Image Segmentation Lab

Otsu's method (1979) finds the threshold t* maximizing between-class variance σ²_B(t) = ω₀ω₁(μ₀−μ₁)². Drag the slider or press Auto Otsu.

Noise σ 0

Original & Histogram

Binary Result THRESHOLD

t 128

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σ²B

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ω₀

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ω₁

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Yellow curve = σ²B(t). Green line = optimal t*. Red line = your slider.

Click to place a seed. The region grows by adding neighbors where |I(q) − μ_R| < τ. Watch it expand in real-time. Try different tolerances to see leakage vs tight segmentation.

Noise σ 0

Click to seed

τ 15 Speed

Seed I

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μR

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Pixels

σR

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Mask View

Region

Frontier

Seed

Low τ → tight, homogeneous region. High τ → leakage through weak boundaries. The mean μR updates adaptively as the region grows.

Live-wire finds the minimum-cost path via Dijkstra. The local cost between pixels p→q is:
l(p,q) = ω_G·f_G(q) + ω_Z·f_Z(q) + ω_D·f_D(p,q)
f_G = inverse gradient magnitude f_Z = Laplacian zero-crossing f_D = gradient direction cost. Click to place anchors. Green dashed line follows your cursor.

Noise σ 0

Live-Wire Contour

Click on the image to place the first anchor point.

ω_G (gradient) 0.43 ω_Z (Laplacian) 0.43 ω_D (direction) 0.14

Smoothing σ 1.0

Anchors

Path len

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Total cost

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Combined Cost Map WEIGHTED

Bright = high cost (path avoids). Dark = low cost (path prefers).
f_G = 1 − G/max(G) — low at strong edges
f_Z = 0 at Laplacian zero-crossings, 1 elsewhere
f_D penalizes turning away from the gradient normal direction
Adjust ω sliders to see how each component shapes the cost map and path.

f_G gradient

f_Z Laplacian

f_D direction

Draw two regions to compare. Region A = ground truth, Region B = prediction. Click Compute to see Dice, Jaccard, sensitivity, specificity and the overlap map.

Region A TRUTH

Brush 12

Region B PREDICTION

Brush 12

Overlap

Dice

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Jaccard

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Sens

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Spec

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