Coded Image

Coded image generation follows detection (thresholding, watershed, or deep learning). Once the binary mask of foreground pixels exists, connected component labeling assigns unique integer IDs:

1. Scan — The algorithm scans the binary mask row by row. At each foreground pixel, it examines already-visited neighbors.
2. Label — If no foreground neighbors exist, a new label is assigned. If one neighbor is foreground, its label is copied. If multiple differently-labeled neighbors are foreground, one label is chosen and an equivalence is recorded.
3. Resolve — After scanning, equivalences are resolved so that each connected component has a single unique label.

The result is a 32-bit integer image where pixel values range from 0 (background) to N (where N is the total number of detected objects). This image can be visualized with pseudo-color (each label mapped to a distinct color) for quality inspection.

Connected component labeling (CCL): The fundamental algorithm behind coded images comes from image topology. Two foreground pixels belong to the same object if and only if a path of foreground pixels connects them. The classic two-pass algorithm scans the image once to assign provisional labels and record equivalences, then scans again to replace provisional labels with their final equivalents. For an M×N image, this runs in O(M×N) time — linear in the number of pixels.

The connectivity dilemma: Consider two foreground pixels touching only at a diagonal corner. Are they the same object? In 4-connectivity, no — only orthogonal neighbors (up, down, left, right) count. In 8-connectivity, yes — diagonal neighbors also count. Neither answer is universally correct. For nuclear detection, 8-connectivity is typical because nuclei are roughly circular and diagonal adjacency usually indicates the same nucleus. For detecting thin structures like membranes, 4-connectivity may be more appropriate to avoid merging parallel structures.

Why integer labels, not colors? A coded image stores identity, not appearance. Using 32-bit integers allows up to ~4 billion unique labels per image — far more than enough for any tissue section. The integer representation enables direct lookup: "give me all measurements for object #47" is a simple equality test on the coded image. Colors would require collision-free color assignment and lossy matching.

From topology to biology: The coded image bridges the gap between "what does the tissue look like" (the fluorescence image) and "what does the tissue contain" (individual cells with measurements). This is conceptually similar to the difference between a photograph of a crowd and a census — both describe the same scene, but the census identifies each individual and tracks their attributes.

After Nuclei Detection runs on a DAPI-stained tissue section containing 12,000 cells:

• The coded image contains values from 0 (background) to 12,000
• Each nucleus's pixels carry its unique label (e.g., all pixels of nucleus #5,847 have value 5847)
• Standard Measurements reads this coded image plus the original fluorescence channels to compute per-nucleus area, mean intensity in each channel, shape descriptors, and centroid coordinates
• Phenotyping reads the same coded image to classify each nucleus based on its measured biomarker expression
• Spatial analysis reads centroids from the coded image to compute distances between cells, density maps, and neighborhood compositions

The coded image is the single source of truth for cell identity throughout the entire analysis pipeline.