Advances in Hyperspectral Image Processing Techniques

20Target Detection Approaches to Hyperspectral Image Classification

Chein‐I Chang^1,2, Bai Xue¹, and Chunyan Yu²

¹ Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore, County, Baltimore, MD, USA

² Center for Hyperspectral Imaging in Remote Sensing (CHIRS), Information and Technology College, Dalian Maritime University, Dalian, China

20.1 Introduction

Generally speaking, detection theory is a statistical binary decision theory which formulates a detection problem as a binary hypothesis testing problem via two hypotheses to describe two different scenarios specified by “null hypothesis” under a probability distribution, p₀, and “alternative hypothesis” H₁, under a probability distribution, p₁. So, for each data sample r, a detector δ(r) is actually a binary decision maker that finds a threshold value, τ, to determine which hypothesis is true for a given data sample r. As a result of using τ as a decision threshold value, there are four decisions, two correct decisions with a decision on H₀ when H₀ is true, known as true negative (TN) and a decision on H₁ when H₁ is true known as true positive (TP), also referred to as detection probability, P_D, and two wrong decisions with a decision on H₁ when H₀ is true, known as type I error, also referred to as false alarm probability, P_F, and a decision on H₀ when H₁ is true, known as type II error, also referred to as miss probability, P_M. Accordingly, a detector δ(r) is in fact determined by two ...