Chaos-based Image Assessment for THz Imagery Erik P. Blasch Air Force Research Lab Information Directorate Rome, NY, 13441 erik.blasch@rl.af.mil Jianbo Gao Mechanical and Materials Eng. Wright State University Dayton, Ohio, 45435 jbgao.pmb@gmail.com Wen-Wen Tung Earth and Atmospheric Sciences Purdue University West Lafayette, Indiana, 47907 wwtung@purdue.edu Abstract – Multiscale image processing is a powerful technique that can determine image characteristics (e.g. clutter), provide denoising, and determine object features. Imagery is highly nonstationary (i.e. mean and variance change with location and time) and multiscaled (i.e. dependent on the spatial or temporal interval lengths). In this paper, we utilize the scale-dependent Lyapunov exponent (SDLE), which unifies the principles of fractal and chaos theory, to characterize the different signal behaviors on a wide range of scales simultaneously. Commonly used complexity measures, including those from information theory, chaos theory, and random fractal theory, can all be related to the values of the SDLE at specific scales, and therefore, SDLE can act as the basis for a unified theory of multiscale analysis of complex imagery data. We describe the power-law and singular- value decomposition (SVD) for image processing and demonstrate a SDLE example using TeraHertz (THz) imagery for concealed target image fusion. Keywords: Image Processing, scale-dependent Lyapunov exponent, TeraHertz, singular-value decomposition 1 Introduction Significant work on image processing covers a broad spectrum of analysis; including target exploitation, image fusion; and video processing. For some types of imagery, there is a need to analyze the multiscale and heavy-tail nature. We utilize a novel technique in multiscale imagery analysis using the SDLE [1] of the singular-value decomposition components of THz images. Image fusion is an important research area [2, 3]. With the numerous image fusion methods, it is important to determine the quality of the image based on a set of standardized metrics [4, 5, 6]. Image fusion is an important component of many applications such as non- destructive evaluation (e.g. eddy current and ultrasonic [7]), night vision [4] and target tracking [8] (e.g. visual and infrared [9]), medical diagnosis (e.g. PET and MRI [10, 11]), and electro-optical (multispectral) targeting [12]. One appealing aspect of image fusion is its natural biological extension of the visual spectrum. The human cognitive interest in image fusion over a variety of sensor modalities must be appropriately assessed to ensure the perceptual fused image quality [13]. Our interest is to determine which metrics are best for different applications, image types, image fusion techniques, and image defects (e.g. distortion, variance, and resolution). [4] For this paper, we are interested in processing THz imagery data that has shown promise for standoff concealed weapons testing, nondestructive evaluation, and medical diagnosis. The available images include visual spectrum data, and THz images collected with no obstruction (normal) and clothing obscurations with a loss (attenuation only) of 30 percent (minus 30) [14, 15]. Figure 1 shows the image result from the raw signals from the THz images [14, 15] of which we will fuse the THz images that simulates a concealed detection analysis. Figure 1. Image Data: Visual(left), THz (Right). [14-15] Being able to fuse THz imagery can add additional context to concealed object detection but is a function of operating conditions [16]. For example, using road information for targeting tracking and identification methods [17, 18] are analogous to human physical models to locate weapons. Bio-inspired image fusion methods can be applied to feature extraction [19] and frequency analysis [20] to support concealed weapon detection. The rest of the paper is organized as follows. Section 2 overviews the multiscale analysis using the SDLE. We first define SDLE, then apply it to characterize low- dimensional chaos, noisy chaos, and random processes with decaying power spectral density (the so-called 1/f α processes). As real world application, Section 3 discusses the image fusion metrics and we apply SDLE to characterize THz data for analysis of image content. Section 4 provides the conclusions. 2 Multiscale Image Analysis Complex imagery collections usually are comprised of multiple subsystems that exhibit both highly nonlinear deterministic, as well as, stochastic (i.e. random) characteristics, and are regulated hierarchically. These systems generate signals, x(n), that exhibit complex characteristics such as sensitive dependence on small The 11th International Conference on Information Sciences, Signal Processing and their Applications: Main Tracks U.S. Government work not protected by U.S. copyright 360