2-D Prony-Huang Transform: A New Tool for 2-D Spectral Analysis

This work proposes an extension of the 1-D Hilbert Huang transform for the analysis of images. The proposed method consists in (i) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode decomposition procedure, and (ii) providing a local spectral analysis of the obtained IMFs in order to get the local amplitudes, frequencies, and orientations. For the decomposition step, we propose two robust 2-D mode decompositions based on non-smooth convex optimization: a "Genuine 2-D" approach, that constrains the local extrema of the IMFs, and a "Pseudo 2-D" approach, which constrains separately the extrema of lines, columns, and diagonals. The spectral analysis step is based on Prony annihilation property that is applied on small square patches of the IMFs. The resulting 2-D Prony-Huang transform is validated on simulated and real data.Comment: 24 pages, 7 figure

Single-shot fringe pattern phase retrieval using improved period-guided bidimensional empirical mode decomposition and Hilbert transform

Fringe pattern analysis is the central aspect of numerous optical measurement methods, e.g., interferometry, fringe projection, digital holography, quantitative phase microscopy. Experimental fringe patterns always contain significant features originating from fluctuating environment, optical system and illumination quality, and the sample itself that severely affect analysis outcome. Before the stage of phase retrieval (information decoding) interferogram needs proper filtering, which minimizes the impact of mentioned issues. In this paper we propose fully automatic and adaptive fringe pattern pre-processing technique - improved period guided bidimensional empirical mode decomposition algorithm (iPGBEMD). It is based on our previous work about PGBEMD which eliminated the mode-mixing phenomenon and made the empirical mode decomposition fully adaptive. In present work we overcame key problems of original PGBEMD – we have considerably increased algorithm’s application range and shortened computation time several-fold. We proposed three solutions to the problem of erroneous decomposition for very low fringe amplitude images, which limited original PGBEMD significantly and we have chosen the best one among them after comprehensive analysis. Several acceleration methods were also proposed and merged to ensure the best results. We combined our improved pre-processing algorithm with the Hilbert Spiral Transform to receive complete, consistent, and versatile fringe pattern analysis path. Quality and effectiveness evaluation, in comparison with selected reference methods, is provided using numerical simulations and experimental fringe data

BEMDEC: An Adaptive and Robust Methodology for Digital Image Feature Extraction

The intriguing study of feature extraction, and edge detection in particular, has, as a result of the increased use of imagery, drawn even more attention not just from the field of computer science but also from a variety of scientific fields. However, various challenges surrounding the formulation of feature extraction operator, particularly of edges, which is capable of satisfying the necessary properties of low probability of error (i.e., failure of marking true edges), accuracy, and consistent response to a single edge, continue to persist. Moreover, it should be pointed out that most of the work in the area of feature extraction has been focused on improving many of the existing approaches rather than devising or adopting new ones. In the image processing subfield, where the needs constantly change, we must equally change the way we think. In this digital world where the use of images, for variety of purposes, continues to increase, researchers, if they are serious about addressing the aforementioned limitations, must be able to think outside the box and step away from the usual in order to overcome these challenges. In this dissertation, we propose an adaptive and robust, yet simple, digital image features detection methodology using bidimensional empirical mode decomposition (BEMD), a sifting process that decomposes a signal into its two-dimensional (2D) bidimensional intrinsic mode functions (BIMFs). The method is further extended to detect corners and curves, and as such, dubbed as BEMDEC, indicating its ability to detect edges, corners and curves. In addition to the application of BEMD, a unique combination of a flexible envelope estimation algorithm, stopping criteria and boundary adjustment made the realization of this multi-feature detector possible. Further application of two morphological operators of binarization and thinning adds to the quality of the operator

Cycle-Consistent Adversarial Networks and Fast Adaptive Bi-Dimensional Empirical Mode Decomposition for Style Transfer

Recently, research endeavors have shown the potentiality of Cycle-Consistent Adversarial Networks (CycleGAN) in style transfer. In Cycle-Consistent Adversarial Networks, the consistency loss is introduced to measure the difference between the original images and the reconstructed in both directions, forward and backward. In this work, the combination of Cycle-Consistent Adversarial Networks with Fast and Adaptive Bidimensional Empirical Mode Decomposition (FABEMD) is proposed to perform style transfer on images. In the proposed approach the cycle-consistency loss is modified to include the differences between the extracted Intrinsic Mode Functions (BIMFs) images. Instead of an estimation of pixel-to-pixel difference between the produced and input images, the FABEMD is applied and the extracted BIMFs are involved in the computation of the total cycle loss. This method enriches the computation of the total loss in a content-to-content and style-to-style comparison by connecting the spatial information to the frequency components. The experimental results reveal that the proposed method is efficient and produces qualitative results comparable to state-of-the-art methods

A novel approach for breast ultrasound classification using two-dimensional empirical mode decomposition and multiple features

Aim: Breast cancer stands as a prominent cause of female mortality on a global scale, underscoring the critical need for precise and efficient diagnostic techniques. This research significantly enriches the body of knowledge pertaining to breast cancer classification, especially when employing breast ultrasound images, by introducing a novel method rooted in the two dimensional empirical mode decomposition (biEMD) method. In this study, an evaluation of the classification performance is proposed based on various texture features of breast ultrasound images and their corresponding biEMD subbands. Methods: A total of 437 benign and 210 malignant breast ultrasound images were analyzed, preprocessed, and decomposed into three biEMD sub-bands. A variety of features, including the Gray Level Co-occurrence Matrix (GLCM), Local Binary Patterns (LBP), and Histogram of Oriented Gradient (HOG), were extracted, and a feature selection process was performed using the least absolute shrinkage and selection operator method. The study employed GLCM, LBP and HOG, and machine learning techniques, including artificial neural networks (ANN), k-nearest neighbors (kNN), the ensemble method, and statistical discriminant analysis, to classify benign and malignant cases. The classification performance, measured through Area Under the Curve (AUC), accuracy, and F1 score, was evaluated using a 10-fold cross-validation approach. Results: The study showed that using the ANN method and hybrid features (GLCM+LBP+HOG) from BUS images' biEMD sub-bands led to excellent performance, with an AUC of 0.9945, an accuracy of 0.9644, and an F1 score of 0.9668. This has revealed the effectiveness of the biEMD method for classifying breast tumor types from ultrasound images. Conclusion: The obtained results have revealed the effectiveness of the biEMD method for classifying breast tumor types from ultrasound images, demonstrating high-performance classification using the proposed approach