Thresholding

Thresholding converts a grayscale image into a binary decision per pixel: keep or discard, foreground or background, edge or not. Despite its simplicity it appears throughout vision pipelines — as explicit image binarization, and implicitly inside detectors and descriptors that compare intensities or scores against a cutoff.

Global thresholding

The simplest form applies one threshold $T$ to the whole image:

$B(x, y) = \begin{cases} 1 & \text{if } I(x, y) > T \\ 0 & \text{otherwise} \end{cases}$

Choosing $T$ by hand is brittle, so Otsu’s method selects it automatically from the intensity histogram: it picks the $T$ that maximizes the between-class variance of the two resulting pixel classes,

$\sigma_B^2(T) = \omega_0(T)\, \omega_1(T)\, \big(\mu_0(T) - \mu_1(T)\big)^2$

where $\omega_0, \omega_1$ are the fractions of pixels below/above $T$ and $\mu_0, \mu_1$ are their mean intensities. Maximizing between-class variance is equivalent to minimizing the within-class variance — the threshold that best separates the histogram into two modes.

Adaptive (local) thresholding

A single global $T$ fails under uneven illumination (shadows, vignetting). Adaptive thresholding computes a per-pixel threshold from a local neighborhood:

$T(x, y) = m_W(x, y) - C$

where $m_W$ is the (plain or Gaussian-weighted) mean over a window $W$ around the pixel and $C$ is a small constant. Each pixel is then compared against its own local threshold. This is how fiducial-marker detectors (ArUco, AprilTag) reliably binarize images before extracting the black-and-white marker grid.

Hysteresis thresholding

Canny edge detection uses two thresholds. Pixels with gradient magnitude above $T_{\text{high}}$ are accepted as strong edges; pixels between $T_{\text{low}}$ and $T_{\text{high}}$ are kept only if they are connected to a strong edge. This preserves long, weak edge segments while rejecting isolated noise responses — a trick worth remembering whenever a single cutoff either fragments good structures or admits too much noise.

Implicit thresholds inside feature pipelines

Thresholding is baked into most feature machinery:

FAST declares a pixel $p$ a corner only if a contiguous arc of circle pixels is brighter than $I_p + t$ or darker than $I_p - t$ ; the threshold $t$ directly controls the detected corner count and is often adapted per image or per grid cell to keep feature counts stable.
BRIEF/ORB descriptors are sequences of 1-bit thresholded intensity comparisons between pixel pairs — each descriptor bit is a tiny threshold test.
Detector responses (Harris score, DoG contrast, matching scores) are all filtered by minimum-response thresholds before non-maximum suppression.
Direct methods select pixels whose gradient magnitude exceeds a threshold, since only high-gradient pixels constrain photometric alignment.

Why it matters for SLAM

SLAM systems are full of thresholds, and knowing the standard techniques for choosing them well separates robust systems from fragile ones. Adaptive thresholding keeps marker- and feature-based pipelines working across lighting changes; the FAST threshold governs the density and stability of the features every downstream module depends on; hysteresis-style two-threshold logic generalizes to many accept/reject decisions (e.g., match filtering). When a SLAM front-end dies indoors-to-outdoors, a hard-coded global threshold is a common culprit.