As regards background suppression, background subspace can be defined globally over the whole scene, or locally, by considering a neighborhood of each test pixel.
That is the image where the targets have been inserted. The simulation was conducted for several different values both of FI and ALFA:
These are detection results. FAR@PD=1, so the lower the better. Specifically we have plots of FAR vs FI and FAR vs ALFA. Results are in favor of the local approach. The global method (blue curve) manages to perform comparably to the local ones for a value of FI=10dB, but its performance quickly degrades for lower FI. (Of course the performance gets better as ALFA increases). Conversely, the local methods manage to detect the target even if it has very low global residual energy. Specifically, LBSE (red curve) provides the best results in most cases. LBSS exhibits a diversity in performance wrt to the number of neighboring pixels considered, for the selection of which no criteria can be invoked. IN fact, here, several configurations had to be tested so as to get good performance.
Matteoli ieee gold_2010_clean
Pisa, 30.11.2007 Stefania Matteoli a Nicola Acito b Marco Diani a Giovanni Corsini a a Dipartimento di Ingegneria dell’Informazione, Università di Pisa, Pisa, Italy b Accademia Navale, Livorno, Italy Livorno, 30.04.2010 Hyperspectral Target Detection via Local Background Suppression South of Italy Chapter Remote Sensing & Image Processing Group
Linear Mixing Model (LMM) <ul><ul><li>random vector associated to the test pixel </li></ul></ul><ul><ul><li>spectral signature of the target </li></ul></ul><ul><ul><li>scalar value accounting for sub-pixel targets </li></ul></ul><ul><ul><li>matrix spanning the background subspace </li></ul></ul><ul><ul><li>vector of background components </li></ul></ul><ul><ul><li>background subspace of dimension </li></ul></ul><ul><ul><li>zero-mean Gaussian random noise vector with covariance matrix </li></ul></ul><ul><ul><li>number of spectral bands </li></ul></ul>
Subspace-based target detection scheme original data space <ul><ul><li>Background is suppressed via orthogonal projection </li></ul></ul>background suppression <ul><ul><li>projection matrix onto </li></ul></ul>residual subspace target detection
Target detection scheme, detection performance Background suppression <ul><ul><li>Target detection performance (P D and P FA ) depends on </li></ul></ul>noise covariance matrix target residual energy P D is expected to be an increasing function of . Target detection
Global background vs local background Global background subspace Local background subspace generally Target detection Background suppression
Global background vs local background Global approach Local approach <ul><li>Global background lies in a high-dimensional subspace </li></ul><ul><li>Low target residual energy after suppression (major risk of target leakage ) </li></ul><ul><li>Provides lower-dimensional subspaces </li></ul><ul><li>Higher residual energy after projection (which benefits to detection performance) </li></ul>Target detection Background suppression <ul><ul><li>The background subspace basis is unknown and has to be estimated from the data </li></ul></ul>
Global background estimation : N-S NWHFC SVD all image pixels N-S subspace dimension (Virtual Dimension, VD) basis vectors <ul><li>N-P based test on covariance and correlation matrix eigenvalues </li></ul><ul><li>based on asymptotic properties </li></ul>Target detection Background suppression
Local background estimation : LBSS local neighborhood LBSS <ul><li>A set of neighboring pixels is let span the background subspace </li></ul>Local Background Subspace Selection <ul><li>The local subspace dimension is imposed by the number of neighboring pixels </li></ul><ul><li>LBSS cannot account for background spatial variability within the scene! </li></ul>LBSS main limitation <ul><li>target leakage (overestimation) </li></ul><ul><li>false alarms (underestimation) </li></ul>Target detection Background suppression
Local background estimation : a new algorithm local neighborhood LBSE <ul><li>Automatic technique </li></ul><ul><li>Adaptive estimation on a per-pixel basis </li></ul><ul><li>Estimated local background subspace tailored to background spatial variability </li></ul>Local Background Subspace Estimation Statistical hypothesis testing SVD LBSE local subspace dimension basis vectors Target detection Background suppression
Target detection step each considered background basis estimation algorithm (N-S, LBSS, and LBSE) should be embodied in a subspace-based target detector Generalized Matched Filter (GMF) defined in the orthogonal complement of the background subspace N-S LBSS LBSE Background suppression Target detection
Results: 2) Simulation methodology N-S, LBSS, LBSE the scalar value allows to set a desired value of the target residual energy on the orthogonal complement of the N-S estimated subspace <ul><li>simulation performed over N=1000 images </li></ul><ul><li>Target detection results averaged over the 1000 images </li></ul>
Results: 2) Simulation (1000 images), [email_address] D =1 LBSS: K L BSS is a user-specified parameter. No criteria exist to set it and several configurations have to be tested in order to assure good performance.
Results: 3) Testing on real data real target detection scenario with ground-truthed targets LBSE histogram ROC curves <ul><li>Best performance obtained with LBSE </li></ul><ul><li>LBSS results exhibit diversity w.r.t. K LBSS </li></ul>
Conclusion LBSE <ul><li>novel and fully automatic algorithm for local background subspace estimation and suppression </li></ul><ul><li>experimental evidence of three main advantages w.r.t exiting methodologies </li></ul>being local , it is able at properly detecting targets with low residual energy w.r.t the global background subspace provides unambiguous results through the automatic computation of a local background dimension for each pixel it is capable of adapting to spatial variations of background complexity within the scene
Pisa, 30.11.2007 Livorno, 30.04.2010 Thanks for your attention! South of Italy Chapter