Fast complexified quaternion Fourier transform

A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex quaternion-valued. It is shown how to compute the transform using four standard complex Fourier transforms and the properties of the transform are briefly discussed

Multilayer Security of RGB Image in Discrete Hartley Domain

In this article, we present RGB image encryption and decryption using random matrix affine cipher (RMAC) associated with discrete Hartley transform (DHT) and random matrix shift cipher (RMSC). The parameters in RMAC and RMSC phases act as two series of secret keys whose arrangement is imperative in the proposed algorithm. The computer simulations with results and examples are given to analyze the efficiency of the proposed approach. Further, security analysis and comparison with the prior techniques successfully supports the robustness and validation of the proposed technique

Complexity over Uncertainty in Generalized Representational\ud Information Theory (GRIT): A Structure-Sensitive General\ud Theory of Information

What is information? Although researchers have used the construct of information liberally to refer to pertinent forms of domain-specific knowledge, relatively few have attempted to generalize and standardize the construct. Shannon and Weaver(1949)offered the best known attempt at a quantitative generalization in terms of the number of discriminable symbols required to communicate the state of an uncertain event. This idea, although useful, does not capture the role that structural context and complexity play in the process of understanding an event as being informative. In what follows, we discuss the limitations and futility of any generalization (and particularly, Shannon’s) that is not based on the way that agents extract patterns from their environment. More specifically, we shall argue that agent concept acquisition, and not the communication of\ud states of uncertainty, lie at the heart of generalized information, and that the best way of characterizing information is via the relative gain or loss in concept complexity that is experienced when a set of known entities (regardless of their nature or domain of origin) changes. We show that Representational Information Theory perfectly captures this crucial aspect of information and conclude with the first generalization of Representational Information Theory (RIT) to continuous domains

Shape basis interpretation for monocular deformable 3D reconstruction

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper, we propose a novel interpretable shape model to encode object non-rigidity. We first use the initial frames of a monocular video to recover a rest shape, used later to compute a dissimilarity measure based on a distance matrix measurement. Spectral analysis is then applied to this matrix to obtain a reduced shape basis, that in contrast to existing approaches, can be physically interpreted. In turn, these pre-computed shape bases are used to linearly span the deformation of a wide variety of objects. We introduce the low-rank basis into a sequential approach to recover both camera motion and non-rigid shape from the monocular video, by simply optimizing the weights of the linear combination using bundle adjustment. Since the number of parameters to optimize per frame is relatively small, specially when physical priors are considered, our approach is fast and can potentially run in real time. Validation is done in a wide variety of real-world objects, undergoing both inextensible and extensible deformations. Our approach achieves remarkable robustness to artifacts such as noisy and missing measurements and shows an improved performance to competing methods.Peer ReviewedPostprint (author's final draft

Hypercomplex Spectral Signal Representations for the Processing and Analysis of Images

In the present work hypercomplex spectral methods of the processing and analysis of images are introduced. The thesis is divided into three main chapters. First the quaternionic Fourier transform (QFT) for 2D signals is presented and its main properties are investigated. The QFT is closely related to the 2D Fourier transform and to the 2D Hartley transform. Similarities and differences of these three transforms are investigated with special emphasis on the symmetry properties. The Clifford Fourier transform is presented as nD generalization of the QFT. Secondly the concept of the phase of a signal is considered. We distinguish the global, the local and the instantaneous phase of a signal. It is shown how these 1D concepts can be extended to 2D using the QFT. In order to extend the concept of global phase we introduce the notion of the quaternionic analytic signal of a real signal. Defining quaternionic Gabor filters leads to the definition of the local quaternionic phase. The relation between signal structure and local signal phase, which is well-known in 1D, is extended to 2D using the quaternionic phase. In the third part two application of the theory are presented. For the image processing tasks of disparity estimation and texture segmentation there exist approaches which are based on the (complex) local phase. These methods are extended to the use of the quaternionic phase. In either case the properties of the complex approaches are preserved while new features are added by using the quaternionic phase

Intrinsic and extrinsic thermodynamics for stochastic population processes with multi-level large-deviation structure

A set of core features is set forth as the essence of a thermodynamic description, which derive from large-deviation properties in systems with hierarchies of timescales, but which are \emph{not} dependent upon conservation laws or microscopic reversibility in the substrate hosting the process. The most fundamental elements are the concept of a macrostate in relation to the large-deviation entropy, and the decomposition of contributions to irreversibility among interacting subsystems, which is the origin of the dependence on a concept of heat in both classical and stochastic thermodynamics. A natural decomposition is shown to exist, into a relative entropy and a housekeeping entropy rate, which define respectively the \textit{intensive} thermodynamics of a system and an \textit{extensive} thermodynamic vector embedding the system in its context. Both intensive and extensive components are functions of Hartley information of the momentary system stationary state, which is information \emph{about} the joint effect of system processes on its contribution to irreversibility. Results are derived for stochastic Chemical Reaction Networks, including a Legendre duality for the housekeeping entropy rate to thermodynamically characterize fully-irreversible processes on an equal footing with those at the opposite limit of detailed-balance. The work is meant to encourage development of inherent thermodynamic descriptions for rule-based systems and the living state, which are not conceived as reductive explanations to heat flows

Spatial Perspective Transform Estimation from Fourier Spectrum Analysis of 2D Patterns in 3D Space

A novel approach to 3D surface imaging is proposed, allowing for the continuous sampling of 3D surfaces to extract localized perspective transformation coefficients from Fourier spectrum analysis of projected patterns. The mathematical relationship for Spatial-Fourier Transformation Pairs is derived, defining the transformation of spatial transformed planar surfaces in the Discrete Fourier Transform spectrum. The mathematical relationship for the twelve degrees of freedom in perspective transformation is defined and validated, asserting congruity with independent and uniform transform pairs for spatial Euclidean, similarity, affine and perspective transformations. This work expands on previously derived affine Spatial-Fourier Transformation Pairs and characterizes its implications towards 3D surface imaging as a means of augmenting (X,Y,Z)-(R,G,B) point-clouds to include additional information from localized sampling of pattern transformations