Threshold & Compare

Note: The existing Otsu Threshold engine provides automatic optimal threshold selection. Within the BOM, manual threshold and comparison operations provide fine-grained control for custom pipeline construction.

Thresholding is the most fundamental segmentation operation in image processing — the point where a continuous grayscale image becomes a discrete binary decision: foreground or background. Despite its simplicity, the choice of threshold method and value profoundly affects every downstream result (Gonzalez & Woods, §10.3).

Global Thresholding & Otsu's Method

Global thresholding applies a single value T to the entire image: g(x,y) = 1 if f(x,y) ≥ T, else 0. The core assumption is histogram bimodality — foreground and background pixels form two separable peaks. Otsu's method formalizes this by finding the threshold that maximizes the between-class variance σ²_B = ω₀ω₁(μ₀ − μ₁)², where ω₀, ω₁ are the class probabilities and μ₀, μ₁ are the class means. This is equivalent to minimizing within-class variance. Otsu's method is optimal when classes have equal variances and the histogram is truly bimodal, but degrades when: (1) one class is much smaller than the other, (2) class variances differ greatly, or (3) noise fills the valley between peaks.

Adaptive Thresholding

When illumination varies across the image — common in large whole-slide scans — no single global threshold works everywhere. Adaptive thresholding computes a local threshold at each pixel from its neighborhood: T(x,y) = mean(neighborhood) + offset. The mean can be unweighted (box filter) or Gaussian-weighted (giving more influence to nearby pixels). Solomon & Breckon describe this as "the workhorse operator" of practical machine vision — a different threshold at each pixel location. The window size is a critical trade-off: too small and the threshold is noisy (responds to individual pixels rather than illumination trends); too large and it loses the ability to adapt to local conditions, approaching global behavior.

Multi-Level & Hysteresis Thresholding

Multi-level Otsu extends the method to more than two classes by maximizing the total between-class variance across multiple thresholds — useful when the histogram has three or more modes (e.g., background, cytoplasm, nuclei). Hysteresis thresholding uses two thresholds (T_low, T_high): pixels above T_high are definitely foreground, pixels below T_low are definitely background, and pixels between the two are foreground only if connected to a definite foreground pixel. This dual-threshold approach is the basis of the Canny edge detector's final stage and is available in StrataQuest's BOM through chained threshold-then-compare operations.

Compare Operations as Boolean Algebra

Binary masks are sets of pixels, and compare operations implement set operations: A > B produces the set where A exceeds B; combining masks with AND computes the intersection, OR computes the union, and XOR computes the symmetric difference. This enables construction of complex ROIs from simple threshold results — for example, (channel_A > T₁) AND (channel_B < T₂) selects pixels that are bright in one marker and dim in another, a common operation in multiplex immunofluorescence analysis.

Global Threshold

Use when illumination is uniform across the image and a single intensity value cleanly separates foreground from background. Check the histogram — if it shows two well-separated peaks with a clear valley, a global threshold at the valley works well. This is essentially manual Otsu: you pick the threshold instead of the algorithm computing it.

Adaptive Threshold

Use when illumination varies across the image (common in large whole-slide scans). The workflow: (1) Compute local mean using Statistical Operations with a large window. (2) Apply adaptive threshold: original > (local_mean + offset). The offset controls sensitivity — larger offset requires objects to be further above local background. Solomon & Breckon describe adaptive thresholding as using "a different threshold at each pixel location."

Comparison Operations

Use for relative intensity analysis between channels or between an image and a reference. Examples:

• Channel ratio masking: A > B creates a mask where channel A is dominant
• Difference masking: (A − B) > threshold detects significant differences between two conditions
• Multi-threshold: chain comparisons with logical operations: (image > T_low) AND (image < T_high) creates a band-pass mask

Three Limitations (Solomon & Breckon)

Global thresholding has three fundamental limitations: (1) no guarantee that thresholded pixels are contiguous, (2) sensitivity to illumination variation, and (3) only works when foreground and background have distinct intensities. Adaptive thresholding addresses limitation 2; connected-component labeling addresses limitation 1.