Fourier correlation function for spatial resolution estimation of 2D/3D digital rock images

# FRC/FSC Resolution UI Desktop UI for estimating effective image resolution of 2D/3D digital rock images from Fourier RingCorrelation (FRC) and Fourier Shell Correlation (FSC) curves. The tool is intended for image-quality and spatial-resolution checks where theimportant question is not only nominal pixel or voxel size, but the smalleststructural features that can be reliably distinguished in the reconstructedimage or volume. ## Contents - `FRC_FSC_UI/` - runnable Windows/Python application.- `FRC_FSC_UI/frc_fsc_ui.py` - Tkinter desktop interface.- `FRC_FSC_UI/frc_fsc_core.py` - FRC/FSC loading, preprocessing, correlation, threshold, and CSV-export logic.- `FRC_FSC_UI/run_frc_fsc_ui.ps1` - PowerShell launcher.- `FRC_FSC_UI/Start FRC-FSC UI.cmd` - double-click Windows launcher.- `FRC_FSC_UI/README_FRC_FSC_UI.md` - shorter usage note included with the app.- `FRC_FSC_UI.zip` - packaged copy of the app folder. ## Requirements The application needs: - Python 3- `numpy`- `Pillow`- `tkinter` On most standard Python installations, `tkinter` is included. The launcher firsttries the bundled Codex Python runtime at: ```text%USERPROFILE%\.cache\codex-runtimes\codex-primary-runtime\dependencies\python\python.exe``` If that is not available, it falls back to `python` on your system `PATH`. ## Launch From the app folder: ```powershellcd ".\FRC_FSC_UI".\run_frc_fsc_ui.ps1``` Or double-click: ```textFRC_FSC_UI\Start FRC-FSC UI.cmd``` You can also run the UI directly: ```powershellcd ".\FRC_FSC_UI"python frc_fsc_ui.py``` ## Supported inputs The UI can load: - common 2D image formats: `.png`, `.jpg`, `.jpeg`, `.bmp`, `.tif`, `.tiff`- multi-page TIFF volumes- NumPy arrays: `.npy`- NumPy archive files: `.npz` For `.npz` files, the first array in the archive is used. ## Analysis modes - `1-FRC (single 2D image)` - splits one 2D image into two stochastic half-images before FRC calculation.- `Cross-FRC / 2-FRC (two 2D images)` - computes FRC between two loaded 2D images, or between selected slices from two loaded 3D volumes.- `1-FSC (single 3D volume)` - splits one 3D volume into two stochastic half-volumes before FSC calculation.- `3D FSC (two 3D volumes)` - computes FSC between two loaded 3D volumes. Available threshold criteria: - `1/7`- `one-bit`- `half-bit` ## Main controls - `Pixel/voxel size` - optional physical sampling interval. If provided, the result is reported both in pixels/voxels and in physical units.- `2D slice index` - slice to use when a 3D volume is loaded for a 2D FRC mode. If left blank, the middle slice is used.- `Crop size` - optional center crop size. Useful for large volumes or for comparing same-sized regions.- `Center crop to square/cube` - forces 2D images to square crops and 3D volumes to cube crops.- `Apply Tukey window` - applies a Tukey window before Fourier correlation.- `Radial bins` - optional number of frequency bins. If blank, the app uses half of the smallest input dimension.- `Min samples 2D` / `Min samples 3D` - minimum number of Fourier samples required for a valid radial bin.- `Consecutive bins` - number of consecutive below-threshold bins required to call the resolution crossing.- `Smooth window` - optional moving-average smoothing width used for crossing detection.- `Split seed` - random seed for the single-image or single-volume split modes. ## Outputs After computation, the UI reports: - threshold crossing frequency- estimated resolution in pixels or voxels- optional physical resolution if pixel/voxel size was entered- FRC/FSC curve plot- input/split preview images Use `Save curve CSV` to export: ```textfrequency, correlation, threshold, n_fourier_samples``` ## Notes and limitations - Pairwise FRC/FSC modes require matching processed array shapes. If the input dimensions differ, use the crop controls to compare same-sized regions.- The resolution estimate is based on the first accepted crossing of the correlation curve below the selected threshold.- Pixel or voxel size is a sampling interval. The FRC/FSC estimate is better interpreted as an effective feature-resolution measure for the processed image or volume.- Very large 3D volumes can be memory-intensive. Use `Crop size` before running full 3D FSC on large datasets.