How the root anatomy pipeline works

A root is imaged as a cross-section, cropped, and split into four quadrants. Quadrants are the unit of segmentation; the root is the unit of analysis. Everything measured per quadrant is averaged back up to the root before any statistics are run, because quadrants from the same root are not independent samples.

Three separate networks do three different jobs. All are YOLOv8, fine-tuned from COCO-pretrained weights on hand-annotated root imagery, and all run on CPU at inference so the pipeline needs no GPU to process new images.

Training augmentation is deliberately conservative: hue is shifted by at most 0.02 and rotation by 5°, because these images have a meaningful orientation and a physically meaningful stain colour. Aggressive augmentation would teach the model to ignore exactly the cues that distinguish a cell wall from a lumen.

The cell segmenter uses the smallest backbone of the three. A larger model was not better here — cells are small, numerous and highly repetitive, and the nano backbone at high confidence gave cleaner masks with far faster inference over thousands of quadrants.

Input

Whole-slide microscopy image (PNG/JPG)

Output

Cropped root + four quadrant images, each with a metadata sidecar

A YOLO object detector locates root cross-sections in the slide image. Where several roots are detected, every one is cropped and saved, but only the highest-confidence detection is carried forward and split — this avoids partially-imaged roots at the frame edge entering the dataset.

The crop is halved on both axes into four quadrants, named by position: TL_, TR_, BL_, BR_. This prefix is load-bearing later: it tells the measurement stage which corner of the quadrant image is the root's centre.

Each quadrant is written alongside a JSON sidecar recording the original image, the crop bounding box in both pixels and µm, and the pixel-to-µm conversion in force — so any measurement can be traced back to its source region.

Input

One quadrant image

Output

One binary mask per cell, plus stele geometry

A YOLO instance-segmentation model proposes a mask for every cell. The confidence threshold is deliberately severe — 0.98 — because a false cell distorts both the area distribution and the file-boundary detection downstream, whereas a missed cell mostly costs sample size. Masks are then refined against local pixel intensity and cleaned with morphological opening and closing.

Three filters run in sequence:

• Inner-part exclusion. A second segmentation model marks the valid inner region of the root. Cells overlapping it by less than the threshold are discarded, removing epidermis, debris and background artefacts.
• Overlap removal. Where two masks overlap by more than 15%, the lower-confidence one is dropped — duplicate detections of the same cell.
• Largest-component retention. Fragmented masks collapse to their single largest connected component.

The same exclusion model supplies the two root-level geometry values — stele area and root radius — measured from its mask rather than from the cells.

Automatic segmentation fails occasionally — a torn section, a focus problem, a badly stained slide. Rather than let those propagate into the statistics, every newly processed image is reviewed before it joins the dataset.

The pipeline starts a local web server and opens a browser gallery of the new images with their detected cell centres drawn on. Each can be kept or rejected by eye; rejecting one deletes its measurement CSV and overlay so it never reaches the master summary. Review covers only new images — previously accepted ones are not re-litigated, which keeps the dataset stable as it grows.

A threshold-based automatic mode is also available, rejecting images outside a plausible cell count, but the results presented here were reviewed manually.

Input

Cell masks for a quadrant

Output

One row per cell: position, radius, angle, area, neighbours

Because each quadrant is one quarter of a circular cross-section, the root's centre lies at the quadrant's inner corner — the corner that was adjacent to the centre before splitting. That corner is inferred from the filename prefix. Every measurement is expressed relative to it.

For a cell with centroid (x, y) and a centre at (cx, cy):

Area is the mask's pixel count, converted to µm² by the squared pixel scale. Cell area and radius in µm are what everything downstream uses.

Each cell also records a local density and its adjacency list — masks are dilated slightly and any cells whose dilated masks touch are recorded as neighbours.

Input

All cells in a quadrant, with radius and area

Output

File count, and a file index per cell (0 = innermost)

Cortical cells are arranged in concentric files — rings running outward from the stele. Counting them by eye is slow and subjective, so they are detected from a signal in the data itself.

The idea. Within a single file, cells sit at a similar radius and a similar size, so plotting area against radius traces a locally smooth run. Crossing from one file into the next, cell size changes character and that run changes slope. Counting significant slope changes therefore counts the boundaries between files — and the number of files is one more than the number of boundaries.

The algorithm, step by step

1. Sort by radius. All cells in the quadrant are ordered by distance from the root centre, giving a sequence that walks outward from the stele.
2. Local slope. A window of 17 consecutive cells slides along that sequence. At each position a straight line is least-squares fitted to area against radius, and its slope is recorded against the window's mean radius. The window shrinks for small samples — never above one third of the cell count, never below 5.
3. Smooth. The resulting slope series is smoothed with a Savitzky–Golay filter (width ≤ 7, quadratic), which suppresses single-cell noise while preserving the position of genuine transitions — the property that matters here.
4. Differentiate again. Taking the first difference of the smoothed slopes gives a curvature signal: large values mark where the area–radius relationship is turning.
5. Threshold adaptively. A change counts as real when its magnitude exceeds 1.7 × the standard deviation of all changes in that quadrant. The threshold is per-image, so it adapts to noisy and clean images alike rather than assuming a fixed scale.
6. Enforce separation. Accepted changes must be at least 2 positions apart, preventing one broad transition from being counted several times.
7. Count. The file count is the number of accepted changes plus one, capped at 30. Quadrants with fewer than 15 cells are not analysed and return a single file.
8. Assign cells. With the count k known, one-dimensional k-means on radius alone partitions cells into k groups. Clusters are then relabelled in ascending mean radius, so file 0 is always the innermost.

Separating counting from assignment is deliberate. K-means needs to be told how many clusters to find and will happily split a uniform gradient into whatever number it is given; the derivative step supplies that number from the structure actually present in the image, so the clustering is constrained by evidence rather than by assumption.

An alternative counter — peak-finding on the empirical distribution of radii — is implemented and can be selected in configuration, but derivative is the method used for all results presented here.

Input

Cell areas and positions for a quadrant

Output

Six shape descriptors, on two different bases

Cell size is not constant across the cortex: it rises from the stele, peaks, then declines toward the epidermis — often with a small rise again at the very edge. That profile is the phenotype of interest, so it is fitted and reduced to six numbers.

Building the curve

Radius and area are each normalised to 0–1 within the quadrant, which removes absolute size so that curve shape can be compared between a large root and a small one. Cells are binned by radius, bin means are taken, and a cubic smoothing spline is fitted through them and evaluated on 200 points.

The six features

Writing ŷ for the fitted curve, p for the peak and m for the post-peak minimum:

The minimum is deliberately searched only after the peak. The decay slope is therefore measured from the peak to that minimum rather than to the curve's end — so it describes the decline itself and is not diluted by any recovery at the epidermis, which the outer-rise magnitude captures separately.

Two bases

Every feature is computed twice, against two different x-axes:

• radius_* — x is the cell's normalised radial position. Uses every cell independently of file detection.
• file_* — x is the normalised cell-file index, using the mean area of each file. Depends on stage 4 having found enough files.

The two answer different questions — one about distance, one about developmental order — and they are reported separately throughout.

Quadrant filenames carry their root's identity: stripping the TL_/TR_/ BL_/BR_ prefix yields a root identifier shared by all four. Every per-quadrant measurement is averaged across whichever quadrants are available to give one row per root.

This matters statistically. Four quadrants of one root are four views of the same organism, not four independent observations; treating them as independent inflates the effective sample size and shrinks p-values artificially. All models are therefore fitted at root level — 1,285 rows rather than 4,511.

Group comparisons

Differences between root types and between water treatments are tested with one-way ANOVA at root level, with effect size reported as η² — the proportion of variance the factor explains. Where ANOVA is significant, Tukey HSD gives all pairwise comparisons with family-wise error controlled at 0.05, so multiple comparisons do not inflate the false-positive rate. A Kruskal–Wallis test is computed alongside as a non-parametric check.

Curve comparisons

To compare profile shape between groups, all binned points from a group are pooled and a single curve is fitted to them — both a cubic polynomial (reporting R², peak and minimum) and the same smoothing spline used per-root. This is done by root type, treatment, species, and population.

Mixed-effects models

Two questions need plant identity accounted for, since several roots may come from one plant:

The first asks whether a shape feature is merely a by-product of root size; the second partitions the remaining variance across experimental factors. Plant enters as a random intercept; where the mixed model fails to converge, an OLS fit is reported and flagged as such.

Everything above treats a cell as a point at a radius. But cells are packed against each other, and which cells touch which is itself anatomy. Every cell therefore also carries an adjacency list.

Building the graph

Adjacency is measured from the masks, not from centroid distance — two cells are neighbours if their masks touch when slightly dilated. This is stricter and more meaningful than a distance cutoff: cells that merely lie near each other across a gap are not counted, while genuinely abutting cells are, regardless of their size.

Each cell stores the IDs of its neighbours and its degree — the number of cells it touches. In a perfectly regular tissue every interior cell would have six; departures from that are what the analysis looks at.

Tracing a path to the stele

The graph supports a question the radial coordinate cannot answer: how many cells do you cross walking from the epidermis to the stele, and how far is it in µm?

1. Pick a sample angle and take the cells lying within a tolerance of it.
2. Start at the outermost of those — the cell with the largest radius.
3. Step to whichever unvisited neighbour has the smallest radius, i.e. move inward through actual cell contacts rather than in a straight line.
4. Repeat until no neighbour lies closer to the centre. That is the stele boundary.
5. Record the path: how many cells it crossed, and the summed physical distance between consecutive centroids in µm.

Because the walk is greedy and forbids revisiting, it terminates at a local radial minimum — which in a well-segmented cortex is the innermost cell file. Paths are drawn back onto the image so a wrong turn is visible rather than silent.

Degree against size

Two relationships are then plotted across the whole dataset: degree against radial position, and degree against cell area. Both are computed raw, binned (20 bins), and as a rolling average (50-cell window), with normalised variants so that roots of different absolute size can be overlaid. The question is whether larger cells systematically touch more neighbours, or whether contact number is set by position in the cortex instead.

Cell centres are binned onto a polar grid — radial bins by angular bins — and each cell is given a local density from the number of cells within a fixed radius of it. That grid supports three views: a polar projection map, a radial profile (density against distance from the centre) and an angular profile (density against direction).

The angular profile matters because a quadrant is a quarter of a circle: if segmentation were failing on one side, the angular profile would show it as a dip rather than hiding it in a whole-image average.

The grid also drives air pocket detection. Regions in the lowest density decile that also sit in the highest cell-area decile are flagged — the signature of intercellular space, where few, large cells occupy a region that should be densely packed. In maize this is how aerenchyma would present.

The six spline features are chosen by hand, which risks describing what was expected rather than what is there. Functional PCA is the check on that. Every root's normalised curve is resampled onto a common grid and treated as a single observation — a whole function, not a set of summary numbers — and PCA is run over those functions.

The output is a set of principal component functions: the dominant ways curves actually vary across the dataset, ranked by how much variance each explains, plus a score per root on each component. If the leading components look like "peak moves outward" and "peak gets taller", the hand-picked features are capturing the real axes of variation. If they look like something else, the feature set is missing something.

Once cells carry a file index, the simplest possible summary is the mean cell area of each file, plotted against file number — a profile that needs no spline and no normalisation. These are produced per image, pooled across the dataset, and normalised so roots with different file counts can be overlaid and compared by group.

This is the most direct view of the phenomenon the whole project is about, and it serves as a sanity check on the fitted curves: the spline is meant to be a smooth description of exactly this, so where the two disagree, the spline is over-smoothing.

A companion regression asks whether file number predicts cell size within a root, and whether the strength of that relationship differs between groups.

A relationship fitted across the whole dataset can be produced entirely by group differences — Simpson's paradox, where a trend that holds overall reverses within every subgroup. The stratified analysis guards against that by refitting the same relationships separately within each treatment, root type and population, and comparing coefficients across strata.

Interaction plots complement this by showing group means for one factor split by another, so a treatment effect that exists only in one root type is visible rather than averaged away. A two-way ANOVA with an interaction term tests the same thing formally.

A separate track fits a single normalised pattern across all images and asks how far each individual departs from it, rather than describing each root independently. Cells are sampled along fixed angles, splines are fitted to those samples, and a cubic model of the pooled data supplies the reference. A clustered variant groups roots first and fits one pattern per cluster, testing whether the dataset is better described by several distinct patterns than by one.

A practical question follows from the anatomy: if measuring a whole root is expensive, which cheap measurements predict the rest? Candidate predictors are drawn from measurements obtainable without the full spline pipeline — first, last and middle cell-file areas, their ratio, overall mean cell area, and total cell count.

An exhaustive search evaluates every combination of one, two or three of those predictors against every target, fitting polynomial regressions (degree 1–3 for single predictors, 1–2 for combinations) on a fixed 75/25 train–test split, and ranks by test R². Geometry is deliberately barred from the predictor pool so that no target is predicted from another geometry measurement — which would report a near-perfect score that reflects a definition rather than a discovery.

The headline result is that cell count predicts file count well, size predicts size well, but the six shape features remain only weakly predictable from any small combination tested — with peak height essentially unpredictable throughout. That is a genuine finding about the anatomy rather than a limitation of the search, which covered every combination available.

The six shape features define a normalised curve, and that curve can be inverted back into a cross-section: absolute cell area per file, a radial thickness per ring, and a cell count per ring. An interactive tool reconstructs any root from its features, which serves as a check that the features capture what they claim to — if a reconstruction from six numbers resembles the original image, little has been lost.

Curve reconstruction uses monotone cubic (Fritsch–Carlson) interpolation between the anchor points implied by the features, chosen because it cannot overshoot — an overshoot would move the peak or minimum away from the values being reconstructed.

Export for structural testing

To test whether the observed arrangement is structural, reconstructions are exported as 3D solids. Two different solids serve two different purposes:

• Display model — each cell as a solid pillar on a base disc. Legible as an object, but not valid for analysis: the base carries load in parallel with the pattern, and the pillars never touch.
• Analysis model — the cortex solid with cell lumens subtracted as voids, from a Voronoi tessellation of the cell centres. Neighbouring cells share walls, load transfers between them as in real tissue, and the material is self-connecting, so no artificial base is needed.

Both extrude to three times the mean cell diameter. Control geometries — uniform cell size, or randomised positions, each matched to the same relative density — are generated by the same code path, so a comparison against them isolates the pattern rather than the porosity.

Incremental, append-only processing

Every stage checks what already exists and processes only what is new. The master summary is appended to, never rebuilt, and existing rows keep their original species and population — so adding a new species cannot silently relabel an old one. Rebuilding from scratch is possible but requires an explicit flag, because it would overwrite exactly that history.

Hand-annotation import

Where the segmentation model does not transfer to a species, cells are annotated manually in Roboflow and exported as COCO polygons. An importer rasterises those polygons and writes the identical measurement format the model path produces — same columns, same plant-centre convention, same neighbour graph — so hand-annotated images are analysed by exactly the same code and are not a parallel path with its own quirks.

• Species imbalance. Maize dominates at 1,615 of 1,708 roots. Cross-species statements rest on 66 pearl millet, 19 tomato and 8 sorghum roots and should be read as indicative.
• Tomato geometry. Hand-segmented images have no stele or root-radius measurement, so tomato is absent from those analyses by construction. Its cell files are also few — the file-based shape features are computable for only a small minority of tomato roots, while the radius-based features are complete.
• Wall thickness in structural models. Cell wall thickness is not measured from the images — it is set as a parameter, either to a chosen relative density or to a supplied value. Structural results are therefore comparative between geometries, not absolute stiffness figures.
• Detector transfer. Segmentation is trained on maize and does not transfer to all species; where it fails, cells are hand-annotated instead, which is accurate but limits throughput.