centerline-svg 0.1.0

Trace the centerline (medial axis) of a solid shape in a PNG and emit an SVG. Pure standard library.

Centerline Extraction (Medial Axis → SVG)

Turn each PNG (a single solid black shape, 1024×1024, white background) into an SVG whose <path> elements follow the centerline (medial axis / skeleton) of the shape — the "pen stroke" a person would draw — instead of tracing its outer contour.

Example: a letter H drawn with a thick stroke should come out as three thin stroked paths (two vertical, one horizontal) joined at the two intersections.

• Sample inputs: challenge_sample/*.png (ampersand, arrow-pointer, arrow-turn-down-left, letter_H, letter_K, number_3, number_6)
• Reference outputs: challenge_sample_results/*.svg
• Constraint: no third-party libraries — everything from PNG decoding to the skeleton is hand-written (the packaged library depends on nothing but the Python standard library).

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Install & use

Packaged as centerline-svg (pure stdlib, no runtime dependencies).

pip install centerline-svg          # from PyPI (see PUBLISHING.md for TestPyPI)

As a library — input is an image (path or bytes), output is an SVG string:

import centerline_svg

svg = centerline_svg.png_to_svg("arrow.png")                 # from a path
svg = centerline_svg.png_to_svg(open("arrow.png", "rb").read())  # from bytes

# optional debug flag: also dump one PNG per pipeline stage
svg = centerline_svg.png_to_svg("arrow.png", steps_dir="steps/")

Command line:

centerline-svg in.png out.svg                 # one file
centerline-svg in_dir/ out_dir/               # batch a folder
centerline-svg in.png out.svg --steps steps/  # + per-stage debug PNGs

Web demo (upload a PNG, get the SVG back) — see webapp/:

pip install -r webapp/requirements.txt && pip install -e .
uvicorn webapp.app:app --reload      # open http://127.0.0.1:8000

Deploy the demo to Railway straight from this source (the Dockerfile does pip install ., so no PyPI publish is needed):

railway init --name pictographic     # create + link a project
railway up -c -y                     # upload current dir, build the Dockerfile, deploy
railway domain                       # get a public URL

Layout:

src/centerline_svg/
├── core.py     # the algorithm + fluent Pipeline (input image → output SVG)
├── render.py   # OPTIONAL step visualization (enabled only via steps_dir / --steps)
├── __init__.py # png_to_svg(...) public API
└── cli.py      # console entry point
webapp/app.py   # FastAPI upload-and-convert demo

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0. What the data tells us (read before coding)

Dissecting challenge_sample_results/letter_H.svg (11 <path> elements) shows the reference is a classic thinning skeleton, split into graph edges, each edge emitted as one densely-sampled polyline:

• Only M + L commands (polylines) — no Béziers, no smoothing, no simplification.
• 5 long paths = the 5 main branches (two left verticals, two right verticals, one horizontal bar).
• 6 short paths (2 points each) = "stubs" connecting each branch tip to the exact junction node at (177,516) and (847,516).
• Attributes: stroke-width="45", stroke-linecap="round", stroke-linejoin="round", fill="none".

Consequences for the approach:

1. Go with thinning skeleton + graph tracing, no curve fitting needed. To match the reference, emitting the skeleton pixel chains directly as polylines is enough.
2. The hint's "contour + perpendiculars + midpoints" method only works for single strokes and breaks at intersections — which is exactly what the challenge grades ("intersections preserve the right topology"). Skip it.
3. All 7 PNGs are RGB 8-bit, no alpha → mask = luminance < 128.

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1. High-level architecture

PNG ─►① binary mask ─►② thinning (Zhang–Suen) ─►②b cleanup ─►③ pixels → graph ─►④ trace + prune ─►⑤ emit SVG
                                                                     ▲
                                             (aux) distance transform: stroke width + prune threshold

Language: pure Python, standard library only (zlib, struct, math, sys). One file (centerline.py), one function per step. Run:

python3 centerline.py in.png out.svg            # one file
python3 centerline.py in_dir/ out_dir/          # whole folder

Runtime ≈ 5 s per 1024² image (the distance transform and the byte-level PNG de-filter are the costs of staying pure-stdlib).

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2. SEQUENCE FLOW — step by step

Each step lists: In → Do → Out → Check. Verify each step before moving on.

Step 1 — Decode PNG into a pixel array (hand-written, using zlib)

• In: path to a .png file.
• Do:
  1. Verify the 8-byte signature 89 50 4E 47 0D 0A 1A 0A.
  2. Walk the chunks [len(4) | type(4) | data(len) | crc(4)]. Read IHDR for width, height, bit_depth, color_type. Concatenate all IDAT data.
  3. zlib.decompress(idat) → decompressed byte stream = the scanlines, each scanline is 1 leading filter-type byte + width × bytes_per_pixel data bytes.
  4. Undo the filters per scanline (the most error-prone part): for each byte x, recover raw per the 5 filter types:
     • 0 None: raw = x
     • 1 Sub: raw = x + raw[a] (a = left pixel)
     • 2 Up: raw = x + raw[b] (b = pixel above)
     • 3 Average: raw = x + (raw[a] + raw[b]) // 2
     • 4 Paeth: raw = x + paeth(a, b, c) (c = upper-left); all mod 256.
  5. Extract RGB channels (color_type=2 → 3 bytes/pixel).
• Out: read_png(path) -> (w, h, pixels) where pixels[y][x] = (r,g,b).
• Check: print w,h = 1024×1024; count dark pixels, expect ~10–30% coverage.
• Note: Paeth predictor: p = a+b-c; pa=|p-a|; pb=|p-b|; pc=|p-c|; return a if pa≤pb and pa≤pc, else b if pb≤pc, else c.

Step 2 — Threshold into a binary mask

• In: pixels.
• Do: mask[y][x] = 1 if 0.299r + 0.587g + 0.114b < 128 (black = foreground), else 0. Pad the mask with a 1-px border of 0 so neighborhood steps never touch the edge.
• Out: mask (2D array of 0/1).
• Check: dump the mask to a PNG/ASCII-art and confirm it matches the shape.

Step 3 — Thinning (Zhang–Suen) → 1-px skeleton

• In: mask.
• Do: iterate until a full pass deletes nothing. Each pass has two sub-iterations:
  • For each foreground pixel P, look at its 8 neighbors P2..P9 (P2 = North, going clockwise).
  • B(P) = number of foreground neighbors; A(P) = number of 0→1 transitions going around P2,P3,…,P9,P2.
  • Sub-iteration 1 marks P for deletion if: 2≤B≤6 and A=1 and P2·P4·P6=0 and P4·P6·P8=0.
  • Sub-iteration 2: 2≤B≤6 and A=1 and P2·P4·P8=0 and P2·P6·P8=0.
  • Within a sub-iteration: evaluate conditions on the old image, delete all marked pixels at the end (never delete in place).
• Out: skel — a mask that is exactly 1 px wide.
• Check: body pixels have ≤2 neighbors; the shape stays connected and holes are preserved (the 6 and the loop of the & still enclose a hole).
• Why it works: see section 3.

Step 3b — Cleanup: remove redundant "staircase" pixels

• In: skel.
• Do: Zhang–Suen leaves 2-px staircase artifacts on diagonal/curved strokes (a smooth run where some pixels have 3–4 raw neighbors). Left alone, Step 4 reads each of those as a junction and shatters the stroke into hundreds of 2-px paths. Remove a pixel P when it is redundant: it has ≥2 neighbors (not an endpoint), its crossing number ≤ 2 (not a real junction), and its foreground neighbors are still 8-connected without it (removing it can't disconnect anything). Iterate to a fixed point. Straight and clean-diagonal line pixels have two non-adjacent neighbor groups, so they are kept.
• Out: a clean skeleton where body pixels really do have degree 2.
• Check: branch count drops from hundreds to a handful (see Results).
• This is the single most important fix for real inputs — see "Bugs / gotchas" below.

Step 4 — Turn the skeleton into a graph

• In: skel.
• Do:
  1. For each skeleton pixel, count its skeleton neighbors (8-connected) = its degree.
  2. Classify: endpoint (degree 1), junction (degree ≥3), body (degree 2).
  3. Merge touching junction pixels into one junction node (take the centroid) to avoid fragmentation.
• Out: the set of special nodes (endpoints + junctions).
• Check: H has 4 endpoints + 2 junctions; the 6 has 1 endpoint + 1 junction + 1 loop.

Step 5 — Trace the branches (graph edges)

• In: skel + the node set.
• Do: from each node, walk along the chain of degree-2 pixels (marking visited) until you hit the next special node → that chain is one branch polyline. Handle:
  • Pure loop (a cycle with no special node, e.g. a circle): pick any pixel as the opening point and trace the loop back to itself.
  • Snap each branch tip to the junction centroid so strokes meet at a single point (like the "stubs" in the reference) → round joins make them merge cleanly.
• Out: a list of polylines (lists of (x,y) points).
• Check: branch count is roughly the reference path count (H≈11, K≈13, &≈18).

Step 6 — Prune spurs + estimate stroke width

• In: the branch list + (aux) distance transform.
• Do:
  • Distance transform (DT): distance to the background for each foreground pixel via a two-pass chamfer (one top-left→bottom-right pass, one reverse). Use it to: estimate stroke width W ≈ 2 × median(DT along the skeleton), and to threshold spur pruning.
  • Prune spurs: delete any branch that ends at an endpoint and is shorter than ~the stroke radius (spurs created by thinning at corners/rounded ends). Be careful not to prune a genuinely short stroke.
• Out: cleaned branch list + W.
• Check: tiny stub branches are gone; the main strokes are intact.

Step 6b — Straighten & smooth (fixing where the medial axis is systematically wrong)

The raw skeleton is topologically right but geometrically wrong in three places, all visible on the arrows. Each gets a targeted fix in Pipeline.smooth():

1. Straight strokes bend at their ends. Near an end cap that isn't cut perpendicular to the stroke, and near any junction, the medial axis hooks sideways (that's what the distance-transform ridge really does there). So a chord through the branch endpoints is rotated off the true axis. Fix (_fit_straight): fit a total-least-squares line to the stable interior only (points ≥ ~1 stroke width of arc length away from both ends), and accept the branch as "straight" only if every interior point is within ~3 px of that line. Then project the endpoints onto the fitted line — the bent tails can no longer tilt the stroke. Curves and L-shaped branches fail the tolerance and skip this.
2. The junction pixel isn't where the strokes actually cross. Thinning leaves the node wherever peeling happened to converge. Fix (_lsq_node): re-solve each junction as the least-squares intersection of the fitted axes of its straight arms, then snap every arm's end to that node — all arms meet, dead straight, at one exact point. (_straighten_junction_ends first removes the medial-axis hook within ~1 stroke width of the node so the fit sees clean data.)
3. Diagonal/curved runs are staircased. For branches that are genuinely curved: RDP (ε≈2 px) removes the staircase, then corner-aware Chaikin rounds the result — splitting at vertices that turn more than ~45° so real corners (H/K joints, the arrow's 90° elbow) stay sharp while gentle curves (3, 6, &) get smooth.

• Check: arrow wings are straight lines meeting at a single node; 3/6/& stay curved.

Step 7 — Emit SVG

• In: the branch list + W.
• Do: each branch → <path d="M x0 y0 L x1 y1 L …" fill="none" stroke="#000" stroke-width="W" stroke-linecap="round" stroke-linejoin="round"/>. Wrap in <svg xmlns=... width=1024 height=1024 viewBox="0 0 1024 1024">…</svg>.
• Out: <name>.svg.
• Check: render and compare side by side with the reference (overlay the faint original to check where the skeleton lands).

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3. Why Zhang–Suen thinning is correct (the core to explain)

Notation: pixel P, 8 neighbors P2..P9 (P2 = North, clockwise). B(P) = number of foreground neighbors, A(P) = crossing number = number of 0→1 transitions going around P2…P9,P2.

• A(P)=1 ⟺ P is a simple boundary point: there is exactly one connected run of foreground around P. Deleting such a point cannot disconnect the local shape, nor create or fill a hole → the topology is preserved (number of connected components and holes). If A≥2 (e.g. P bridges two branches or sits next to a hole), deleting P would break something — this condition blocks that.
• B≥2 preserves line ends: an endpoint has exactly one neighbor (B=1), so it is never deleted → strokes are not eaten back. B≤6 avoids deleting an almost-surrounded interior pixel (not a boundary point worth simplifying).
• The two alternating sub-iterations (c)(d) vs (c')(d') only allow deletions on the south-east boundary, then the north-west boundary. Peeling symmetrically from both sides keeps the skeleton centered, and prevents deleting a whole 2-px-wide line in one pass (which would break the line).
• Iterate to convergence → a 1-px-wide, 8-connected skeleton with the same topology as the shape. That is exactly the "skeleton a person would draw with a pen."

Known limitations: leaves slight staircasing on diagonal strokes and short spurs at corners/rounded ends (hence the prune step). Improvements: Guo–Hall thinning has fewer spurs, or add a staircase-removal pass.

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4. Code structure

src/centerline_svg/core.py   # the algorithm + fluent Pipeline
│   ├── decode_png / read_png            # Step 1  (chunk parse + zlib + de-filter)
│   ├── to_mask(...)                     # Step 2
│   ├── zhang_suen(W, grid)              # Step 3
│   ├── cleanup_skeleton(W, skel)        # Step 3b (remove staircase pixels)
│   ├── distance_transform(...)          # aux (stroke width + prune threshold)
│   ├── trace_branches(W, skel)          # Steps 4+5 (graph + trace, uses crossing number)
│   ├── prune(branches, deg, ...)        # Step 6
│   ├── _fit_straight / _lsq_node        # Step 6b (axis fit + junction re-solve)
│   ├── smooth_polyline (RDP+Chaikin)    # Step 6b (corner-aware smoothing for curves)
│   ├── to_svg(polylines, ...)           # Step 7
│   └── class Pipeline                   # wires the steps; png_to_svg() drives it
src/centerline_svg/render.py # OPTIONAL step visualization (steps_dir / --steps only)

See Install & use at the top for the png_to_svg() API and the centerline-svg CLI. The step visualization is a flag, not a separate program: pass steps_dir=... (--steps DIR on the CLI) to also dump one PNG per stage; omit it for SVG-only.

Results (this implementation vs the reference)

All 7 outputs land on the correct centerline with the right topology (junctions and loops preserved). Path counts are lower than the reference because I trace long branches straight through junctions instead of splitting into many stubs — same geometry, fewer <path> elements.

shape	my paths	ref paths	notes
letter_H	4	11	✓
letter_K	5	13	✓
number_3	3	5	✓
number_6	2	5	✓ loop + tail
ampersand	7	18	✓ self-crossing (deg-4) + loop
arrow-pointer	3	31	✓ (arrowhead Y-axis, see below)
arrow-turn-down-left	3	10	✓

Stroke width is derived from the distance transform (2×median radius, ≈ 64–72 px here) rather than the reference's fixed 45; it tracks the original stroke thickness more closely. Either is acceptable per the brief.

Bugs / gotchas I hit (owning every line)

1. Neighbor index vs offset. My crossing-number helper first did (i + d) in skel where d was already an absolute neighbor index, not an offset → every lookup missed and every pixel read as degree 0. Fix: test the neighbor indices directly. Lesson: pick one representation (indices or offsets) and stick to it.
2. Infinite loop in tracing. Before Step 3b, staircase body pixels had extra raw neighbors, so the branch/loop walk could bounce forever. Fixed by (a) consuming interior pixels and never stepping onto a used one, and (b) a hard step cap = skeleton size. Step 3b then removed the root cause, collapsing hundreds of spurious paths to a handful.
3. Raw degree ≠ topological degree. Counting raw 8-neighbors calls staircase pixels junctions. The crossing number (number of connected neighbor runs) is the correct degree and is what makes junction detection robust.

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5. Where the output diverges from the reference (and why)

• Rounded stroke ends (H, K): the skeleton stops ~one stroke-radius short of the tip (the medial axis of a rounded end terminates at the center of the end-cap arc). stroke-linecap="round" plus the stroke width W fills that back in, so it looks matching. Endpoints landing slightly inside is correct (the reference does the same).
• Arrows (arrow-pointer): the medial axis of a solid triangle is a Y (three spokes to the three corners) — not a single pen stroke. This produces extra branches at the arrowhead. This is an inherent divergence of the medial axis itself; the two short spokes can be pruned to leave a single axis.
• Diagonal strokes (K, &): Zhang–Suen leaves staircasing. The reference emits the raw staircase; we instead straighten/smooth it (Step 6b), so our output is cleaner than the reference — straight strokes are dead straight at the true axis angle. This is a deliberate divergence.
• Junction position: the reference keeps the thinning node as-is; we re-solve it as the least-squares intersection of the stroke axes (Step 6b), which can shift it a few px — toward where the strokes actually cross.
• Self-crossing & : the overlap is a degree-4 junction; the graph keeps the topology correct, yielding many paths (~18).

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6. What I'd improve with more time

• Replace Zhang–Suen with Guo–Hall or a distance-transform + ridge method for a smoother, spur-free skeleton.
• Fit circular arcs / Béziers on curved strokes (3, 6, &) instead of dense polylines.
• Smarter spur pruning using the DT (real spur vs real short stroke) instead of length alone.
• Pair opposite arms through crossings (the & self-intersection): join the two arms whose tangents line up into one continuous path through the node, so the two pen strokes glide through each other instead of four arms parking at one point.
• Handle arrowheads: detect the head triangle and replace the Y-spur with a single sharp tip.

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7. Status

Implemented, packaged, and working — all 7 sample shapes produce correct centerlines (see Results). The algorithm lives in src/centerline_svg/core.py, one function per step, so each part is readable and independently verifiable; it is published as the pure-stdlib centerline-svg package with a png_to_svg() API, a centerline-svg CLI, and a FastAPI web demo in webapp/.

Regenerate the sample outputs:

centerline-svg challenge_sample/ out/

Publishing (TestPyPI then PyPI): see PUBLISHING.md.