Image Enhancement by Elliptic Discrete Fourier Transforms

This paper describes a method of enhancement of grayscale and color image in the frequency domain by the pair of two elliptic discrete Fourier transforms (EDFT). Unlike the traditional discrete Fourier transform (DFT), the EDFT is parameterized and the parameter defines ellipses (not circles) around which the input data are rotated. Methods of the traditional DFT are widely used in image enhancement, and the transform rotates data of images around the circles. The presented method of image enhancement proposes processing images on different set of ellipses for the direct and inverse transforms. Our preliminary experimental examples show effectiveness of the proposed method. The Illustrative examples of image enhancement are given

Robust hashing for image authentication using quaternion discrete Fourier transform and log-polar transform

International audienceIn this work, a novel robust image hashing scheme for image authentication is proposed based on the combination of the quaternion discrete Fourier transform (QDFT) with the log-polar transform. QDFT offers a sound way to jointly deal with the three channels of color images. The key features of the present method rely on (i) the computation of a secondary image using a log-polar transform; and (ii) the extraction from this image of low frequency QDFT coefficients' magnitude. The final image hash is generated according to the correlation of these magnitude coefficients and is scrambled by a secret key to enhance the system security. Experiments were conducted in order to analyze and identify the most appropriate parameter values of the proposed method and also to compare its performance to some reference methods in terms of receiver operating characteristics curves. The results show that the proposed scheme offers a good sensitivity to image content alterations and is robust to the common content-preserving operations, and especially to large angle rotation operations

Elliptical Monogenic Wavelets for the analysis and processing of color images

International audienceThis paper studies and gives new algorithms for image processing based on monogenic wavelets. Existing greyscale monogenic filterbanks are reviewed and we reveal a lack of discussion about the synthesis part. The monogenic synthesis is therefore defined from the idea of wavelet modulation, and an innovative filterbank is constructed by using the Radon transform. The color extension is then investigated. First, the elliptical Fourier atom model is proposed to generalize theanalytic signal representation for vector-valued signals. Then a color Riesz-transform is defined so as to construct color elliptical monogenic wavelets. Our Radon-based monogenic filterbank can be easily extended to color according to this definition. The proposed wavelet representation provides efficient analysis of local features in terms of shape and color, thanks to the concepts of amplitude, phase, orientation, and ellipse parameters. The synthesis from local features is deeply studied. We conclude the article by defining the color local frequency, proposing an estimation algorithm

Quaternion-Based Improved Artificial Bee Colony Algorithm for Color Remote Sensing Image Edge Detection

As the color remote sensing image has the most notable features such as huge amount of data, rich image details, and the containing of too much noise, the edge detection becomes a grave challenge in processing of remote sensing image data. To explore a possible solution to the urgent problem, in this paper, we first introduced the quaternion into the representation of color image. In this way, a color can be represented and analyzed as a single entity. Then a novel artificial bee colony method named improved artificial bee colony which can improve the performance of conventional artificial bee colony was proposed. In this method, in order to balance the exploration and the exploitation, two new search equations were presented to generate candidate solutions in the employed bee phase and the onlookers phase, respectively. Additionally, some more reasonable artificial bee colony parameters were proposed to improve the performance of the artificial bee colony. Then we applied the proposed method to the quaternion vectors to perform the edge detection of color remote sensing image. Experimental results show that our method can get a better edge detection effect than other methods

Denoising of Sphere- and SO(3)-Valued Data by Relaxed Tikhonov Regularization

Manifold-valued signal- and image processing has received attention due to modern image acquisition techniques. Recently, Condat (IEEE Trans. Signal Proc.) proposed a convex relaxation of the Tikhonov-regularized nonconvex problem for denoising circle-valued data. Using Schur complement arguments, we show that this variational model can be simplified while leading to the same solution. Our simplified model can be generalized to higher dimensional spheres and to SO(3)-valued data, where we rely on the quaternion representation of the latter. Standard algorithms from convex analysis can be applied to solve the resulting convex minimization problem. As proof-of-the-concept, we use the alternating direction method of minimizers to demonstrate the denoising behavior of the proposed approach

Data-driven time-frequency analysis of multivariate data

Empirical Mode Decomposition (EMD) is a data-driven method for the decomposition and time-frequency analysis of real world nonstationary signals. Its main advantages over other time-frequency methods are its locality, data-driven nature, multiresolution-based decomposition, higher time-frequency resolution and its ability to capture oscillation of any type (nonharmonic signals). These properties have made EMD a viable tool for real world nonstationary data analysis. Recent advances in sensor and data acquisition technologies have brought to light new classes of signals containing typically several data channels. Currently, such signals are almost invariably processed channel-wise, which is suboptimal. It is, therefore, imperative to design multivariate extensions of the existing nonlinear and nonstationary analysis algorithms as they are expected to give more insight into the dynamics and the interdependence between multiple channels of such signals. To this end, this thesis presents multivariate extensions of the empirical mode de- composition algorithm and illustrates their advantages with regards to multivariate non- stationary data analysis. Some important properties of such extensions are also explored, including their ability to exhibit wavelet-like dyadic filter bank structures for white Gaussian noise (WGN), and their capacity to align similar oscillatory modes from multiple data channels. Owing to the generality of the proposed methods, an improved multi- variate EMD-based algorithm is introduced which solves some inherent problems in the original EMD algorithm. Finally, to demonstrate the potential of the proposed methods, simulations on the fusion of multiple real world signals (wind, images and inertial body motion data) support the analysis