Spot-based image alignment

Note

New for version 0.4.4. More documentation planned.

Some microscopes will will have a shift (or translate) images slightly different when switching imaging channels (most likely dues to mirror alignments).

With deconwolf it is possible to estimate such shifts using detected dots, check out the CLI interface with:

dw align-dots --help

The program works by loading the dots from two files, we will denote those sets as \(X = \{X_i | i = 1, .., m\}\) and \(Y=\{Y_i | i = 1, ..., n\}\).

The method has the following steps:

  1. A KD-Tree is constructed, using all offsets, \(s_{ij} = X_i - Y_j\) where \(d(X_i,Y_j) < t_0\).

  2. A KDE consturcted with the points in the KDTree, with a fixed Gaussian kernel determined by parameter X.

  3. A grid search is carried out to find the approximate maxima of the KDE.

  4. Based on the rough location from the grid search, the position of the maxima is refined to give at least a few decimals points.

Analyzing the output

The first columns, contain dx, dy, and dz, which are the components of \(\Delta\). They describe how to shift second image to best overlap the first one. Units are in pixels.

The 4th column give \(kde(\Delta)\), the density of overlapping dots for the given shift. Depending on the input data this can be a high or low number. For an image with a single bead, a kde value of 1 would mean that the two beads were correctly shifted to overlap. For more complex images aim for a kde value of at least 3.

The goodness provides the contrast of the maxima, i.e. \(kde(\Delta)/kde(\gamma)\) where \(\gamma\) is the location having the 2nd higest kde value (\(d(\Delta,\gamma) > xxx\)).

Trouble shooting

Not that much should go wrong if this is used for the intended data. If the shifts are large (the program does not find it) try increasing the search radius for the initial pairing. This will cost more processing time and consume more memory. Also, if there are strong non-linear differences between the images, increasing the KDE sigma might increase robustness.

Going further

It is possible to manually tune the magnification and the rotation of the second point set but typically this kind of adjustments make little sense to do prior to the alignment. It is better to use this rigid shift alignment as the input for a more advanced correction model, like what is described elsewhere [1]. Ask for that to be be implemented or send a pull request!