During the last decade, there has been an increased focus on representing images using mathematical expressions. The initial stages towards achieving this process have already been accomplished in the literature. However, several efforts are still required to convert the image into fully mathematical expressions. The majority of the work involved transforming the image into simplified representations using a codebook, which poses a challenge to achieving the main goal. In this work, a new transformation has been introduced to represent an image as small units. This approach enables direct manipulation of image blocks rather than individual pixels. The transformation is denoted as the self-encoded chimera transform (SECT). Being different from traditional transforms such as discrete cosine transform (DCT), and discrete wavelet transform (DWT), the image representation via the SECT remains in the time domain. The SECT can be calculated across multiple layers to enhance the quality of reconstruction. Each layer is represented by three encoded arrays. The encoding arrays are calculated using simple statistics. The SECT is applied to several standard images and achieved better quality in compare to both State-of-the-art and Standard transforms. Further analysis indicates that quality of the reconstruction improves when number of layers of the SECT has increased.

Mathematically representing an image with only a small number of coefficients has been attempted a few times. These attempts represent initial steps to achieve this goal and showed promising results by either working on a small image block size or utilizing a codebook built using a complex operation. The use of the codebook complicated the entire transformation process. In this work, we overcome these difficulties by developing a new scheme called systematic multichimera transform (SMCT). This transform employs simple mathematical functions called fractal half functions to independently build a codebook of image contents and size. These functions satisfy the symmetry under fractal form while breaking the orthogonality condition. The transform can deal with different image block sizes such as 8×8, 16×16, and 32×32. The encoding process is conducted by repetitively finding the similarity between image blocks and codebook blocks to achieve data reduction and preserve important information. The coefficients of the matching process are then employed in the decoding process to reconstruct the image. SMCT produced the highest structural similarity index (SSIM) and a competitive Peak Signal to Noise Ratio (PSNR) over the standard discrete wavelet transform (DWT) and discrete cosine transform (DCT) without degrading important image content.

We present a fast heuristic approach for solving a binary multiple instance learning (MIL) problem, which consists in discriminating between two kinds of item sets: the sets are called bags and the items inside them are called instances. Assuming that only two classes of instances are allowed, a common standard hypothesis states that a bag is positive if it contains at least a positive instance and it is negative when all its instances are negative. Our approach constructs a MIL separating hyperplane by preliminary fixing the normal and reducing the learning phase to a univariate nonsmooth optimization problem, which can be quickly solved by simply exploring the kink points. Numerical results are presented on a set of test problems drawn from the literature.

In the multiple instances learning framework, instances are arranged into bags, each bag contains several instances, the labels of each instance are not available but the label is available for each bag. Whilst in a single instance learning each instance is connected with the label that contains a single feature vector. This paper examines the distinction between these paradigms to see if it is appropriate, to cast the problem within a multiple instance framework. In single-instance learning, two datasets are applied (students’ dataset and iris dataset) using Naïve Bayes Classifier (NBC), Multilayer perceptron (MLP), Support Vector Machine (SVM), and Sequential Minimal Optimization (SMO), while SimpleMI, MIWrapper, and MIBoost in multiple instances learning. Leave One Out Cross-Validation (LOOCV), five and ten folds Cross-Validation techniques (5-CV, 10-CV) are implemented to evaluate the classification results. A comparison of the result of these techniques is made, several algorithms are found to be more effective for classification in the multiple instances learning. The suitable algorithms for the students' dataset are MIBoost with MLP for LOOCV with an accuracy of 75%, whereas SimpleMI with SMO for the iris dataset is the suitable algorithm for 10-CV with an accuracy of 99.33%.

With the development of mobile technology, the usage of media data has increased dramatically. Therefore, data reduction represents a research field to maintain valuable information. In this paper, a new scheme called Multi Chimera Transform (MCT) based on data reduction with high information preservation, which aims to improve the reconstructed data by producing three parameters from each 16×16 block of data, is proposed. MCT is a 2D transform that depends on constructing a codebook of 256 picked blocks from some selected images which have a low similarity. The proposed transformation was applied on solid and soft biometric modalities of AR database, giving high information preservation with small resulted file size. The proposed method produced outstanding performance compared with KLT and WT in terms of SSIM and PSNR. The highest SSIM was 0.87 for the proposed scheme MCT of the full image of AR database, while the existed method KLT and WT had 0.81 and 0.68, respectively. In addition, the highest PSNR was 27.23 dB for the proposed scheme on warp facial image of AR database, while the existed methods KLT and WT had 24.70 dB and 21.79 dB, respectively.

A novel scheme is presented for image compression using a compatible form called Chimera. This form represents a new transformation for the image pixels. The compression methods generally look for image division to obtain small parts of an image called blocks. These blocks contain limited predicted patterns such as flat area, simple slope, and single edge inside images. The block content of these images represent a special form of data which be reformed using simple masks to obtain a compressed representation. The compression representation is different according to the type of transform function which represents the preprocessing operation prior the coding step. The cost of any image transformation is represented by two main parameters which are the size of compressed block and the error in reconstructed block. Our proposed Chimera Transform (CT) shows a robustness against other transform such as Discrete Cosine Transform (DCT), Wavelet Transform (WT) and Karhunen-Loeve Transform (KLT). The suggested approach is designed to compress a specific data type which are the images, and this represents the first powerful characteristic of this transform. Additionally, the reconstructed image using Chimera transform has a small size with low error which could be considered as the second characteristic of the suggested approach. Our results show a Peak Signal to Noise Ratio (PSNR) enhancement of 2.0272 for DCT, 1.179 for WT and 4.301 for KLT. In addition, a Structural Similarity Index Measure (SSIM) enhancement of 0.1108 for DCT, 0.051 for WT and 0.175 for KLT.

Image compression is one of the most interesting fields of image processing that is used to reduce image size. 2D curve-fitting is a method that converts the image data (pixel values) to a set of mathematical equations that are used to represent the image. These equations have a fixed form with a few coefficients estimated from the image which has been divided into several blocks. Since the number of coefficients is lower than the original block pixel size, it can be used as a tool for image compression. In this paper, a new curve-fitting model has been proposed to be derived from the symmetric function (hyperbolic tangent) with only three coefficients. The main disadvantages of previous approaches were the additional errors and degradation of edges of the reconstructed image, as well as the blocking effect. To overcome this deficiency, it is proposed that this symmetric hyperbolic tangent (tanh) function be used instead of the classical 1st- and 2nd-order curve-fitting functions which are asymmetric for reformulating the blocks of the image. Depending on the symmetric property of hyperbolic tangent function, this will reduce the reconstruction error and improve fine details and texture of the reconstructed image. The results of this work have been tested and compared with 1st-order curve-fitting, and standard image compression (JPEG) methods. The main advantages of the proposed approach are: strengthening the edges of the image, removing the blocking effect, improving the Structural SIMilarity (SSIM) index, and increasing the Peak Signal-to-Noise Ratio (PSNR) up to 20 dB. Simulation results show that the proposed method has a significant improvement on the objective and subjective quality of the reconstructed image.

Image compression is one of the most important fields of image processing. Because of the rapid development of image acquisition which will increase the image size, and in turn requires bigger storage space. JPEG has been considered as the most famous and applicable algorithm for image compression; however, it has shortfalls for some image types. Hence, new techniques are required to improve the quality of reconstructed images as well as to increase the compression ratio. The work in this paper introduces a scheme to enhance the JPEG algorithm. The proposed scheme is a new method which shrinks and stretches images using a smooth filter. In order to remove the blurring artifact which would be developed from shrinking and stretching the image, a hyperbolic function (tanh) is used to enhance the quality of the reconstructed image. Furthermore, the new approach achieves higher compression ratio for the same image quality, and/or better image quality for the same compression ratio than ordinary JPEG with respect to large size and more complex content images. However, it is an application for optimization to enhance the quality (PSNR and SSIM), of the reconstructed image and to reduce the size of the compressed image, especially for large size images.

We introduce a method for edge detection which is based on clustering the pixels representing any given digital image into two sets (the edge pixels and the non-edge ones). The process is based on associating to each pixel an appropriate vector representing the differences in brightness w.r.t. the surrounding pixels. Clustering is driven by the norms of such vectors, thus it takes place in \(\mathbb {R}\), which allows us to use a (simple) DC (Difference of Convex) optimization algorithm to get the clusters. A novel thinning technique, based on calculation of the edge phase angles, refines the classification obtained by the clustering algorithm. The results of some numerical experiments are also provided.

In this paper, a new approach is introduced to detect the edges of any kind of grayscale image by using the k-means clustering algorithm, where three novel features are proposed by taking the advantage of the similarity of the image pixel with its eight surrounding neighbors through feeding these features as attributes to the clustering system. This method of edge detection does not use either any smoothing filter or threshold values. The experimental results show that an acceptable detection of the edges is done.

We describe an optimization-based method for tackling the classic image processing problem known as edge detection and we formulate it in the form of a classification one. The novelty of the approach is in the use of spherical separation as a classification tool in the image processing framework. Spherical separation consists in separating by means of a sphere two given discrete point-sets in a finite dimensional Euclidean space; in our context the two sets are the edge points and the non-edge points, respectively, in the digital representation of a given image. Assuming that the center of the sphere is fixed, the problem reduces to the minimization of a convex and nonsmooth function of just one variable, which can be effectively solved by means of an “ad hoc” bisection method. The results of our experiments on some edge detection benchmark images are provided.

In this paper an Electronic Nose (ENose) is presented which is designed for both at identifying the gas type and if it is pure or not, and at estimating the concentrations of the components of that mixture of LPG gases (Methane, Hexane, or Hydrogen) and Hydrogen Sulfide produced always inside the refineries. Our system contains 8 sensors, 5 of them are gas sensors (of the class TGS from FIGARO USA, INC., the sensing element of two of them is catalytic (TGS-6810 and TGS-6812), the other two its sensing element is a tin dioxide (SnO2) semiconductor (TGS-825 and TGS-2611) and the last one is an oxygen sensor (KE-50)), the remaining three sensors are auxiliary sensors for measuring a temperature and humidity (HTG–3535), and a pressure sensor (XFAM from Fujikura Ltd.). The proposed hardware–software system uses some least squares principles for classification and regression to identify at first a new gas sample, if it is pure or mixture, and then to estimate their concentrations, respectively. In particular we adopt a training model using the least squares approach to teach the system how to discriminate among different gases.

The E-nose system reported is designed to address the problem of early and distributed detection of dangerous gas mixtures. It is made of a selection of Commercial Off-The-Shelf (COTS) sensors, facing a small volume chamber, whose signals are conditioned and sampled by a multifunction board connected to a personal computer. A program, implementing efficient Support Vector Machine and least square model algorithms, executes the gas classification, the concentration estimation and warns about set risk thresholds overcoming. The system training was performed in laboratory, over a wide range of concentrations in air of: methane, hexane, pentane, and hydrogen sulfide. Other boundary conditions, such as oxygen concentration, temperature and RH are also taken into account. The overall cost of the system can be made very low, adopting an embedded architecture approach, allowing to overcome the limitations of the monitoring systems deployment inside refinery plants due to the high costs of traditional GC systems.

Electronic noses are intelligent systems having the ability to identify and quantify different gases. They are capable to handle large data sets and to perform quite complex signal processing by employing commercial sensors. In this paper we examine four different gases (ethanol, methanol, acetone and benzene). The data are acquired and processed by a prototype multi-sensor monitoring system (electronic nose) which has been designed at University of Calabria. It includes five gas sensors plus two auxiliary sensors, for temperature and humidity, respectively. The system is equipped by an appropriate interface to a PC for visualizing and analyzing the data. We introduce an analytical power law model of sensor response. Least square regression is performed to estimate model parameters. The model is then used for both gas classification and concentration estimate. The results of the numerical experiments on 172 gas samples are reported.

We describe an Electronic Nose (ENose) system which is able to identify the type of analyte and to estimate its concentration. The system consists of seven sensors, five of them being gas sensors (supplied with different heater voltage values), the remainder being a temperature and a humidity sensor, respectively. To identify a new analyte sample and then to estimate its concentration, we use both some machine learning techniques and the least square regression principle. In fact, we apply two different training models; the first one is based on the Support Vector Machine (SVM) approach and is aimed at teaching the system how to discriminate among different gases, while the second one uses the least squares regression approach to predict the concentration of each type of analyte.

We present an Electronic Nose (ENose), which is aimed at identifying the presence of one out of two gases, possibly detecting the presence of a mixture of the two. Estimation of the concentrations of the components is also performed for a volatile organic compound (VOC) constituted by methanol and acetone, for the ranges 40-400 and 22-220 ppm (parts-per-million), respectively.Our system contains 8 sensors, 5 of them being gas sensors (of the class TGS from FIGARO USA, INC., whose sensing element is a tin dioxide (SnO(2)) semiconductor), the remaining being a temperature sensor (LM35 from National Semiconductor Corporation), a humidity sensor (HIH-3610 from Honeywell), and a pressure sensor (XFAM from Fujikura Ltd.).Our integrated hardware-software system uses some machine learning principles and least square regression principle to identify at first a new gas sample, or a mixture, and then to estimate the concentrations. In particular we adopt a training model using the Support Vector Machine (SVM) approach with linear kernel to teach the system how discriminate among different gases. Then we apply another training model using the least square regression, to predict the concentrations.The experimental results demonstrate that the proposed multiclassification and regression scheme is effective in the identification of the tested VOCs of methanol and acetone with 96.61% correctness. The concentration prediction is obtained with 0.979 and 0.964 correlation coefficient for the predicted versus real concentrations of methanol and acetone, respectively.

We present an Electronic Nose (ENose) which is aimed both at identifying the type of gas and at estimating its concentration. Our system contains 8 sensors, 5 of them being gas sensors (of the class TGS from FIGARO USA, INC., whose sensing element is a tin dioxide (SnOz) semiconductor), the remaining being a temperature sensor (LM35 from National Semiconductor Corporation), a humidity sensor (HIH-3610 from Honeywell), and a pressure sensor (XFAM from Fujikura Ltd.). Our integrated hardware-software system uses some machine learning principles and least square regression principle to identify at first a new gas sample, and then to estimate its concentration, respectively. In particular we adopt a training model using the Support Vector Machine (SVM) approach to teach the system how discriminate among different gases, then we apply another training model using the least square regression, for each type of gas, to predict its concentration.