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New method for feature extraction based on fractal behavior
Abstract
In this paper, a novel approach to feature extraction based on fractal theory is presented as a powerful technique in pattern recognition. This paper presents a new fractal feature that can be applied to extract the feature of two-dimensional objects. It is constructed by a hybrid feature extraction combining wavelet analysis, central projection transformation and fractal theory. New fractal feature and fractal signatures are reported. A multiresolution family of the wavelets is also used to compute information conserving micro-features. We employed a central projection method to reduce the dimensionality of the original input pattern. A wavelet transformation technique to transform the derived pattern into a set of sub-patterns. Its fractal dimension can readily be computed, and to use the fractal dimension as the feature vectors. Moreover, a modified fractal signature is also used to distinguish the distinct handwritten signatures. We expect that the proposed fractal method can also be used for improving the extraction and classification of features in pattern recognition.
... Image is an important carrier of information. The extraction of image invariant feature is one of key technologies in the fields of computer vision, pattern recognition etc. [1][2][3][4][5][6][7][8][9][10][11][12][13][14]17,18 Affine transform, which includes rotation, translation, scaling, and shearing transform, may be used as an approximation to viewpoint related changes of objects. 1,2 As an important tool in object recognition, the extraction of affine invariant features has been applied in many fields, such as shape retrieval, watermarking, identification of aircrafts, texture classification, image registration and contour matching. ...
... Although the AMIs have small amount of calculation, the higher-order moment is sensitive to noise. Central projection transform (CPT) 10 can convert the object into a closed curve, and realize the combination of contour-based and region-based methods. It can be used in objects with several parts for feature extraction and inherits the advantage of less amount of calculation of the contour-based method. ...
Affine transform is to describe the same target at different viewpoints to obtain the relationship between images of approximate model. Affine invariant feature extraction plays an important role in object recognition and image registration. Firstly, the definition of polar radius integral transform (PRIT) is put forward by means of the characterization of affine transform mapping straight line into straight line, where PRIT computes the integral along the polar radius direction and converts images into closed curves which keep the same affine transform with original images. Secondly, in order to extract affine invariant feature, an affine invariant feature extraction algorithm is also given based on PRIT. The proposed algorithm can be used to combine contour-based methods with region-based methods. It has some advantages of fewer amounts of computations and feasibility of feature extraction for objects with several components. Finally, the capability of anti-noise (Gaussian noise, salt and pepper noise) of PRIT is discussed. The simulation experiment results show that PRIT can effectively extract the affine invariant features, but also the low order PRIT has very strong robustness to noise.
... To estimate the fractal dimension of two-dimensional data (i.e., images), Tang et al. (Tang et al., 2002) proposed a new method of coverage ( Fig. 1). Briefly, in a three-dimensional space, a "blanket" covering the entire thickness of the image gray surface formed by all points on the grayscale surface of the image is used to distinguish between the space "on the carpet," abbreviated uy, and the space "under the carpet," abbreviated by. ...
Optimal wheel alignment improves fuel efficiency, safety, and driver comfort. An explicit formula for determining kingpin parameters, namely, caster and kingpin inclination angle (KIA), in four-wheel alignment is lacking. Currently, caster and KIA values are estimated by repetitive large-scale computing with a mathematical model aimed at obtaining values infinitely close to real solutions. In this study, a four-wheel aligner calibration device was used to collect large amounts of data for a variety of four-wheel aligner measurements with a short data interval. The data were subjected to the local fractal dimension analysis with fractional dimension-based blanket technology (BT) to optimize the number of measurement points. Dramatic changes in data were attributable to local areas with a large fractional number dimension. Appropriate increase in the number of calibration measuring points in areas with a relatively low fractional number dimension can reduce the overall quantity of measuring points. The results provide a scientific basis for the development of alignment calibration standards and demonstrate that these parameters can be assessed based on a small number of measurements. Our BT-based methodology can facilitate factory inspection and performance testing of four-wheel aligners and may improve the accuracy of wheel positioning parameter assessments.
... The data Data is are quantizsed symbol of the information. Data clustering is a process to find the effective information and hidden structure feature based on data collection and reasonable division by a similarity measure, which is an important data mining technique for unsupervised learning and have an is important and widely used in pattern recognition [1][2][3], machine learning [4,5], image processing [6,7] and other fields. In the era of Big Data, a great deal of valuable data information is produced at all times with the rapid development of economy, science and technology. ...
Clustering as a fundamental unsupervised learning is considered an important method of data analysis, and K -means is demonstrably the most popular clustering algorithm. In this paper, we consider clustering on feature space to solve the low efficiency caused in the Big Data clustering by K -means. Different from the traditional methods, the algorithm guaranteed the consistency of the clustering accuracy before and after descending dimension, accelerated K -means when the clustering centeres and distance functions satisfy certain conditions, completely matched in the preprocessing step and clustering step, and improved the efficiency and accuracy. Experimental results have demonstrated the effectiveness of the proposed algorithm.
... The term texture is used to describe the surface of the object as being fine, smooth, or rough. In US imaging, it is a function of the pixel intensity, which can be calculated from the gray levels [5]. There are several textural analysis methods that have been used to extract features from images such as Gabor filters, fractal dimension (FD), gray level co-occurrence matrices, run length, and Laws' texture energy [6]. ...
Breast cancer is among the leading causes of mortality in women worldwide. Early detection can increase the survival rate and limit cancer metastasis to other organs. Recently, the role of ultrasound (US) imaging in the diagnosis and monitoring of breast tumors besides X-ray mammography has been increasing. Several computer-aided diagnosis (CAD) systems were proposed to improve the classification of breast tumors. This work presents a fast and computationally-efficient technique to distinguish between malignant and benign breast tumors. The technique applies wavelet packet transform (WPT) on conventional brightness mode (B-mode) US images, and then extracts several textural and morphological features from the approximation decomposition part. Features include first-order statistics (FOS), fractal dimension texture analysis (FDTA), spatial gray-level dependence matrices (SGLDM), area, perimeter, and compactness of the lesion. When the support vector machine was applied for classification on original US images, the classifier exhibited 97.4% accuracy, 98.3% sensitivity, and 92.1% specificity. These performance parameters were slightly changed to 96.9% accuracy, 96.7% sensitivity, and 97% specificity, when the same features were extracted from WPT. However, the frame classification time was reduced drastically from 1.1284s using original US images to 0.0604s after incorporating WPT. Hence, the proposed CAD system using WPT was able to decrease the computational complexity and processing time by, at least, eight times. This shall improve the early detection of breast cancer via developing real-time and noninvasive computer-aided diagnostic software.
... Recently, the unsupervised learning methods, has been one of the most hot topics in the field of HSI data processing. For example, in the view point of feature extraction, 20,21,23,24,[32][33][34][35] the dimensionality reduction (DR) tools transform the high-dimensional data into a lower-dimensional space. In this way, they can remove the redundant information from HSI data, and combat the Hughes phenomenon at the same time. ...
The high dimensionality and heterogeneity of the hyperspectral image (HSI) make a challenge to the application of machine learning methods, such as sparse subspace clustering (SSC). SSC is designed to represent data as an union of affine subspaces, while it cannot capture the latent structure of the given data. In Mosers theory, the distribution can represent the intrinsic structure efficiently. Hence, we propose a novel approach called spatial distribution preserving-based sparse subspace clustering (SSC-SDP) in this paper for HSI data, which can help sparse representation preserve the underlying manifold structure. Specifically, the density constraint is added by minimizing the inconsistency of the densities estimated in the HSI data and the corresponding sparse coefficient matrix. In addition, we incorporate spatial information into the density estimation of the original data, and the optimization solution based on alternating direction method of multipliers (ADMM) is devised. Three HSI data sets are conducted to evaluate the performance of our SSC-SDP compared with other state-of-art algorithms.
... In the past decades extensive study has been done by the researchers on numerous feature extraction approaches for texture characterization. Representative methods include textural features, morphological features, wavelet based features, Gabor features and fractal dimension [1], [2], [3], [4] to characterize thyroid nodules. The use of LBP variants as texture descriptors for medical images is discussed by Lorris et al. [5], [6]. ...
... Also the representation of complex patterns in an ultrasound image using a parameter fractal dimension obtained from fractal geometry is presented in Yuan Y. Tang et. al [7]. The use of SVMs for the selection of significant textural features and to classify the nodular lesion of a thyroid is discussed by Chan-Yu Chang et. ...
Thyroid nodules have diversified internal components and dissimilar echo patterns in ultrasound images. Textural features are used to characterize these echo patterns. This paper presents a classification scheme that uses shearlet transform based textural features for the classification of thyroid nodules in ultrasound images. The study comprised of 60 thyroid ultrasound images (30 with benign nodules and 30 with malignant nodules). Total of 22 features are extracted. Support vector machine (SVM) and K nearest neighbor (KNN) are used to differentiate benign and malignant nodules. The diagnostic sensitivity, specificity, F1_score and accuracy of both the classifiers are calculated. A comparative study has been carried out with respect to their performances. The sensitivity of SVM with radial basis function (RBF) kernel is 100% as compared to that of KNN with 96.33%. The proposed features can increase the accuracy of the classifier and decrease the rate of misdiagnosis in thyroid nodule classification.
Flotation is the most widely used technology for mineral separation and purification. The flotation production process has complex mechanism characteristics and is influenced by multiple variables that are coupled with each other, which has always been a difficulty in controlling the beneficiation process. The flotation system of mineral processing plants mostly relies on manual control, which is influenced by subjective factors such as worker experience, technical level, and sense of responsibility, making it difficult to optimize control parameters and maximize production efficiency. This paper systematically summarized the automation systems of flotation equipment such as automatic dosing device, automatic liquid level detection device, automatic feed concentration adjustment device, and automatic feed flow adjustment device. The accurate extraction methods of physical and dynamic characteristics such as color, texture, size, and moving speed of flotation froth were reviewed. The traditional data-driven model and image feature-based prediction methods for prediction of the grade, recovery rate, ash content in the concentrate, and tailings were combed. On this basis, a technical route for achieving intelligent flotation process was proposed with the aim of providing theoretical and practical references through the collaborative operation of flotation devices, detection sensors, and machine learning algorithms.
The assessment of the condition of the technical infrastructure is a crucial role in civil engineering, the implementation of BIM technology, 3D cadasters, for the existing infrastructure modernization works and other specialized technical activities. In the time of dynamically developing investment processes, the exact location of the utilities network is important in the context of their subsequent modernization and construction works located in its immediate vicinity. Accurate location data are important not only in the context of construction works, but also in the context of occupational health and safety. In the event of backfilling a non-inventoried underground network, the inventory of such an object may only be performed by non-invasive measurements, e.g. a GPR-Ground Penetrating Radar. Currently, the classification of the network from GPR images was based on the existing reference data obtained from the National Geodetic and Cartographic Resource-NGCR. The aim of the study was to analyze the possibility of using various methods of extraction and classification to distinguish types of utilities networks on the images obtained by GPR. The authors proposed a new algorithm of hyperbolic detection based on appropriate data filtering It shortened the time of image interpretation and automates the process of selecting underground objects. The authors' motivation to take up the research topic was the automation of the process of detection and classification of underground objects, and thus the reduction of data processing time. GPR test images (radargrams) were acquired in several series of measurements and in various areas located on the campus of the Military University of Technology in Warsaw. The work presents the preliminary results of the detection and classification of objects using geometric, wavelet and fractal analysis and optimization methods based on the analytic hierarchy process (AHP). A new methodology of the detection and extraction of hyperbolas was presented based on the analysis of geometric, radiometric and textural objects contained in GPR images. The detection results are promising as preliminary studies have shown the detection of hyperbolas at 79-91%. The effectiveness of hyperbola detection was assessed by comparing the number of objects detected in the target image and the original image (after pre-processing).
Fatigue cracking of asphalt materials directly affects the performance and safety of asphalt pavements. It is necessary to identify the materials condition with acoustic emission (AE) as the real time monitoring technique. The objective of this study was to diagnose the damage behavior of asphalt mixtures from the time and frequency characteristics of AE signals. Firstly, the semi-circular bending (SCB) fatigue test and AE detection were conducted to explore the AE response of asphalt mixtures subjected to cyclic loads. Then, the Fast Fourier Transform (FFT) and Continuous Wavelet Transform (CWT) were applied to discuss the dominant frequency characteristics and time–frequency distribution of AE waveforms. Finally, an index (RBD), defined as the ratio of fractal dimension of AE waveforms decomposed by the Discrete Wavelet Transform (DWT), was proposed to evaluate the damage state of asphalt mixtures. The results show that AE energy rate exhibits distinct variation signatures at different damage stages. The average frequency (AF) and rise angle (RA) of AE signals reveal that the coupling effect of tensile and shear cracks promotes the deterioration of asphalt mixtures. Most of the dominant frequencies of AE events generated from cracks are concentrated within the range of 13 to 30 kHz. The discrepancies in the time–frequency distribution of AE events could effectively discriminate the types of damage sources. The proposed index RBD is sensitive to the change of damage state of asphalt mixtures, producing corresponding reductions.
The structure of any DNA sequence is most certainly non-deterministic. Fuzzy logic is used inaccuracies and uncertainties of any situation. Fractals are infinitely complex pattern that are self similar across the different scales. It is irregular shape what we see in nature. The main aim of this paper is use of Fuzzy logic in Fractals based on DNA sequences using human signature. DNA fingerprinting is the analysis of DNA patterns to identify specific individuals. It is used to diagnosis inherited disorders and developing cure for that, biological evidence. It is also helpful in solving crimes by comparing the pattern of DNA profile with those victim and suspect, The comparison is then used to draw conclusion whether the suspect was present at the crime scene.
As a powerful unsupervised learning technique, clustering is the fundamental task of big data analysis. However, many traditional clustering algorithms for big data that is a collection of high dimension, sparse and noise data do not perform well both in terms of computational efficiency and clustering accuracy. To alleviate these problems, this paper presents Feature K-means clustering model on the feature space of big data and introduces its fast algorithm based on Alternating Direction Multiplier Method (ADMM). We show the equivalence of the Feature K-means model in the original space and the feature space and prove the convergence of its iterative algorithm. Computationally, we compare the Feature K-means with Spherical K-means and Kernel K-means on several benchmark data sets, including artificial data and four face databases. Experiments show that the proposed approach is comparable to the state-of-the-art algorithm in big data clustering.
Fractal geometry is a new language used to describe, model and analyze complex forms found in nature.
The term fractal is commonly used to describe the family of non-differentiable functions that are infinite in length.
Over the past few years fractal geometry has been used as a language in theoretical, numerical and experimental investigations.
Fractals had been applied in image processing for some uses such as: (Fractal Compression, Fractal Classification, Fractal Segmentation, Fractal Analysis, Fractal Detection) we will discuss the Fractal Detection in this seminar.
To improve the performance of smoke recognition, it is important to extract representative and discriminative features for smoke. We propose a learning based method to automatically extract discriminative features from raw pixels. First, patch-based local differences rather than single-pixel-based differences are computed. Then a sampling strategy is learnt to extract dominant local differences. Third, the sampled differences are used to learn a codebook, through which differences are projected into a discriminative feature space. Thus, feature matrices consisting of discriminative differences can be obtained according to the codebook. At last, the feature maps are encoded without quantization, thus final feature is computed. Experimental results demonstrate that the proposed method achieves better performance than some existing handcrafted and learning based feature extraction methods.
Nonnegative matrix factorization (NMF) is a promising method to represent facial images using nonnegative features under a low-rank nonnegative basis-image matrix. The facial images usually reside on a low-dimensional manifold due to the variations of illumination, pose and facial expression. However, NMF has no ability to uncover the manifold structure of data embedded in a high-dimensional Euclidean space, while the manifold structure contains both local and nonlocal intrinsic features. These two kinds of features are of benefit to class discrimination. To enhance the discriminative power of NMF, this paper proposes a novel NMF algorithm with manifold structure (Mani-NMF). Two quantities related to adjacent graph and non-adjacent graph are incorporated into the objective function, which will be minimized by solving two convex suboptimization problems. Based on the gradient descent method and auxiliary function technique, we acquire the update rules of Mani-NMF and theoretically prove the convergence of the proposed Mani-NMF algorithm. Three publicly available face databases, Yale, pain expression and CMU databases, are selected for evaluations. Experiments results show that our algorithm achieves a better performance than some state-of-the-art algorithms.
With the extensive attention and research of the scholars in deep learning, the convolutional restricted Boltzmann machine (CRBM) model based on restricted Boltzmann machine (RBM) is widely used in image recognition, speech recognition, etc. However, time consuming training still seems to be an unneglectable issue. To solve this problem, this paper mainly uses optimized parallel CRBM based on Spark, and proposes a parallel comparison divergence algorithm based on Spark and uses it to train the CRBM model to improve the training speed. The experiments show that the method is faster than traditional sequential algorithm. We train the CRBM with the method and apply it to breast X-ray image classification. The experiments show that it can improve the precision and the speed of training compared with traditional algorithm.
Radon transform is not only robust to noise, but also independent on the calculation of pattern centroid. In this paper, Radon–Mellin transform (RMT), which is a combination of Radon transform and Mellin transform, is proposed to extract invariant features. RMT converts any object into a closed curve. Radon–Fourier descriptor (RFD) is derived by applying Fourier descriptor to the obtained closed curve. The obtained RFD is invariant to scaling and rotation. (Generic) R-transform and some other Radon-based methods can be viewed as special cases of the proposed method. Experiments are conducted on some binary images and gray images.
Face liveness detection is a significant research topic in face-based online authentication. The current face liveness detection approaches utilize either static or dynamic features, but not both. In fact, the dynamic and static features have different advantages in face liveness detection. In this paper, we propose a scheme combining dynamic and static features to capture merits of them for face liveness detection. First, the dynamic maps are captured from the inter-frame motion in the video, which investigates motion information of the face in the video. Then, with a Convolutional Neural Network (CNN), the dynamic and static features are extracted from the dynamic maps and the frame images, respectively. Next, in CNN, the fully connected layers containing the dynamic and static features are concatenated to form a fused feature. Finally, the fused features are used to train a binary Support Vector Machine (SVM) classifier, which classifies the frames into two categories, i.e. frame with real or fake face. Experimental results and the corresponding analysis demonstrate that the proposed scheme is capable of discovering face liveness by fusing dynamic and static features and it outperforms the current state-of-the-art face liveness detection approaches.
Appearance information such as clothing and hairstyle can provide rich clues to identify a person in surveillance videos. This paper proposes a Faster R-CNN based multi-task neural network to recognize attributes such as gender, nationality, etc. from clothing of a person. Toward this end, a fine-tuned Faster R-CNN is applied to locate people in images. Then hierarchical features are extracted from these regions to perform attributes recognition. The recognition network and Faster R-CNN share the same weights, and they can be trained in an end-to-end manner. Experiments are conducted on a newly collected and well-labeled image dataset. The experimental results show that our network can locate a human body and identify its attributes efficiently.
With the wide applications of face recognition techniques, spoofing detection is playing an important role in the security systems and has drawn much attention. This research presents a multispectral face anti-spoofing method working with both visible (VIS) and near-infrared (NIR) spectra imaging, which exploits VIS–NIR image consistency for spoofing detection. First, we use part-based methods to extract illumination robust local descriptors, and then the consistency is calculated to perform spoofing detection. In order to further exploit multispectral correlation in local patches and to be free from manually chosen regions, we learn a confidence factor map for all the patches, which is used in final classifier. Experimental results of self-collected datasets, public Msspoof and PolyU-HSFD datasets show that the proposed approach gains promising results for both intra-dataset and cross-dataset testing scenarios, and that our method can deal with different illumination and both photo and screen spoofing.
The multi-task learning (MTL) methods consider learning a problem together with other related problems simultaneously. The major challenge of MTL is how to selectively screen the shared information. The information of each task must be related to the others, but when sharing information between two unrelated tasks it degenerates the performance of both tasks. To ensure the related problems are related to the main task is the most important point in MTL. In this paper, we will design a novel algorithm to calculate the degrees of relationship among tasks by using a semantical space of features in each task and then build semantical tree to achieve better learning performance. We propose an MTL method under this algorithm which achieves good experimental performance. Our experiments are taken on both image classification and video action recognition, compared with the state-of-the-art MTL methods. Our method proposes good performance in the four public datasets.
Human detection serves as an important basis to achieve certain video surveillance-oriented biometrics such as gait, face and actions since the first step is to find and locate human targets in surveillance scenes. In the literature, channel feature-based methods and deep neural network-based methods are two most popular kinds of human detection approaches, with their own advantages. However, there is not much effort on the study of their combination to take full advantage of these two kinds of approaches. Therefore in this paper, we propose an effective human detection approach by combining multiple state-of-the-art deep neural network-based and channel feature-based methods with an adaptive late fusion strategy. The key idea of our approach is to explore complementary information of different state-of-the-art detection methods and to find an appropriate way to combine their strong points for better performance. The proposed approach is evaluated on several standard human detection benchmarks, and shows its effectiveness by achieving superior performances to the other state-of-the-art methods on most evaluation settings.
For face recognition, conventional dictionary learning (DL) methods have some disadvantages. First, face images of the same person vary with facial expressions and pose, illumination and disguises, so it is hard to obtain a robust dictionary for face recognition. Second, they don't cover important components (e.g., particularity and disturbance) completely, which limit their performance. In the paper, we propose a novel robust and discriminative DL (RDDL) model. The proposed model uses sample diversities of the same face image to learn a robust dictionary, which includes class-specific dictionary atoms and disturbance dictionary atoms. These atoms can well represent the data from different classes. Discriminative regularizations on the dictionary and the representation coefficients are used to exploit discriminative information, which improves effectively the classification capability of the dictionary. The proposed RDDL is extensively evaluated on benchmark face image databases, and it shows superior performance to many state-of-the-art dictionary learning methods for face recognition.
Facial landmarking locates the key facial feature points on facial data, which provides not only information on semantic facial structures, but also prior knowledge for other types of facial analysis. However, most of the existing works still focus on the 2D facial image which is quite sensitive to the lighting condition changes. In order to address this limitation, this paper proposed a coarse-to-fine method only based on the 3D facial scan data extracted from professional equipment to automatically and accurately estimate the landmark localization. Specifically, we firstly trained a convolutional neural network (CNN) to initialize the face landmarks instead of the mean shape. Then the proposed cascade regression networks learn the mapping function between 3D facial geometry feature and landmarks location. Tested on Bosphorus database, the experimental results demonstrated effectiveness and accuracy of the proposed method for (Formula presented.) landmarks. Compared with other methods, the results in several points demonstrate state-of-the-art performance.
Clustering is a fundamental learning task in a wide range of research fields. The most popular clustering algorithm is arguably the K-means algorithm, it is well known that the performance of K-means algorithm heavily depends on initialization due to its strong non-convexity nature. To overcome the initialization issue, in this paper, we first relax the K-means model as an optimization problem with non-convex constraints, then employ the Proximal Alternating Linearized Minimization (PALM) method to solve the relaxed non-convex optimization model. The convergence analysis of PALM algorithm for the clustering problem is also provided. Experimental results on several benchmark datasets are conducted to evaluate the efficiency of our approach.
In this paper, we propose a novel approach for 3D face reconstruction from multi-facial images. Given original pose-variant images, coarse 3D face templates are initialized to reconstruct a refined 3D face mesh in an iteration manner. Then, we warp original facial images to the 2D meshes projected from 3D using Sparse Mesh Affine Warp (SMAW). Finally, we weight the face patches in each view respectively and map the patch with higher weight to a canonical UV space. For facial images with arbitrary pose, their invisible regions are filled with the corresponding UV patches. Poisson editing is applied to blend different patches seamlessly. We evaluate the proposed method on LFW dataset in terms of texture refinement and face recognition. The results demonstrate competitive performance compared to state-of-the-art methods.
This paper presents a novel method for video-based face recognition (VFR) based on M-estimator and image set collaborative representation. Since a video is essentially an image set, the VFR problem can be cast as a special case of the image set-based face recognition (FR) problem. To measure the distance between the query image set and the gallery image set, we develop an M-estimator-based image set collaborative representation (MISCR) model. To implement MISCR, we devise an efficient half-quadratic-based optimization algorithm to tackle the complicated optimization problem. We also establish the convergence property of the devised algorithm. Our other contribution is to propose an MISCR-based classifier for the general image set classification problem, including VFR as a special case. The experiments using real-world benchmark databases demonstrate the efficacy and robustness of the proposed method for VFR.
Biologically inspired model (BIM) for image recognition is a robust computational architecture, which has attracted widespread attention. BIM can be described as a four-layer structure based on the mechanisms of the visual cortex. Although the performance of BIM for image recognition is robust, it takes the randomly selected ways for the patch selection, which is sightless, and results in heavy computing burden. To address this issue, we propose a novel patch selection method with oriented Gaussian-Hermite moment (PSGHM), and we enhanced the BIM based on the proposed PSGHM, named as PBIM. In contrast to the conventional BIM which adopts the random method to select patches within the feature representation layers processed by multi-scale Gabor filter banks, the proposed PBIM takes the PSGHM way to extract a small number of representation features while offering promising distinctiveness. To show the effectiveness of the proposed PBIM, experimental studies on object categorization are conducted on the CalTech05, TU Darmstadt (TUD), and GRAZ01 databases. Experimental results demonstrate that the performance of PBIM is a significant improvement on that of the conventional BIM.
Hyperspectral image (HSI) classification draws a lot of attentions in the past decades. The classical problem of HSI classification mainly focuses on a single HSI scene. In recent years, cross-scene classification becomes a new problem, which deals with the classification models that can be applied across different but highly related HSI scenes sharing common land cover classes. This paper presents a cross-scene classification framework combining spectral–spatial feature extraction and manifold-constrained feature subspace learning. In this framework, spectral–spatial feature extraction is completed using three-dimensional (3D) wavelet transform while manifold-constrained feature subspace learning is implemented via multitask nonnegative matrix factorization (MTNMF) with manifold regularization. In 3D wavelet transform, we drop some coefficients corresponding to high frequency in order to avoid data noise. In feature subspace learning, a common dictionary (basis) matrix is shared by different scenes during the nonnegative matrix factorization, indicating that the highly related scenes should share than same low-dimensional feature subspace. Furthermore, manifold regularization is applied to force the consistency across the scenes, i.e. all pixels representing the same land cover class should be similar in the low-dimensional feature subspace, though they may be drawn from different scenes. The experimental results show that the proposed method performs well in cross-scene HSI datasets.
This paper presents a pork quality evaluation method based on the hyperspectral image datasets of 96 pork samples in the range of 400-1000nm. First, through the K-medoids clustering algorithm based on manifold distance, 30 important wavelengths are selected from 753 wavelengths, and final 8 optimum wavelengths are obtained based on the discriminant value and the spectral resolution. Then, the two-dimensional Gabor wavelet transform is used to extract the eight texture features of the image under the final eight wavelengths respectively, to form a 64-dimensional features of pork quality. Finally, using the fussy C-means (FCM) algorithm based on Isomap dimension reduction, the pork quality evaluation model is constructed. The result of wavelength extraction experiments show that although there is a strong linear correlation between adjacent bands in the hyperspectral image, there is an obvious nonlinear manifold relation in the whole band. Therefore, the K-medoids clustering algorithm based on manifold distance in this paper is more reasonable than the traditional principal component analysis (PCA) in characteristic wavelength selection. According to the experiment of pork quality evaluation, two-dimensional Gabor wavelet transform can extract the texture characteristics of pork better. Compared with the FCM algorithm based on PCA, the FCM algorithm based on Isomap can better solve the high-dimensional clustering problem, and can distinguish fresh chilled meat, frozen-thawed meat and spoiled meat accurately. The study shows that hyperspectral image technology can be used in pork quality evaluation.
Subspace learning (SL) is an important technology to extract the discriminative features for hyperspectral image (HSI) classification. However, in practical applications, some acquired HSIs are contaminated with considerable noise during the imaging process. In this case, most of existing SL methods yield limited performance for subsequent classification procedure. In this paper, we propose a robust subspace learning (RSL) method, which utilizes a local linear regression and a supervised regularization function simultaneously. To effectively incorporate the spatial information, a local linear regression is used to seek the recovered data from the noisy data under a spatial set. The recovered data not only reduce the noise effect but also include the spectral-spatial information. To utilize the label information, a supervised regularization function based on the idea of Fisher criterion is used to learn a discriminative subspace from the recovered data. To optimize RSL, we develop an efficient iterative algorithm. Extensive experimental results demonstrate that RSL greatly outperforms many existing SL methods when the HSI data contain considerable noise.
As a powerful classifier, sparse representation-based classification (SRC) has successfully been applied in various visual recognition problems. However, due to the highly correlated bands and insufficient training samples of hyperspectral image (HSI) data, it still remains a challenging problem to effectively apply SRC in HSI. Considering the rich information of spatial structure of materials in HSI, that means the adjacent pixels belong to the same class with a high probability, in this paper, we propose an efficient superpixel-based sparse representation framework for HSI classification. Each superpixel can be regarded as a small region consisting of a number of pixels with similar spectral characteristics. The proposed framework utilizes superpixel to exploit spatial information which can greatly improve classification accuracy. Specifically, SRC is firstly used to classify the HSI data. Meanwhile, an efficient segmentation algorithm is applied to divide the HSI into many disjoint superpixels. Then, each superpixel is used to fuse the SRC classification results in superpixel level. Experimental results on two real-world HSI data sets have shown that the proposed superpixel-based SRC (SP-SRC) framework has a significant improvement over the pixel-based SRC method.
Band selection plays a key role in the hyperspectral image classification since it helps to reduce the expensive cost of computation and storage. In this paper, we propose a supervised hyperspectral band selection method based on differential weights, which depict the contribution degree of each band for classification. The differential weights are obtained in the training stage by calculating the sum of weight differences between positive and negative classes. Using the effective one-class Support Vector Machine (SVM), the bands corresponding to large differential weights are extracted as discriminative features to make the classification decision. Moreover, label information from training data is further exploited to enhance the classification performance. Finally, experiments on three public datasets, as well as comparison with other popular feature selection methods, are carried out to validate the proposed method.
In this paper, we address the problem of removing striping noise in hyperspectral images (HSI). To this end, we develop a novel destriping method by taking advantage of the spectral and spatial information of the hyperspectral image simultaneously. To obtain satisfactory destriped results, our consideration is two-fold: (1) To model the spectral information of HSI, we utilize low-rank representation to exploit the low-rank property of HSI; (2) To incorporate the spatial information into our method, we adopt the Huber-Markov random field (HMRF) prior model to preserve the edge information of HSI while reducing the striping noise. Finally, we integrate the spectral and spatial model into a unified objective function. In addition, we also devise an effective optimization algorithm to minimize the objective function. The experimental results on real-world HSI data validate the efficacy of the proposed scheme for destriping of HSI.
This paper investigates the problem of event-triggered reliable control for Markovian jump systems subject to nonuniform sampled data (SD). Compared with recent existing results, a new mode-dependent event-triggered mechanism (ETM) is proposed which makes full use of the information of ETM and nonuniform SD. By constructing a newly Lyapunov-Krasovskii functional and utilizing a convex optimization approach, some sufficient criteria for reliable control are deduced in an inequality form. Finally, a numerical example is given to demonstrate the effectiveness of the theoretical results.
High resolution and large field of view are two major development trends in optical remote sensing imaging. But these trends will cause the difficult problem of mass data processing and remote sensor design under the limitation of conventional sampling method. Therefore, we will propose a novel optical remote sensing imaging method based on compressed sensing theory and fractal feature extraction in this study. We could utilize the result of fractal classification to realize the selectable partitioned image recovery with undersampling measurement. The two experiments illustrate the availability and feasibility of this new method. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
The central projection transform can be employed to extract invariant features by combining contour-based and region-based methods. However, the central projection transform only considers the accumulation of the pixels along the radial direction. Consequently, information along the radial direction is inevitably lost. In this paper, we propose the Mellin central projection transform to extract affine invariant features. The radial factor introduced by the Mellin transform, makes up for the loss of information along the radial direction by the central projection transform. The Mellin central projection transform can convert any object into a closed curve as a central projection transform, so the central projection transform is only a special case of the Mellin central projection transform. We prove that closed curves extracted from the original image and the affine transformed image by the Mellin central projection transform satisfy the same affine transform relationship. A method is provided for the extraction of affine invariants by employing the area of closed curves derived by the Mellin central projection transform. Experiments have been conducted on some printed Chinese characters and the results establish the invariance and robustness of the extracted features.
Offline signature in one of the most widely used method to verify the identification. An individual's signature differs according to time and situation. Therefore, it is necessary to create an authentication system based on signature. Obviously, offline signature has no dynamic features and just can use a sample is presented based on fractal theory using Fourier transformation for the signature feature extraction, and then, MLP neural network is used for classifying signature to evaluate the effect of fractal dimension on this system. A sample of 1010 signatures (original and fake signatures) have been examined by this system, and the results of this technic are composed with different number of input data.
The features, used in many current medical image retrieval systems, are usually low-level hand-crafted features. This limitation may adversely affect the retrieval performance. To address this problem, this paper proposes a simple yet discriminative feature, called histogram of compressed scattering coefficients (HCSCs), for medical image retrieval. In the proposed work, the scattering transform, a particular variation of deep convolutional networks, is first performed to yield more abstract representations of a medical image. A projection operation is then conducted to compress the obtained scattering coefficients for efficient processing. Finally, a bag-of-words (BoW) histogram is derived from the compressed scattering coefficients as the features of the medical image. The proposed HCSCs take the advantages of both scattering transform and BoW model. Experiments on three benchmark medical computer tomography image databases demonstrate that HCSCs outperform several state-of-the-art features.
The feature extraction and classification of brain signal is very significant in brain-computer interface (BCI). In this study, we describe an algorithm for motor imagery (MI) classification of electrocorticogram (ECoG)-based BCI. The proposed approach employs multi-resolution fractal measures and local binary pattern (LBP) operators to form a combined feature for characterizing an ECoG epoch recording from the right hemisphere of the brain. A classifier is trained by using the gradient boosting in conjunction with ordinary least squares (OLS) method. The fractal intercept, lacunarity and LBP features are extracted to classify imagined movements of either the left small finger or the tongue. Experimental results on dataset I of BCI competition III demonstrate the superior performance of our method. The cross-validation accuracy and accuracy is 90.6% and 95%, respectively. Furthermore, the low computational burden of this method makes it a promising candidate for real-time BCI systems.
A novel fractal compressive sensing (CS) imaging method is proposed in this paper to solve some bottlenecks of CS application in remote sensing imaging. On the one hand, multi-scale lens would be used to reduce the massive computation cost, which is caused by the traditional CS imaging based on sparse representation under large field of view. On the other hand, l1-norm minimization, as the object function of traditional CS imaging, is replaced by fractal dimension for improving the quality of middle and high resolution remote sensing imaging in image details. Experimental results show that, multi-scale fractal CS imaging method can not only meet the timeliness requirement of remote sensing imaging but also improve the imaging quality in details level.
A method is proposed by combining contour-based methods with region-based methods. A closed contour is derived from the object by central projection transformation, and invariant features are extracted from this closed contour. The affine invariance of the closed curve derived by central projection transformation has been proved. An algorithm is provided to extract affine invariant features by employing stationary wavelet transform. Some Chinese characters and 26 capital letters are used to evaluate the proposed method. Experimental results show that the proposed method can efficiently extract invariant features. Compared to traditional methods, the proposed method is robust to noise.
To achieve the design of an automatic shiitake grading system, the images of four varieties such as Tian pai-hua Shiitake, Pai-hua Shiitake, Tsa-hua Shiitake, and Smooth Cap Shiitake were taken as research objects. Shiitake texture is a vital indicator of shiitake quality. The more white texture of the shiitake pileus, the higher its price. Shiitake grading was mainly processed by a manual operation for a long time. The grading operation was heavy workload, inefficient, and not conducive to automatic production. So the shiitake market was eager for shiitake grading equipment. This study designed an automatic shiitake grading system based on machine vision. The grading system was divided into three subsystems, including a mechanical system, a single chip microcomputer system and a machine vision system. The mechanical system played an important role in the shiitake feeding and grading process. The single chip microcomputer system was responsible for the entire system control and coordination. The machine vision system performed the operation of image acquisition and processing. Texture was a significant image feature. Many experts researched texture across the world, and various texture models had been developed in recent years. This study selected three models to describe pileus texture. The first texture model was derived from a gray histogram and grey level co-occurrence matrix. The second model was called a Gauss Makov Random Field. The third model was defined by fractal dimention. The shiitake grading process was described as follows. First, the texture analysis region was intercepted from shiitake pileus by an appropriate rectangle. Five texture feature parameters were extracted from the texture analysis region according to the gray histogram; another five texture feature parameters were extracted according to grey level co-occurrence matrix; twelve texture feature parameters were extracted according to a Gauss Makov Random Field; the fractal dimension extracted from the fractal model was the last of the texture feature parameters. Three texture models could describe texture information from different perspectives. Each texture feature expressed specific physical meanings. However, it was relevant among texture features in most cases. This study chose a sequential feature selection algorithm to eliminate the defect. An sequential features selection algorithm could remove the correlation among features, and six effective features were selected after the correlation-removal operation. Finally, the K-nearest neighbor's classifier was constructed as the shiitake species classifier, and then the test shiitake samples could be classified with the six effective features mentioned above by the K-nearest neighbor's classifier. Experimental results showed that the final accuracy reached to 93.57%, which could meet the requirements of production.
In this paper we use fractal method for detection and diagnosis of abnormalities in mammograms. We have used 168 images that were carefully selected by a radiologist and their abnormalities were also confirmed by biopsy. These images included asymmetric lesions, architectural distortion, normal tissue and mass lesion where in case of mass lesion they included circumscribed benign, ill-defined and spiculated malignant masses. At first, by using wavelet transform and piecewise linear coefficient mapping, image enhancement were done. Secondly detection of lesions was done by fractal method as a ROI. Since in investigation of breast cancer, it is important that fibroglandular tissues in both breasts be symmetric and for each asymmetric density, evaluation for malignancy is necessary, we define new fractal features based on extracting asymmetric information from lesions. The fractal features were evaluated on 5 data sets using SVM classifier which enabled to achieve high accuracy in classification of mammograms and diagnostic results. We have also investigated the performance of image enhancement in classification of each data set which shows different effects of enhancement on different lesion types. © 2015 Nałecz Institute of Biocybernetics and Biomedical Engineering.
Malaria is an endemic, global and life threatening disease. Technically skilled person or an expert is needed to analyze the microscopic blood smears for long hours. This paper presents an efficient approach to segment the parasites of malaria. Three different colour space namely LAB, HSI and gray has been used effectively to pre-process and segment the parasite in digital images with noise, debris and stain. L and B plane of LAB, S plane of HSI of input image is extracted with convolution and DCT. Fuzzy based segmentation has been proposed to segment the malaria parasite. Colour features, fractal features are extracted and feature vectors are prepared as a result of segmentation. Adaptive Resonance Theory Neural Network (ARTNN), Back Propagation Network (BPN) and SVM classifiers are used with Fuzzy segmentation and fractal feature extraction methods. Automated segmentation with ARTNN has recorded an accuracy of 95 % compared to other classifiers.
Textures are classified based on the change in their properties with changing resolution. The area of the gray level surface is measured at serveral resolutions. This area decreases at coarser resolutions since fine details that contribute to the area disappear. Fractal properties of the picture are computed from the rate of this decrease in area, and are used for texture comparison and classification. The relation of a texture picture to its negative, and directional properties, are also discussed.
This paper deals with the problem of recognizing and segmenting
textures in images. For this purpose the authors employ a technique
based on the fractal dimension (FD) and the multi-fractal concept. Six
FD features are based on the original image, the above average/high gray
level image, the below average/low gray level image, the horizontally
smoothed image, the vertically smoothed image, and the multi-fractal
dimension of order two. A modified box-counting approach is proposed to
estimate the FD, in combination with feature smoothing in order to
reduce spurious regions. To segment a scene into the desired number of
classes, an unsupervised K-means like clustering approach is used.
Mosaics of various natural textures from the Brodatz album as well as
microphotographs of thin sections of natural rocks are considered, and
the segmentation results to show the efficiency of the technique.
Supervised techniques such as minimum-distance and k-nearest neighbor
classification are also considered. The results are compared with other
techniques
Multiresolution representations are effective for analyzing the
information content of images. The properties of the operator which
approximates a signal at a given resolution were studied. It is shown
that the difference of information between the approximation of a signal
at the resolutions 2j+1 and 2j (where j is an
integer) can be extracted by decomposing this signal on a wavelet
orthonormal basis of L 2( R n), the
vector space of measurable, square-integrable n -dimensional
functions. In L 2( R ), a wavelet orthonormal
basis is a family of functions which is built by dilating and
translating a unique function ψ( x ). This decomposition
defines an orthogonal multiresolution representation called a wavelet
representation. It is computed with a pyramidal algorithm based on
convolutions with quadrature mirror filters. Wavelet representation lies
between the spatial and Fourier domains. For images, the wavelet
representation differentiates several spatial orientations. The
application of this representation to data compression in image coding,
texture discrimination and fractal analysis is discussed
As the interest in fractal geometry rises, the applications are getting more and more numerous in many domains. This paper deals with the problem of recognizing and classification to optical character recognition. For this purpose, we present a new method of feature extraction based on the principles of fractal geometry and wavelet. This allows us to establish a classification of Chinese character in order to apply to each of the isolated categories the most adapt recognition methods. In particular, the proposed method reduces the dimensionality of a two-dimensional pattern by way of a central projection approach, and thereafter, performs Daubechies' wavelet transformation on the derived one-dimensional pattern to generate a set of wavelet transformation sub-patterns, namely, curves that are non-self-intersecting. Further from the resulting non-self-intersecting curves, the divider dimensions are computed with modified box-counting approach. These divider dimensions constitute a new feature vector for the original two-dimensional pattern, defined over the curve's fractal dimensions. We have conducted several experiments in which a set of printed alphanumeric symbols and Chinese characters of varying fonts and orientation were classified, based on the formulation of our new feature vector. The results obtained from these experiments have consistently shown the character recognition method with the proposed feature vector can yield an excellent classification rate 100%.
Multiresolulion representations are very effective for analyzing the information content of images. We study the properties of the operator which approximates a signal at a given resolution. We show that the difference of information between the approximation of a signal at the resolutions 2 j + l and 2 j can be extracted by decomposing this signal on a wavelet orthonormal basis of L2 (Rn). In L2 (R), a wavelet orthonormal basis is a family of functions (√2j Ψ (2 Jx - π))j,n,ez2+ which is built by dilating and translating a unique functiOn Ψ(x). This decomposition defines an orthogonal multiresolulion representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror lilters. For images, the wavelet representation differentia1es several spatial orientations. We study the application of this representation to data compression in image coding, texture discrimination and fractal analysis.
This paper addresses the problems of 1) representing natural shapes such as mountains, trees, and clouds, and 2) computing their description from image data. To solve these problems, we must be able to relate natural surfaces to their images; this requires a good model of natural surface shapes. Fractal functions are a good choice for modeling 3-D natural surfaces because 1) many physical processes produce a fractal surface shape, 2) fractals are widely used as a graphics tool for generating natural-looking shapes, and 3) a survey of natural imagery has shown that the 3-D fractal surface model, transformed by the image formation process, furnishes an accurate description of both textured and shaded image regions. The 3-D fractal model provides a characterization of 3-D surfaces and their images for which the appropriateness of the model is verifiable. Furthermore, this characterization is stable over transformations of scale and linear transforms of intensity. The 3-D fractal model has been successfully applied to the problems of 1) texture segmentation and classification, 2) estimation of 3-D shape information, and 3) distinguishing between perceptually ``smooth'' and perceptually ``textured'' surfaces in the scene.
"...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature
An analysis is presented of the imaging of surfaces modeled by
fractal Brownian elevation functions of the sort used in computer
graphics. It is shown that, if Lambertian reflectance modest surface
slopes and the absence of occlusions and self shadowing are assumed, a
fractal surface with Fourier power spectrum proportional to f
β produces an image with power spectrum proportional to
f 2-β; here, f is the spatial frequency
and β is related to the fractional dimension value. This allows one
to use the spectral falloff of the images to predict the fractal
dimension of the surface
Towards automatic fractal feature extraction for image recognition Feature Extraction, Construction and Selection: a Data Mining Perspective Texture segmentation using fractal dimension
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Feature Extraction, Construction and Selection: a Data Mining Perspective
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