Maider Marin-McGee, Ph.D. student; Miguel Velez-Reyes, Faculty advisor Contact Information, {maider.marin, migel.velez-reyes}@upr.edu

Using Hyperspectral Imaging (HSI) with its capacity of sampling the electromagnetic spectrum using hundreds of narrow and contiguous spectral bands is a valuable remote sensing technology for many defense and security applications. Noise introduced by the Hyperspectral sensor and the interfering medium, in addition to the natural spectral variability of the materials, make information extraction more difficult. Pre-processing methods for image enhancement that take full advantage of available spectral information are proposed here to enhance spatial features of interest and denoising. Tensor Anisotropic Nonlinear Diffusion (TAND) is one way to deal with the problem of denoising a HSI. The idea is to use the structure tensor to find the direction where the edges that separate the regions in the scene are. The tensor information is then used either to prevent diffusion from happening across edges (Edge Enhancement Diffusion (EED)) or to enhance or complete the edges or other linear structures (Coherence Enhancement Diffusion (CED)). A new structure tensor is proposed here that gives higher weight to spectral bands with edge information. This variable weighting improves EED and CED enhancement. Results of this method are presented for HSI images of different spatial characteristics to demonstrate the potential capabilities of the method. The proposed image enhancement algorithm can be an integral part of a target detection system using HSI.

Advances to the State of the Art • Defines a new weighted structure tensor

• Weights depend on data • They are based on the heat operator

• Proposing a more versatile function to define the eigenvalues of the CED tensor

This work is based on TAND proposed by [4]

The proposed enhancement improves the capability of image analysts and machine-based detection of threads and regions of interest in surveillance systems.

This material is based upon work supported by the U.S. Department of Homeland Security under Award Number 2008-ST-061-ML0002 and partially funded by the U.S. DHS Award Number 2008-ST-061-ED0001.

The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied of the U.S. Department of Homeland Security.

Algorithms developed in MATLAB can be used as a basis to transition algorithms for companies interested in incorporating the approach into Hyperspectral Target Detection Systems. Incorporation into the UPRM HSI Analysis Toolbox will facilitate access to algorithms in an easy to use environment to evaluate the technology.

Develop a method to combine CED and EED diffusion for further image enhancement. Work on the transition to the UPRM Hyperspectral Image Analysis Toolbox. Improve computational efficiency. Finish dissertation in Spring 2012.

1. M. Marin-McGee and M. Velez-Reyes,

“Enhancement of Flow-Like Structures in

Hyperspectral Imagery Using Tensor

Nonlinear Anisotropic Diffusion,” in Proc. SPIE

8048, 2011, p. 80480E-80480E-9.

2. M. Marin-McGee and M. Velez-Reyes, “A

Structure Tensor for Hyperspectral Images,” in

Proceedings of the 3rd IEEE Workshop on

Hyperspectral Image and Signal Processing:

Evolution in Remote Sensing, Lisbon, 2011.

3. J. Weickert, “Coherence-Enhancing

Diffusion Filtering,” International Journal of

Computer Vision 31, 111-127 (1999).

4. J. Weickert, Anisotropic Diffusion in Image

Processing, Teubner-Verlag (1998).

Tensor Anisotropic Nonlinear Diffusion for Hyperspectral Image Enhancement

Technical Approach Abstract

Relevance

Accomplishments Through Current Year

Future Work

Other References

Publications Acknowledging DHS Support Opportunities for Transition to Customer

A TAND algorithm based on a weighted structure tensor has been developed. Weights are defined using the heat operator. Diffusion algorithms have been implemented in MATLAB. Experiments with HS data of different spatial characteristics have been performed and analyzed. Two papers have been published.

Smoothed Gradient vs. Structure Tensor.

Original Image

Structure Tensor

Gradient Orientation 𝜎 = 0.5

Gradient Orientation 𝜎 = 2.5

Individual Cell Extraction–CED

Original Image 𝑡 = 10 𝑡 = 30 𝑡 = 50

𝑡 = 80 𝑡 = 100 𝑡 = 200 𝐼 − 𝐼120 |80𝑡ℎ 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒

Region of Interest of thyroid tissue

Eigenvalue-function with contrast parameter for CED

CED vs. EED

Original Image CED t =20

EED t =20

Isotropic vs. Anisotropic- EED for Detection of Traces of Materials

Original Image Anisotropic EED Nonlinear EED

Classical vs. Weighted Structure Tensor– EED

Left to right : Diffusion Tensor components λ, β,ν. t = 2. First Row Classical. Second Row weighted

Original Image

𝜕𝑢

𝜕𝑡− 𝛁 ⋅ 𝐷𝛁𝑢 = 0, in Ω × 𝐼

𝑢 𝑥, 0 = 𝑢0 𝑥 , in Ω. (1) 𝐷𝛁𝑢 , 𝒏 = 0, on Γ × 𝐼.

Nonlinear Tensor Diffusion Model

𝑢𝜎 ≔ 𝐺𝜎 ∗ 𝑢 ⋅, 𝑡 , 𝜎 > 0 𝐷𝜌 = 𝐺𝜌 ∗ (𝑤𝛁𝑢)(𝑤𝛁𝑢)𝑇

𝑤 = exp −𝑡∆𝑀 /sum(𝑤);

∆𝑀 : Laplace-Beltrami Operator.

Weighted Gradient 𝑤𝛁𝑢𝜎

Structure Tensor

𝐷𝜌 = 𝜔1 𝜔2𝜇1 00 𝜇2

𝜔1

𝜔2

𝜌 = 0 ⇒ EED

𝜌 > 0 ⇒ CED

Diffusion Tensor

𝐷 = 𝜔1 𝜔2𝜅1 00 𝜅2

𝜔1

𝜔2=

𝜆 𝛽𝛽 𝜈

𝜅1 =

1 𝜇1 = 0

𝛼 + (1 − 𝛼) −𝑐

𝜇1𝜓

4 𝑒𝑙𝑠𝑒

𝜅2 = 1,

𝜅1 = 𝛼, 0 < 𝛼 ≪ 1

𝜅2 =

𝛼 𝜇 = 0

𝛼 + (1 − 𝛼) −𝑐

𝜇𝜓

4 𝑒𝑙𝑠𝑒

Proposed [1]

λ 𝛽 𝜈

λ 𝛽 𝜈

State of the art [3]

Proposed

State of the art

Original Image

t = 2

t = 2

Enhancement for Target Detection

Original Image After EED 𝜆 𝜈

𝜎 = .5, 𝑡 = 1

Acknowledgements

The Authors thank Professor Badrinath Roysan from the University of Houston for providing the Thyroid Tissue image data set and the Jet propulsion Laboratory for making available the AVIRIS data. They also thank Isnardo Arenas and professors Paul Castillo from UPRM and Olga Drblìková from Slovak University of Technology in Bratislava for useful comments during the implementation process.