Spectral Matching and Target Detection Techniques

Hyperspectral images provide detailed information about the spectral characteristics of materials for several spectral bands over a wide range of wavelengths. You can use the abundant spectral information from hyperspectral images to identify materials and detect targets that are difficult to detect using spectral information from a small number of wavelengths as in grayscale, RGB, or multispectral images.

You can use spectral matching and target detection techniques for a wide variety of applications in diverse domains.

• Agriculture — Detect nutrient deficiencies and pest infestations in crops.

• Environment Monitoring — Monitor water quality in water bodies.

• Mining — Identify mineral composition.

• Defense — Identify concealed threats.

• Remote Sensing — Classify land cover.

• Medical Imaging — Detect tumors and skin lesions.

• Food Industry — Assess freshness of fruits.

• Forensics — Identify trace evidence such as fingerprints and bloodstains at crime scenes.

Spectral matching identifies the class of an endmember material by comparing its spectra with one or more reference spectra. You can also use spectral matching to identify materials or detect specific targets in a hyperspectral image when the spectral signature of the target is distinct from other regions in the hyperspectral image. However, when the spectral contrast between the target and other regions is low, spectral matching becomes more challenging. In such cases, more sophisticated target detection algorithms that consider the entire hyperspectral data cube and use statistical or machine learning methods are required.

• Spectral matching techniques compare individual pixel spectra with the spectral signature of the target using the geometrical characteristics of the pixel spectra, its probability distribution values, or both. Techniques that utilize both geometrical characteristics and probability distribution values have higher discrimination capabilities than the individual approaches. A low distinction between the individual pixel spectrum and the target spectral signature indicates a high probability of the presence of the target at that pixel. Use spectral matching techniques when there is limited variability in the spectral signature of the target, the spectral signature of the target is significantly different from the background, and the spectral signatures of the background are somewhat homogenous.

• Target detection techniques use the information from the entire hyperspectral data cube along with statistical, machine learning, or subspace projection methods to detect targets. Use target detection techniques when there is significant variability in the spectral signature of the target, the spectral signature of the target is not significantly different from the background, or the spectral signatures of the background are complex or heterogeneous.

Spectral Matching Techniques

This table summarizes the spectral matching techniques that you can use with the spectralMatch function. The spectral matching score returned by the spectralMatch function indicates the distinction between the target spectral signature and the spectrum of each pixel in the hyperspectral image. Lower score indicates a higher possibility of the presence of the target.

Technique	Algorithm	Function
Spectral angle mapper (SAM)	The SAM method measures the angle between the target spectrum t and the pixel spectrum x. $$score={\cos }^{-1}\left(\frac{t^{T}x}{\sqrt{t^{T}t}\sqrt{x^{T}x}}\right)$$ The SAM method is insensitive to illumination changes.	spectralMatch function with Method specified as "sam" sam function
Spectral information divergence (SID)	The SID method measures the divergence between the probability distributions of the target spectrum t and the pixel spectrum x $$score={\displaystyle \sum _i{t}_i}\log \left(\frac{t_i}{x_i}\right)+x_i\log \left(\frac{x_i}{t_i}\right)$$ ti and xi are the elements of the vectors t and x, respectively. The SID method is efficient in identifying mixed pixel spectra.	spectralMatch function with Method specified as "sid" sid function
SID-SAM	The SID-SAM method computes the product of the SID score and the tangent of the SAM score. $$score=SID\times \tan (\alpha )$$ SID is the SID score and α is the SAM score. The SID-SAM method has better discrimination capability compared to SID and SAM individually.	spectralMatch function with Method specified as "sidsam" sidsam function
Jeffries Matusita - Spectral angle mapper (JMSAM)	The JMSAM method computes the product of the JM distance and the tangent of the SAM score. $$\begin{array}{l}score=J{M}_{dist}\times \tan (\alpha )\\ J{M}_{dist}=2\left(1-e^{-B}\right)\\ B_{dist}=\frac{1}{8}{\left({\mu }_x-{\mu }_t\right)}^T{\left[\frac{{\sigma }_x+{\sigma }_t}{2}\right]}^{-1}\left({\mu }_x-{\mu }_t\right)+\frac{1}{2}\ln \left[\frac{\left|\frac{{\sigma }_x+{\sigma }_t}{2}\right|}{\sqrt{\left|{\sigma }_x\right|\left|{\sigma }_t\right|}}\right]\end{array}$$ JMdist is the JM distance, α is the SAM score, and Bdist is the Bhattacharya distance. μt and μx are the means of t and x, respectively. σt and σx are the standard deviations of t and x, respectively. The JMSAM method is particularly efficient in discriminating spectrally close targets.	spectralMatch function with Method specified as "jmsam" jmsam function
Normalized spectral similarity score (NS3)	The NS3 method computes the spectral matching score from the Euclidean distance and the SAM score. $$\begin{array}{l}score=\sqrt{{\left(E_{dist}\right)}^2+{\left(1-\cos (\alpha )\right)}^2}\\ E_{dist}=\sqrt{\frac{1}{C}{(x-t)}^T(x-t)}\end{array}$$ Edist is the Euclidean distance, α is the SAM score, and C is the number of bands in the spectrum. The NS3 method has high discrimination capability, but requires extensive reference data for high accuracy.	spectralMatch function with Method specified as "ns3" ns3 function

Target Detection Techniques

This table summarizes the target detection techniques that you can use with the detectTarget function. The target detection score returned by the detectTarget function indicates the probability of the presence of the target at each pixel in the hyperspectral image. A higher score indicates a higher probability of the presence of the target.

Technique	Algorithm	Function
Constrained energy minimization (CEM)	The CEM method uses an FIR filter whose response to a pixel spectrum, x is greater when the spectrum is more similar to the target spectrum t. $$score=\frac{t^T{C}_{\mathrm{cov}}{}^{-1}x}{t^T{C}_{\mathrm{cov}}{}^{-1}t}$$ Ccov is the covariance of the background. Use the CEM method when the background noise is minimal.	detectTarget function with method specified as "CEM"
Adaptive cosine estimator (ACE)	The ACE method computes the squared dot-product of the mean-subtracted pixel spectrum x and the mean-subtracted target spectrum t in a whitened coordinate space. $$score=\frac{{(t^T{C}_{\mathrm{cov}}{}^{-1}x)}^2}{(t^T{C}_{\mathrm{cov}}{}^{-1}t)(x^T{C}_{\mathrm{cov}}{}^{-1}x)}$$ Ccov is the covariance of the background. Use the ACE method when the hyperspectral image has significant background clutter.	detectTarget function with method specified as "ACE"
Signed adaptive cosine estimator (Signed ACE)	The Signed ACE method is similar to ACE but differentiates between positive and negative correlations between the mean-subtracted pixel spectrum x and the mean-subtracted target spectrum t. $$score=\frac{(x^T{C}_{\mathrm{cov}}{}^{-1}t)\left|x^T{C}_{\mathrm{cov}}{}^{-1}t\right|}{(t^T{C}_{\mathrm{cov}}{}^{-1}t)(x^T{C}_{\mathrm{cov}}{}^{-1}x)}$$ Ccov is the covariance of the background. Use the Signed ACE method when the hyperspectral image has significant background clutter.	detectTarget function with method specified as "SignedACE"
Matched filter (MF)	The MF method uses an FIR filter whose response to a mean-subtracted pixel spectrum, x is greater when the spectrum is more similar to the mean-subtracted target spectrum t. $$score=\frac{t^T{C}_{\mathrm{cov}}{}^{-1}x}{t^T{C}_{\mathrm{cov}}{}^{-1}t}$$ Ccov is the covariance of the background. Use the MF method when the background noise is additive white Gaussian noise.	detectTarget function with method specified as "MF"
Generalized likelihood ratio test (GLRT)	The GLRT method computes the target detection score between the mean-subtracted target spectrum t and the mean-subtracted pixel spectrum x in a manner similar to the ACE method. $$score=\frac{{(t^T{C}_{\mathrm{cov}}{}^{-1}x)}^2}{(t^T{C}_{\mathrm{cov}}{}^{-1}t)(1+x^T{C}_{\mathrm{cov}}{}^{-1}x)}$$ Ccov is the covariance of the background. Use the GLRT method when the hyperspectral image has significant background clutter.	detectTarget function with method specified as "GLRT"
Adaptive matched subspace detector (AMSD)	The AMSD method computes the ratio of the likelihood that the pixel spectrum x belongs to the target subspace to the likelihood that x belongs to the background subspace. $$\begin{array}{l}score=\frac{x^T{P}_{B}x}{x^T(P_B-P_E)x}\\ P_B=I-B{(}^{B^T}B\\ P_E=I-E{(}^{E^T}E\end{array}$$ I is the identity matrix, B is the background subspace, and E is the combined subspace of the background and target. This method uses the endmembers of the hyperspectral image for target detection. Use the AMSD method when the target spectral signature has variability and spans a subspace.	detectTarget function with method specified as "AMSD"
Orthogonal subspace projection (OSP)	The OSP method uses an FIR filter whose response to a pixel spectrum, x is greater when the spectrum is more similar to the mean-subtracted target spectrum t $$\begin{array}{l}score=\frac{t^T{P}_{B}x}{t^T{P}_{B}t}\\ P_B=I-B{(}^{B^T}B\end{array}$$ I is the identity matrix and B is the background subspace. This method uses the endmembers of the hyperspectral image for target detection. Use the OSP method when the hyperspectral image has significant background clutter.	detectTarget function with method specified as "OSP"