Image Stitching

Tiled-mosaic stitching: mosaic size and efficiency from the overlap, blend weights and seam gradient, and how tile position errors grow when chained versus after global optimisation.

Model: Textbook approximation

Mosaic size

2356 × 2356

5 × 5 = 25 tiles, overlap 51 × 51 px

Stitching efficiency

84.70 %

Mosaic pixels / acquired pixels

Worst tile, global optimisation

0.73 px

RMS over tiles 0.59 px, per axis

Worst tile, chained

1.41 px

σ√(C + R − 2); RMS over tiles 1.00 px

Grid columns CGrid rows ROverlap (% of the tile)Tile width (px)Tile height (px)Blend width (px, at most the overlap)Pairwise registration error σ (px, per axis)Gain mismatch between tiles (%)

Seam without blending

5.0 % step

A tile-to-tile gain mismatch shows as a sharp edge

Seam with blending, peak gradient

0.100 %/px

The same step spread over 50 px: weights sum to 1, so no bright or dark band

Blend weights across the seam

Worst-tile position error in an n × n grid

Key Formulas

Mosaic width: W = C·w − (C − 1)·round(o·w), and the same for the height with h

Efficiency: η = W·H / (C·R·w·h)

Blend: I = α·I_A + (1 − α)·I_B, α = 1 − t or cos²(πt/2), t ∈ [0, 1]

Chained: σ_ij = σ·√(i + j) for tile (i, j) placed from tile (0, 0)

Global: σ_ij = σ·√R_eff(00, ij), the effective resistance of the tile grid with unit edges

Each pair of neighbouring tiles is registered with an independent error σ per axis, and the first tile is the anchor. Chaining adds errors like a random walk; a global least-squares fit over all pairwise offsets (as in Preibisch's stitching plugin) has the variance of an electrical network, which grows only logarithmically with the grid size. The blend sum shows a gain mismatch spread across the blend; multiband blending is not modelled.

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

Mosaic geometry is exact. Neighbouring tiles are registered with independent errors σ per axis; a chain adds them as √(i + j), the global least-squares fit has variance σ²·R_eff, the effective resistance of the unit tile grid (computed exactly). Linear and cos² blends; multiband blending is not modelled.

Preibisch S., Saalfeld S., Tomancak P. (2009). Globally optimal stitching of tiled 3D microscopic image acquisitions. Bioinformatics 25(11), 1463–1465. Global optimisation of pairwise tile offsets. doi:10.1093/bioinformatics/btp184
Barooah P., Hespanha J. P. (2007). Estimation on graphs from relative measurements. IEEE Control Syst. Mag. 27(4), 57–74. Error covariance of the best linear estimate as an effective resistance. doi:10.1109/MCS.2007.384125

Report a problem

Related calculators

Image Registration

Rigid, similarity and affine registration: the transform matrix, RMS displacement over the image, control-point target registration error (Fitzpatrick) and the Cramér–Rao bound for intensity-based alignment.