Sparse representation of two- and three-dimensional images with fractional Fourier, Hartley, linear canonical, and Haar wavelet transforms

Sparse recovery aims to reconstruct signals that are sparse in a linear transform domain from a heavily underdetermined set of measurements. The success of sparse recovery relies critically on the knowledge of transform domains that give compressible representations of the signal of interest. Here we consider two- and three-dimensional images, and investigate various multi-dimensional transforms in terms of the compressibility of the resultant coefficients. Specifically, we compare the fractional Fourier (FRT) and linear canonical transforms (LCT), which are generalized versions of the Fourier transform (FT), as well as Hartley and simplified fractional Hartley transforms, which differ from corresponding Fourier transforms in that they produce real outputs for real inputs. We also examine a cascade approach to improve transform-domain sparsity, where the Haar wavelet transform is applied following an initial Hartley transform. To compare the various methods, images are recovered from a subset of coefficients in the respective transform domains. The number of coefficients that are retained in the subset are varied systematically to examine the level of signal sparsity in each transform domain. Recovery performance is assessed via the structural similarity index (SSIM) and mean squared error (MSE) in reference to original images. Our analyses show that FRT and LCT transform yield the most sparse representations among the tested transforms as dictated by the improved quality of the recovered images. Furthermore, the cascade approach improves transform-domain sparsity among techniques applied on small image patches. © 2017 Elsevier Lt

Diabetic plantar pressure analysis using image fusion

Plantar pressure images analysis is the key issue of designing comfortable shoe products through last customizing system, which has attracted the researchers’ curiosity toward image fusion as an application of medical and industrial imaging. In the current work, image fusion has been applied using wavelet transform and compared with Laplace Pyramid. Using image fusion rules of Mean-Max, we presented a plantar pressure image fusion method employing haar wavelet transform. It was compared in different composition layers with the Laplace pyramid transform. The experimental studies deployed the haar, db2, sym4, coif2, and bior5.5 wavelet basis functions for image fusion under decomposition layers of 3, 4, and 5. Evaluation metrics were measured in the case of the different layer number of wavelet decomposition to determine the best decomposition level and to evaluate the fused image quality using with different wavelet functions. The best wavelet basis function and decomposition layers were selected through the analysis and the evaluation measurements. This study established that haar wavelet transform with five decomposition levels on plantar pressure image achieved superior performance of 89.2817% mean, 89.4913% standard deviation, 5.4196 average gradient, 14.3364 spatial frequency, 5.9323 information entropy and 0.2206 cross entropy

Numerical Solution for Linear State Space Systems using Haar Wavelets Method

في هذا البحث، تم استخدام طريقة الموبجات الشعرية لإيجاد حل تقريبي لأنظمة فضاء الحالة الخطية. وان تقنية الحل هي تحويل أنظمة فضاء الحالة الخطية إلى نظام من المعادلات الخطية للفاصل الزمني من 0 إلى . كما يمكن تعزيز دقة متغيرات الحالة عن طريق زيادة دقة موجات هار ويفلت. تم تطبيق الطريقة المقترحة لأمثلة مختلفة وتم توضيح نتائج المحاكاة بالرسوم البيانية ومقارنتها بالحل الدقيق.In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Connected Attribute Filtering Based on Contour Smoothness

A new attribute measuring the contour smoothness of 2-D objects is presented in the context of morphological attribute filtering. The attribute is based on the ratio of the circularity and non-compactness, and has a maximum of 1 for a perfect circle. It decreases as the object boundary becomes irregular. Computation on hierarchical image representation structures relies on five auxiliary data members and is rapid. Contour smoothness is a suitable descriptor for detecting and discriminating man-made structures from other image features. An example is demonstrated on a very-high-resolution satellite image using connected pattern spectra and the switchboard platform

Machine learning techniques for high dimensional data

This thesis presents data processing techniques for three different but related application areas: embedding learning for classification, fusion of low bit depth images and 3D reconstruction from 2D images. For embedding learning for classification, a novel manifold embedding method is proposed for the automated processing of large, varied data sets. The method is based on binary classification, where the embeddings are constructed so as to determine one or more unique features for each class individually from a given dataset. The proposed method is applied to examples of multiclass classification that are relevant for large scale data processing for surveillance (e.g. face recognition), where the aim is to augment decision making by reducing extremely large sets of data to a manageable level before displaying the selected subset of data to a human operator. In addition, an indicator for a weighted pairwise constraint is proposed to balance the contributions from different classes to the final optimisation, in order to better control the relative positions between the important data samples from either the same class (intraclass) or different classes (interclass). The effectiveness of the proposed method is evaluated through comparison with seven existing techniques for embedding learning, using four established databases of faces, consisting of various poses, lighting conditions and facial expressions, as well as two standard text datasets. The proposed method performs better than these existing techniques, especially for cases with small sets of training data samples. For fusion of low bit depth images, using low bit depth images instead of full images offers a number of advantages for aerial imaging with UAVs, where there is a limited transmission rate/bandwidth. For example, reducing the need for data transmission, removing superfluous details, and reducing computational loading of on-board platforms (especially for small or micro-scale UAVs). The main drawback of using low bit depth imagery is discarding image details of the scene. Fortunately, this can be reconstructed by fusing a sequence of related low bit depth images, which have been properly aligned. To reduce computational complexity and obtain a less distorted result, a similarity transformation is used to approximate the geometric alignment between two images of the same scene. The transformation is estimated using a phase correlation technique. It is shown that that the phase correlation method is capable of registering low bit depth images, without any modi�cation, or any pre and/or post-processing. For 3D reconstruction from 2D images, a method is proposed to deal with the dense reconstruction after a sparse reconstruction (i.e. a sparse 3D point cloud) has been created employing the structure from motion technique. Instead of generating a dense 3D point cloud, this proposed method forms a triangle by three points in the sparse point cloud, and then maps the corresponding components in the 2D images back to the point cloud. Compared to the existing methods that use a similar approach, this method reduces the computational cost. Instated of utilising every triangle in the 3D space to do the mapping from 2D to 3D, it uses a large triangle to replace a number of small triangles for flat and almost flat areas. Compared to the reconstruction result obtained by existing techniques that aim to generate a dense point cloud, the proposed method can achieve a better result while the computational cost is comparable

Registration of histology and magnetic resonance imaging of the brain

Combining histology and non-invasive imaging has been attracting the attention of the medical imaging community for a long time, due to its potential to correlate macroscopic information with the underlying microscopic properties of tissues. Histology is an invasive procedure that disrupts the spatial arrangement of the tissue components but enables visualisation and characterisation at a cellular level. In contrast, macroscopic imaging allows non-invasive acquisition of volumetric information but does not provide any microscopic details. Through the establishment of spatial correspondences obtained via image registration, it is possible to compare micro- and macroscopic information and to recover the original histological arrangement in three dimensions. In this thesis, I present: (i) a survey of the literature relative to methods for histology reconstruction with and without the help of 3D medical imaging; (ii) a graph-theoretic method for histology volume reconstruction from sets of 2D sections, without external information; (iii) a method for multimodal 2D linear registration between histology and MRI based on partial matching of shape-informative boundaries