Fig. 3

Sparse search under 2D translation. The optimizer (fully described in Additional file 2: Section A.2) restricts the search space to all translations indicated by non-dark-blue grid points. a Search space under initial radius r=r ₀=8 and threshold ν _thresh=0.6 times the maximal intensity; (b) Search space after second iteration with r=4 and ν _thresh=0.6·0.5; (c) third iteration with r=2 and ν _thresh=0.6·0.5²; (d) final iteration with r=1, ν _thresh=0.6·0.5³. Panel (e) shows the complete score map of all possible translations. The efficiency of the optimizer results from the fact that only few points of the complete score map need to be evaluated. While in this example, the grid radius r is treated identical for all parameters of the transformation, we generally compute a separate radius for each parameter using self-registration based initial radius estimation