Distance Maps

Take a mask of epithelium: white where epithelium is, black everywhere else. A Distance Map Outside writes into each black pixel how far it is to the nearest white pixel, so the epithelium is the zero reference and the numbers grow as you walk into the stroma. The three engines share that idea and differ in direction, storage and reach. All three sit in a layerLoading...'s Pre-Processing section, under Add Operations (advanced).

Distance Map Outside (global). Seeds is an 8-bit maskLoading... of the areas of interest. Distances are stored as 32-bit values and displayed with the Parula colormap, blue for short distances and red for long ones, so read exact values with the Pixel Inspector. The engine works across fields of view (FOVs), one FOV per iteration, up to Maximum iterations (default 7).

Distance Map Outside (local). It measures in the same direction but stores an 8-bit grayscale map, which the Engines Reference calls less accurate than the global variant. Distances above 255 are approximated with Max scaling. The reference warns that it is not suited to areas of interest one FOV apart.

Distance Map – inside (global). Events is a coded image, and each foreground pixel gets its distance to the closest background pixel: the inner distance from the event's contour. Values are highest deep inside large structures. It works on stitched, global objects and handles macrostructures spanning several FOVs, such as the glomeruli in the reference's kidney example.

Both global engines also take a Mask, and distances are computed only along paths inside its white areas. A path that must stay inside the white area cannot cut across what the mask leaves out, so you can measure distance within tissue instead of straight across an empty gap.

The distance transform. In image processing generally, a distance map is called a distance transform, and textbooks such as Gonzalez and Woods describe three common metrics. Euclidean distance is the straight line, with circular contours of equal distance; city-block distance follows the grid axes and draws diamonds; chessboard distance lets a diagonal step cost one and draws squares. StrataQuest's Accurate mode uses the Euclidean distance. The reference says only that Fast is an approximation; approximations built from small neighbor steps generally draw polygons instead of circles, which fits the hexagonal patterns it warns about.

Every buffer at once. Cut a Euclidean distance map at a value d and you get every pixel within d of the structure, the same set a dilationLoading... by a disk of radius d would give. One map holds every such buffer, so you can try a new distance without recomputing anything. Proximity AreasLoading... makes exactly these cuts, at a list of distances you give it.

Depth and shape. Inside a convex object the inner distance peaks at the center, and the peak equals the radius of the largest circle that fits inside. Where two objects touch, a saddle of lower values marks the neck between them, which is why the textbook watershedLoading... recipe floods an inverted inner distance map to split touching objects. StrataQuest's own Watershed (global) example uses a distance map computed with the membranes as reference as its Topographic Map, with the fat cell bodies as seeds.

Distance to a structure, not to a cell. A distance map measures from pixels to the nearest foreground structure. Cell-to-cell distances between two phenotypes, such as each tumor cell's nearest CD8+ T cell, come from Phenotype InteractionsLoading... and its Minimum Range, which the reference doesn't describe as using a distance map.

Pick the engine by direction first, then by reach: the global engines follow structures across fields of view and keep 32-bit values. Use Accurate when the distances will be measured or gated. Because the global maps are shown through a colormap, check a value with the Pixel Inspector rather than by its color. Derived MeasurementsLoading... notes that event distances are usually in pixels and converts them with the pixel size.

Source: StrataQuest 8.1 Engines Reference, ch. 13 (p. 404), ch. 14–16 (pp. 405–416), ch. 36 (pp. 500–503), ch. 41 (p. 538), ch. 43 (pp. 547–549).

Suppose you want to see how CD8+ T cells are distributed with distance from the epithelium in a colorectal cancer section.

1. Detect the epithelial area and make it a mask, as the Engines Reference does in its colorectal cancer example.
2. Add Distance Map Outside (global) with that mask as Seeds and Mode set to Accurate. Every stromal pixel now holds its distance from the nearest epithelium, and the epithelium reads zero.
3. In the layer that holds the CD8+ T cells, add Standard MeasurementsLoading... with the distance map as Shades and select Minimum. Each cell now carries the distance of its closest pixel to the epithelium.
4. Plot that measurement on a histogramLoading... and gateLoading... bands such as 0, 0–20, 20–50 and 50–100 µm. For fixed bands, Proximity AreasLoading... with Assign classes to objectsLoading... gives each cell its band number instead.

Bands differ in area, so compare densities rather than raw counts. In immuno-oncology generally, T cells concentrated inside and at the epithelium read as an inflamed pattern, cells held in the surrounding stroma as an excluded pattern, and few cells anywhere as a desert.