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**Maximum Likelihood / Bayesian (4) — full decision rule.** The pixel is assigned to the class for which **D** is the **lowest**: $$ D \;=\; \log_e(a_c) \;-\; \tfrac{1}{2}\log_e(|V_c|) \;-\; \tfrac{1}{2}(X - M_c)^{\!T}\,V_c^{-1}(X - M_c) $$ - **X** — measurement vector of the candidate pixel. - **M_c** — mean vector of the data in class *c*. - **V_c** — covariance matrix of class *c*. - **|V_c|** — determinant of V_c. - **V_c⁻¹** — inverse of V_c. - **T** — transposition. - **a_c** — prior probability that class *c* occurs in the image (equal for all classes, or user-entered from a priori knowledge). - The third term is the **Mahalanobis distance** squared — distance from the pixel to the class mean, **scaled by the class's covariance**. Mahalanobis alone (without the first two log terms) is its own decision rule.

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