SMV: Simplex of maximal volume based upon the Gram-Schmidt process

Jairo Salazar-Vazquez; Andres Mendez-Vazquez

doi:10.1117/12.2194402

15 October 2015 SMV⊥: Simplex of maximal volume based upon the Gram-Schmidt process

Jairo Salazar-Vazquez, Andres Mendez-Vazquez

Proceedings Volume 9643, Image and Signal Processing for Remote Sensing XXI; 96430U (2015) https://doi.org/10.1117/12.2194402
Event: SPIE Remote Sensing, 2015, Toulouse, France

Abstract

In recent years, different algorithms for Hyperspectral Image (HI) analysis have been introduced. The high spectral resolution of these images allows to develop different algorithms for target detection, material mapping, and material identification for applications in Agriculture, Security and Defense, Industry, etc. Therefore, from the computer science’s point of view, there is fertile field of research for improving and developing algorithms in HI analysis. In some applications, the spectral pixels of a HI can be classified using laboratory spectral signatures. Nevertheless, for many others, there is no enough available prior information or spectral signatures, making any analysis a difficult task. One of the most popular algorithms for the HI analysis is the N-FINDR because it is easy to understand and provides a way to unmix the original HI in the respective material compositions. The N-FINDR is computationally expensive and its performance depends on a random initialization process. This paper proposes a novel idea to reduce the complexity of the N-FINDR by implementing a bottom-up approach based in an observation from linear algebra and the use of the Gram-Schmidt process. Therefore, the Simplex of Maximal Volume Perpendicular (SMV⊥) algorithm is proposed for fast endmember extraction in hyperspectral imagery. This novel algorithm has complexity O(n) with respect to the number of pixels. In addition, the evidence shows that SMV⊥ calculates a bigger volume, and has lower computational time complexity than other poular algorithms on synthetic and real scenarios.

Citation Download Citation

Jairo Salazar-Vazquez and Andres Mendez-Vazquez "SMV⊥: Simplex of maximal volume based upon the Gram-Schmidt process", Proc. SPIE 9643, Image and Signal Processing for Remote Sensing XXI, 96430U (15 October 2015); https://doi.org/10.1117/12.2194402

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available