Joseph P. Havlicek

Multidimensional quasi-eigenfunction approximations and multicomponent AM-FM models

We develop multicomponent AM-FM models for multidimensional signals. The analysis is cast in a general n-dimensional framework where the component modulating functions are assumed to lie in certain Sobolev spaces. For both continuous and discrete linear shift invariant (LSI) systems with AM-FM inputs, powerful new approximations are introduced that provide closed form expressions for the responses in terms of the input modulations. The approximation errors are bounded by generalized energy variances quantifying the localization of the filter impulse response and by Sobolev norms quantifying the smoothness of the modulations. The approximations are then used to develop novel spatially localized demodulation algorithms that estimate the AM and FM functions for multiple signal components simultaneously from the channel responses of a multiband linear filterbank used to isolate components. Two discrete computational paradigms are presented. Dominant component analysis estimates the locally dominant modulations in a signal, which are useful in a variety of machine vision applications, while channelized components analysis delivers a true multidimensional multicomponent signal representation. We demonstrate the techniques on several images of general interest in practical applications, and obtain reconstructions that establish the validity of characterizing images of this type as sums of locally narrowband modulated components.

The analytic image

We introduce a novel directional multidimensional Hilbert transform and use it to define the complex-valued analytic image associated with a real-valued image. The analytic image associates a unique pair of instantaneous amplitude and frequency functions with an image, and also admits many of the other important properties of the one-dimensional analytic signal.

Image watermarking using wavelets

This paper proposes a novel image watermarking scheme. This technique uses a 2-D discrete wavelet transform to decompose an image into various frequency channels. A scaled image is used as the watermark and inserted into a mid-frequency wavelet channel. The watermark embedded image is produced by taking the inverse 2-D discrete wavelet transform of the altered wavelet decomposition. The image size, the non-zero scaling factor, the channel in which the watermark is inserted, and the wavelet transform filters can be used as security keys for the extraction of the inserted watermark. The propose watermark extraction technique is independent of the original image. A compromise between visually perceptible artifacts and resiliency in preserving the watermark from attacks by JPEG compression, median filtering, and image cropping can be achieved by adjusting the scaling factor.

Oriented texture completion by AM-FM reaction-diffusion

We provide an automated method to repair broken, occluded oriented image textures. Our approach is based on partial differential equations (PDEs) and AM-FM image modeling. Reconstruction of the texture occurs via simultaneous PDE-generated diffusion and reaction. In the diffusion process, the image is adaptively smoothed, preserving important boundaries and features. The reaction process produces the reconstructed textural information in the occluded image regions. Gabor (1946) filters are designed and used in the reaction process using an AM-FM dominant component analysis. An AM-FM model of the texture image is constructed, making it possible to localize the reaction filters spatio-spectrally. In contrast to previous disocclusion techniques that depend on interpolation, on continuity of the connected components within the image level sets, or on texture estimation, the reaction-diffusion process proposed here yields a seamless transition between the recreated region and the unoccluded image regions. Using AM-FM dominant component analysis, we avoid the ad hoc parameter selection typified with other reaction-diffusion approaches. As a useful example, we focus on the repair of broken, occluded fingerprints. We also treat several exemplary natural textures to demonstrate the techniques generality.

Skewed 2D Hilbert transforms and computed AM-FM models

Computed AM-FM models represent images in terms of instantaneous amplitude and frequency modulations. However, the instantaneous amplitude and frequency of a real valued image are ambiguous. We apply the directional 2D Hilbert transform to compute a complex extension for a real image. This extension, called the analytic image, admits most of the attractive properties of the 1D analytic signal. However, the analytic image is not unique: for a given real image, taking the Hilbert transform in the horizontal and vertical directions yields different complex extensions and differing computed AM-FM models. We show that these two differing models are essentially equivalent and develop explicit formulations relating them.

AM-FM image segmentation

We introduce a new modulation domain texture segmentation algorithm. The approach begins by constructing a dominant component AM-FM image model, where the dominant amplitude and frequency modulations are used as segmentation features. Statistical clustering is applied in this feature space to compute an initial segmentation which is then refined by morphological filtering and connected components labeling. The algorithm, which consistently delivers correct pixel classification rates exceeding 94%, is only partially unsupervised at present since the desired number of regions must be known a priori. Our future work is focused on developing strategies to make the approach fully unsupervised.

Limits on discrete modulated signals

We develop theorems of a general nature that apply to the analysis of AM-FM signals of the form a(m)exp [j/spl phi/(m)] or a(m) cos [/spl phi/(m)] and to their behavior both in linear systems and in simple nonlinear systems comprised of products of linear elements. Such product-systems include interesting nonlinear demodulation operators, such as the Teager-Kaiser (1990) operator. Expressions for the approximate system responses to AM-FM signals are derived by making an analogy to the eigenfunction interpretation of sinusoids in linear systems; for the case of sinusoidal signals, the approximations are exact. These expressions are collectively called quasieigenfunction approximations (QEAs). For nonsinusoidal AM-FM signals, the approximations have errors that are tightly bounded by functionals that express the smoothness of the AM and FM information signals and the durations of the involved system impulse responses. The bounds are independent of the bandwidths of the AM and FM functions. Two general applications are considered. First, the approximations are found to be useful for analyzing discrete-time nonlinear energy operators, including the Teager-Kaiser operator. Next, the approximation theorems lead to the selection of an optimal class of bandpass filters for use in a discrete multiband AM-FM demodulation system. The filter class selected is optimal in the sense of achieving the lower bound of a novel discrete uncertainty principle.

Modulation models for image processing and wavelet-based image demodulation

AM-FM modulation models for two- and higher-dimensional complex-valued nonstationary signals and images that are locally coherent but globally wideband are studied. Demodulation techniques are studied for demodulating both one-component and multicomponent signals. For the case of multicomponent signals immersed in noise, the individual components must be isolated by spectrally localized multiband filtering prior to demodulation. An algorithm for demodulating the filtered signal components is developed using a quasi-eigenfunction approximation, and bounds for the approximation error are given. After multiband filtering with Gabor wavelets, the filtered demodulation algorithm is used to estimate the dominant emergent frequencies of multicomponent images.<<ETX>>

A New Centralized Sensor Fusion-Tracking Methodology Based on Particle Filtering for Power-Aware Systems

In this paper, we address the problem of target tracking in a collaborative acoustic sensor network. To cope with the inherent characteristics and constraints of wireless sensor networks, we present a novel target-tracking algorithm with power-aware concerns. The underlying tracking methodology is described as a multiple-sensor tracking/fusion technique based on particle filtering. As discussed in the most recent literature, particle filtering is defined as an emerging Monte Carlo state estimation technique with proven superior performance in many target-tracking applications. More specifically, in our proposed method, each activated sensor transmits the received acoustic intensity and the direction of arrival (DOA) of the target to the sensor fusion center (a dedicated computing and storage platform, such as a microserver). The fusion center uses each received DOA to generate a set of estimations based on the state partition technique, as described later in this paper. In addition, a set of sensor weights is calculated based on the acoustic intensity received by each activated sensor. Next, the weighted sum of the estimates is used to generate the proposal distribution in the particle filter for sensor fusion. This technique renders a more accurate proposal distribution and, hence, yields more precise and robust estimations of the target using fewer samples than those of the traditional bootstrap filter. In addition, since the majority of the signal processing efficiently resides on the fusion center, the computation load at the sensor nodes is limited, which is desirable for power-aware systems. Last, the performance of the new tracking algorithm in various tracking scenarios is thoroughly studied and compared with standard tracking methods. As shown in the theory and demonstrated by our experimental results, the state-partition-based centralized particle filter reliably outperforms the traditional method in all experiments.

Entropy-based uncertainty measures for L/sup 2/(/spl Ropf//sup n/), /spl lscr//sup 2/(/spl Zopf/), and /spl lscr//sup 2/(/spl Zopf//N/spl Zopf/) with a Hirschman optimal transform for /spl lscr//sup 2/(/spl Zopf//N/spl Zopf/)

A process for the production of a permanently bonded polyester-polyolefin film laminate is disclosed herein. The process involves exposing the surface of polyester or polyolefin film to contact with a flame so as to prime the surface thereof and thereafter coating the primed surface of the film with a layer of a molten polyolefin or polyester, respectively. Flame priming of the polyester or polyolefin film results in a permanent surface modification of the film. Thus, the time lapse between the priming of the polyester or polyolefin film and the subsequent coating with the molten polymer may be a matter of days, if desired. Multi-layer laminates which comprise a substrate-polyester-polyolefin laminate, e.g., paperboard-polyester-polyolefin laminates, can be provided by the process of the present invention by providing a previously formed laminate of a substrate and a polyester film and flame priming the polyester surface of the laminate. Thereafter, a layer of a molten polyolefin is coated onto the primed polyester surface.