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Fig. 10 | BMC Bioinformatics

Fig. 10

From: ATMAD: robust image analysis for Automatic Tissue MicroArray De-arraying

Fig. 10

Correspondence between the ideal grid and the observed distorted grid. At iteration m, the estimated deformation \(\mathcal {D}^{(m)}\) maps each point \(\mathbf {y}^{\star }_{\mathbf {p}}\) of the ideal square grid Λ (shown in square dots on the left) onto a point \(\mathbf {y}^{(m)}_{\mathbf {p}} = \mathcal {D}^{(m)} \big (\mathbf {y}^{(m)}_{\mathbf {p}}\big) \) in the warped grid Λ(m) (circled dots on the right) which fits the observed set of points \(\mathcal {X}_{0}\) (blue crosses). A position \(\mathbf {x}_{0, n} \in \mathcal {X}_{0}\) is associated to a position \(\mathbf {y}^{\star }_{\mathbf {p}}\) if x0,n is located within a radius δ from \(\mathbf {y}^{(m)}_{\mathbf {p}}\) (blue dotted circles). Associated positions are marked in red

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