Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport

In this work, we propose a novel method for quantifying distances between Toeplitz structured covariance matrices. By exploiting the spectral representation of Toeplitz matrices, the proposed distance measure is defined based on an optimal mass transport problem in the spectral domain. This may then be interpreted in the covariance domain, suggesting a natural way of interpolating and extrapolating Toeplitz matrices, such that the positive semi-definiteness and the Toeplitz structure of these matrices are preserved. The proposed distance measure is also shown to be contractive with respect to both additive and multiplicative noise, and thereby allows for a quantification of the decreased distance between signals when these are corrupted by noise. Finally, we illustrate how this approach can be used for several applications in signal processing. In particular, we consider interpolation and extrapolation of Toeplitz matrices, as well as clustering problems and tracking of slowly varying stochastic processes

Matrix-valued Monge-Kantorovich Optimal Mass Transport

We formulate an optimal transport problem for matrix-valued density functions. This is pertinent in the spectral analysis of multivariable time-series. The "mass" represents energy at various frequencies whereas, in addition to a usual transportation cost across frequencies, a cost of rotation is also taken into account. We show that it is natural to seek the transportation plan in the tensor product of the spaces for the two matrix-valued marginals. In contrast to the classical Monge-Kantorovich setting, the transportation plan is no longer supported on a thin zero-measure set.Comment: 11 page

Analyzing eyebrow region for morphed image detection

Facial images in passports are designated as primary identifiers for the verification of travelers according to the International Civil Aviation Organization (ICAO). Hence, it is important to ascertain the sanctity of the facial images stored in the electronic Machine-Readable Travel Document (eMRTD). With the introduction of automated border control (ABC) systems that rely on face recognition for the verification of travelers, it is even more crucial to have a system to ensure that the image stored in the eMRTD is free from any alteration that can hinder or abuse the normal working of a facial recognition system. One such attack against these systems is the face-morphing attack. Even though many techniques exist to detect morphed images, morphing algorithms are also improving to evade these detections. In this work, we analyze the eyebrow region for morphed image detection. The proposed method is based on analyzing the frequency content of the eyebrow region. The method was evaluated on two datasets that each consisted of morphed images created using two algorithms. The findings suggest that the proposed method can serve as a valuable tool in morphed image detection, and can be used in various applications where image authenticity is critical

Conal Distances Between Rational Spectral Densities

This paper generalizes Thompson and Hilbert metrics to the space of spectral densities. The resulting complete metric space has the differentiable structure of a Finsler manifold with explicit geodesics. The corresponding distances are filtering invariant, can be computed efficiently, and admit geodesic paths that preserve rationality; these are properties of fundamental importance in many engineering applications.European Research Counci

Analysis of Heat Transfer on Turbulence Generating Ribs using Dynamic Mode Decomposition

Ducts with turbulence-promoting ribs are common in heat transfer applications. This study uses a recent modal extraction technique called Dynamic Mode Decomposition (DMD) to determine mode shapes of the spatially and temporally complex flowfield inside a ribbed duct. One subject missing from current literature is a method of directly linking a mode to a certain engineering quantity of interest. Presented is a generalized methodology for producing such a link utilizing the data from the DMD analysis. Theory suggests exciting the modes which are identified may cause the flow to change in such a way to promote the quantity of interest, in this case, heat transfer. This theory is tested by contouring the walls of the duct by the extracted mode shapes. The test procedure is taken from an industrial perspective. An initial, unmodified geometry provides a baseline for comparison to later contoured models. The initial case is run as a steady-state Reynolds-Averaged Navier-Stokes model. Large-Eddy Simulation generates the necessary data for the DMD analysis. Several mode shapes extracted from the flow are applied to the duct walls and run again in the RANS model, then compared to the baseline, and their relative performance examined

PHOTOTHERMAL AND PHOTOCHEMICAL STRATEGIES FOR LIGHTINDUCED SHAPE-MORPHING OF SOFT MATERIALS

Engineering materials with the capability to transform energy from photons into mechanical work is an outstanding technical challenge with implications across myriad disciplines. Despite decades of work in this area, comprehensive understanding of how to prescribe shape change and work output in photoactive systems remains limited. To this end, this dissertation explores strategies to assemble photothermal and photochemical moieties in soft material systems to fabricate photoaddressable devices capable of specific shape changes upon illumination. Chapters 2 and 3 describe a methodology for spatially patterning plasmonic nanoparticles in liquid crystal elastomer fibers and sheets to specify local photothermally-induced strain profiles. Using this platform, devices capable of deployment into specific 3D configurations in response to both waveguided light and flood illumination are demonstrated. Next, to circumvent the inherent limitation of approaches based on photothermal effects, two new strategies for shape programming azobenzene-containing materials are explored for athermal photoactuation. In Chapter 4, a new material platform is presented that uses azobenzene incorporated into the backbone of polymers to modulate crystallinity on-demand via photoisomerization for next-generation shape memory systems. Next, host-guest cyclodextrin-azobenzene systems are shown in Chapter 5 to enable robust, re-programmable shape changes in hydrogels. Lastly, in Chapter 6 an outlook for the future of the field and an identification of areas in need of further study are presented

Face morphing detection in the presence of printing/scanning and heterogeneous image sources

Face morphing represents nowadays a big security threat in the context of electronic identity documents as well as an interesting challenge for researchers in the field of face recognition. Despite of the good performance obtained by state-of-the-art approaches on digital images, no satisfactory solutions have been identified so far to deal with cross-database testing and printed-scanned images (typically used in many countries for document issuing). In this work, novel approaches are proposed to train Deep Neural Networks for morphing detection: in particular generation of simulated printed-scanned images together with other data augmentation strategies and pre-training on large face recognition datasets, allowed to reach state-of-the-art accuracy on challenging datasets from heterogeneous image sources