Fig. 6

Procedure for forming the APR in 3D. a 2D slice of exemplar dataset 10 (courtesy of Lemaire lab, CRBM (CNRS) and Hufnagel lab, EMBL^34,35). b First, the intensity gradient magnitude |∇I(y)| and c the Local Intensity Scale σ(y) are calculated from the input image. These two are then combined to compute the Local Resolution Estimate L(y) (d). e The Pulling Scheme (red arrow) uses L(y) to compute the optimal Implied Resolution Function R^*(y). f This is then used to define the Optimal Valid Particle Cell set \({\cal V}\) and the particle locations \({\cal P}\), which together form the APR. The APR is visualized both as particles with color encoding intensity and size encoding local resolution, and as a piecewise constant reconstruction \(\hat{I}({\mathbf{y}})\) of the image. Scale bar indicates 40 pixels