Set Of Benchmark Images Research Articles

A comparative study of evolutionary computation and swarm-based methods applied to color quantization

Color Quantization (CQ) is a complex and hard problem because selecting the best set of colors from many available colors and using that set to obtain a good quality image is an NP-complete problem. The use of evolutionary computation and swarm-based methods to solve search and optimization problems has increased dramatically in recent years. This article compares some of these methods in order to solve the CQ problem. The following methods were used to generate CQ images: Particle swarm optimization, Artificial bee colony, Adaptive differential evolution, Success-history based adaptive differential evolution (with and without linear population size reduction), Cuckoo search, Firefly algorithm and Shuffled-frog leaping algorithm. For the first two methods, two variants were considered. Thus, a total of ten metaheuristics were compared with four classical CQ methods (Variance-based, Median-cut, Binary splitting and Wu’s methods) applying them to a set of benchmark images and considering four different palette sizes (32, 64, 128, and 256 colors). Three error measures were considered to compare the methods: the mean squared error, the mean absolute error and the peak signal-to-noise ratio. Some of the swarm-based methods analyzed include a recently proposed CQ method using ants. Although they have a slow computational speed in the experimental studies, the ant-based methods are significantly better than all other methods according to the Wilcoxon signed rank test. In general, despite their speed, classical methods underperform the other ten methods both qualitatively and quantitatively.

A Novel Color Visual Cryptography Approach Based on Harris Hawks Optimization Algorithm

Hundreds of millions of people worldwide use computing devices and services, including smartphones, laptops, and messaging apps. Visual cryptography (VC) is one of the most secure encryption methods for image encryption in many applications, such as voting security, online transaction security, and privacy protection. An essential step in VC is encrypting secret images into multiple digital shares to hide them with the intention of successfully reverting them to their original form. Hence, a single share cannot reveal information about the secret image. Issues including pixel enlargement, high processing costs, and low decryption quality influence the current state of VC. We address these issues by introducing a novel technique based on (2, 2) secret sharing and the algorithm of Harris hawks optimization (HHO) for color photos. For the encryption process, the appropriate color levels are determined using the HHO algorithm. Consequently, images are decrypted with improved quality and a small impact on the overall processing complexity. The suggested scheme is also non-expandable due to the equal size of the initial secret image and the shared images. This results in lower memory requirements and improved image quality. The approach is applied to a set of well-known benchmark images. Moreover, a set of standard metrics is used to assess the robustness of the proposed scheme, including its capability in defending against cryptanalytic attacks, a correlation, a histogram, and the quality of encryption. According to the findings, the proposed solution provides better reconstructed image quality, time-efficient encryption, and nearly optimal statistical properties compared to previous approaches.

An Improved Search and Rescue Algorithm for Global Optimization and Blood Cell Image Segmentation

Image segmentation has been one of the most active research areas in the last decade. The traditional multi-level thresholding techniques are effective for bi-level thresholding because of their resilience, simplicity, accuracy, and low convergence time, but these traditional techniques are not effective in determining the optimal multi-level thresholding for image segmentation. Therefore, an efficient version of the search and rescue optimization algorithm (SAR) based on opposition-based learning (OBL) is proposed in this paper to segment blood-cell images and solve problems of multi-level thresholding. The SAR algorithm is one of the most popular meta-heuristic algorithms (MHs) that mimics humans' exploration behavior during search and rescue operations. The SAR algorithm, which utilizes the OBL technique to enhance the algorithm's ability to jump out of the local optimum and enhance its search efficiency, is termed mSAR. A set of experiments is applied to evaluate the performance of mSAR, solve the problem of multi-level thresholding for image segmentation, and demonstrate the impact of combining the OBL technique with the original SAR for improving solution quality and accelerating convergence speed. The effectiveness of the proposed mSAR is evaluated against other competing algorithms, including the L'evy flight distribution (LFD), Harris hawks optimization (HHO), sine cosine algorithm (SCA), equilibrium optimizer (EO), gravitational search algorithm (GSA), arithmetic optimization algorithm (AOA), and the original SAR. Furthermore, a set of experiments for multi-level thresholding image segmentation is performed to prove the superiority of the proposed mSAR using fuzzy entropy and the Otsu method as two objective functions over a set of benchmark images with different numbers of thresholds based on a set of evaluation matrices. Finally, analysis of the experiments' outcomes indicates that the mSAR algorithm is highly efficient in terms of the quality of the segmented image and feature conservation, compared with the other competing algorithms.

Image thresholding segmentation based on weighted Parzen-window and linear programming techniques

Image segmentation by thresholding is an important and fundamental task in image processing and computer vision. In this paper, a new bi-level thresholding approach based on weighted Parzen-window and linear programming techniques is proposed to use in image thresholding segmentation. First, by proposing a weighted Parzen-window to describe the gray level distribution status, we obtain the boundaries for the foreground and background of the image. Then the image thresholding problem can be transformed into the problem of solving a linear programming problem for computing the coefficient values of weighted Parzen-window. The results of testing on synthetic, NDT and a set of benchmark images indicate that the proposed method can achieve a higher segmentation accuracy and robustness in comparison to some classical thresholding methods, such as inter class variance method (OTSU), Kapur’s entropy-based method (KSW), and some state-of-art methods that consider spatial information, such as CHPSO, GLLV histogram method and GABOR histogram method.

An improved whale optimization algorithm based on multilevel threshold image segmentation using the Otsu method

In this paper, an improved multithreshold image segmentation method based on the whale optimization algorithm (RAV-WOA) is proposed, with the between-class variance (Otsu method) as the objective function. The proposed RAV-WOA is able to select satisfactory optimal thresholds while ensuring high efficiency and quality when performing image segmentation on grayscale and color images In the current work, a reverse learning strategy was introduced into the initialization of RAV-WOA populations to improve the quality of the initial population of whales. An adaptive weighting strategy was introduced into the RAV-WOA algorithm, which is influenced by the fitness value and the number of iterations, to balance the global search capability of the algorithm with the local exploitation capability. The proposed RAV-WOA is then applied to the Otsu method to solve the multilevel thresholding image segmentation problem. To better verify the effectiveness of the proposed method, this paper compares the RAV-WOA with some classical heuristic algorithms and performs image segmentation experiments on a set of benchmark images with low and high thresholds. The experimental results show that the convergence speed and convergence accuracy of RAV-WOA are significantly better than other algorithms, and the segmentation results of RAV-WOA in multithreshold image segmentation have better quality and stability than other algorithms.

Design of Convolutional Neural Network Based on FPGA

Recently with the rapid development of artificial intelligence AI, various deep learning algorithms represented by Convolutional Neural Networks (CNN) have been widely utilized in various fields, showing their unique advantages; especially in Skin Cancer (SC) imaging Neural networks (NN) are methods for performing machine learning (ML) and reside in what's called deep learning (DL). DL refers to the utilization of multiple layers during a neural network to perform the training and classification of data. The Convolutional Neural Networks (CNNs), a kind of neural network and a prominent machine learning algorithm go through multiple phases before they get implemented in hardware to perform particular tasks for a specific application. State-of-the-art CNNs are computationally intensive, yet their parallel and modular nature make platforms like Field Programmable Gate Arrays (FPGAs) compatible with the acceleration process. The objective of this paper is to implement a hardware architecture capable of running on an FPGA platform of a convolutional neural network CNN, for that, a study was made by describing the operation of the concerned modules, we detail them then we propose a hardware architecture with RTL scheme for each of these modules using the software ISE (Xilinx). The main objective is to show the efficiency of such a realization compared to a GPU based execution. An experimental study is accomplished for the PH2 database set of benchmark images. The proposed FPGA-based CNN design gives competitive results and shows well its efficiency.

Population-based self-adaptive Generalised Masi Entropy for image segmentation: A novel representation

Image segmentation is an indispensable part of computer vision applications, and image thresholding is a popular one due to its simplicity and robustness. Generalised Masi entropy (GME) is an image thresholding method that exploits the additive/non-extensive information using entropic measure (r). r shows the measure of degree of extensibility and non-extensibility available in an image. From the literature, all research considered it as a fixed coefficient, while finding a proper value for r can enhance the efficacy of thresholding. This paper proposes a simple yet effective approach for adaptively finding a proper value for r without any background knowledge regarding the distribution of histogram. To this end, a new representation is proposed so that it can be used with any type of population-based metaheuristic (PBMH) algorithms. For the optimisation process, we use differential evolution (DE), as a representative. In addition, to further improve efficacy, we improve DE algorithm based on one-step k-means clustering, random-based sampling, Gaussian-based sampling, and opposition-based learning. Our extensive experiments compared to the most recent approaches on a set of benchmark images and in terms of several criteria clearly show that the proposed approach not only can find the proper value for r automatically but also it can improve the efficacy of GME-based image thresholding methods.

A Grouping Differential Evolution Algorithm Boosted by Attraction and Repulsion Strategies for Masi Entropy-Based Multi-Level Image Segmentation.

Masi entropy is a popular criterion employed for identifying appropriate threshold values in image thresholding. However, with an increasing number of thresholds, the efficiency of Masi entropy-based multi-level thresholding algorithms becomes problematic. To overcome this, we propose a novel differential evolution (DE) algorithm as an effective population-based metaheuristic for Masi entropy-based multi-level image thresholding. Our ME-GDEAR algorithm benefits from a grouping strategy to enhance the efficacy of the algorithm for which a clustering algorithm is used to partition the current population. Then, an updating strategy is introduced to include the obtained clusters in the current population. We further improve the algorithm using attraction (towards the best individual) and repulsion (from random individuals) strategies. Extensive experiments on a set of benchmark images convincingly show ME-GDEAR to give excellent image thresholding performance, outperforming other metaheuristics in 37 out of 48 cases based on cost function evaluation, 26 of 48 cases based on feature similarity index, and 20 of 32 cases based on Dice similarity. The obtained results demonstrate that population-based metaheuristics can be successfully applied to entropy-based image thresholding and that strengthening both exploitation and exploration strategies, as performed in ME-GDEAR, is crucial for designing such an algorithm.

Multiscale, multiwavelength extraction of sources and filaments using separation of the structural components:getsf

High-quality astronomical images delivered by modern ground-based and space observatories demand adequate, reliable software for their analysis and accurate extraction of sources, filaments, and other structures, containing massive amounts of detailed information about the complex physical processes in space. The multiwavelength observations with highly variable angular resolutions across wavebands require extraction tools that preserve and use the invaluable high-resolution information. Complex fluctuating backgrounds and filamentary structures appear differently on various scales, calling for multiscale approaches for complete and reliable extraction of sources and filaments. The availability of many extraction tools with varying qualities highlights the need to use standard model benchmarks for choosing the most reliable and accurate method for astrophysical research. This paper presentsgetsf, a new method for extracting sources and filaments in astronomical images using separation of their structural components, designed to handle multiwavelength sets of images and very complex filamentary backgrounds. The method spatially decomposes the original images and separates the structural components of sources and filaments from each other and from their backgrounds, flattening their resulting images. It spatially decomposes the flattened components, combines them over wavelengths, detects the positions of sources and skeletons of filaments, and measures the detected sources and filaments, creating the output catalogs and images. The fully automated method has a single user-defined parameter (per image), the maximum size of the structures of interest to be extracted, that must be specified by users. This paper presents a realistic multiwavelength set of simulated benchmark images that can serve as the standard benchmark problem to evaluate qualities of source- and filament-extraction methods. This paper describeshires, an improved algorithm for the derivation of high-resolution surface densities from multiwavelength far-infraredHerschelimages. The algorithm allows creating the surface densities with angular resolutions that reach 5.6″ when the 70 μm image is used. If the shortest-wavelength image is too noisy or cannot be used for other reasons, slightly lower resolutions of 6.8−11.3″ are available from the 100 or 160 μm images. These high resolutions are useful for detailed studies of the structural diversity in molecular clouds. The codesgetsfandhiresare illustrated by their applications to a variety of images obtained with ground-based and space telescopes from the X-ray domain to the millimeter wavelengths.

An Evolutionary Approach to Improve the Halftoning Process

The techniques of halftoning are widely used in marketing because they reduce the cost of impression and maintain the quality of graphics. Halftoning converts a digital image into a binary image conformed by dots. The output of the halftoning contains less visual information; a possible benefit of this task is the reduction of ink when graphics are printed. The human eye is not able to detect the absence of information, but the printed image stills have good quality. The most used method for halftoning is called Floyd-Steinberger, and it defines a specific matrix for the halftoning conversion. However, most of the proposed techniques in halftoning use predefined kernels that do not permit adaptation to different images. This article introduces the use of the harmony search algorithm (HSA) for halftoning. The HSA is a popular evolutionary algorithm inspired by the musical improvisation. The different operators of the HSA permit an efficient exploration of the search space. The HSA is applied to find the best configuration of the kernel in halftoning; meanwhile, as an objective function, the use of the structural similarity index (SSIM) is proposed. A set of rules are also introduced to reduce the regular patterns that could be created by non-appropriate kernels. The SSIM is used due to the fact that it is a perception model used as a metric that permits comparing images to interpret the differences between them numerically. The aim of combining the HSA with the SSIM for halftoning is to generate an adaptive method that permits estimating the best kernel for each image based on its intrinsic attributes. The graphical quality of the proposed algorithm has been compared with classical halftoning methodologies. Experimental results and comparisons provide evidence regarding the quality of the images obtained by the proposed optimization-based approach. In this context, classical algorithms have a lower graphical quality in comparison with our proposal. The results have been validated by a statistical analysis based on independent experiments over the set of benchmark images by using the mean and standard deviation.

Highly interpretable hierarchical deep rule-based classifier

Pioneering the traditional fuzzy rule-based (FRB) systems, deep rule-based (DRB) classifiers are able to offer both human-level performance and transparent system structure on image classification problems by integrating zero-order fuzzy rule base with a multi-layer image-processing architecture that is typical for deep learning. Nonetheless, it is frequently observed that the inner structure of DRB can become over sophisticated and not interpretable for humans when applied to large-scale, complex problems. To tackle the issue, one feasible solution is to construct a tree structural classification model by aggregating the possibly huge number of prototypes identified from data into a much smaller number of more descriptive and highly abstract ones. Therefore, in this paper, we present a novel hierarchical deep rule-based (H-DRB) approach that is capable of summarizing the less descriptive raw prototypes into highly generalized ones and self-arranging them into a hierarchical prototype-based structure according to their descriptive abilities. By doing so, H-DRB can offer high-level performance and, most importantly, full transparency and human-interpretability on various problems including large-scale ones. The proposed concept and generical principles are verified through numerical experiments based on a wide variety of popular benchmark image sets. Numerical results demonstrate that the promise of H-DRB.

Symbiotic Organisms Search Optimization for Multilevel Image Thresholding

Determination of optimum thresholds is the prime concern of any multilevel image thresholding technique. The traditional methods for multilevel thresholding are computationally expensive, time-consuming, and also suffer from lack of accuracy and stability. To address this issue, the authors propose a new methodology for multilevel image thresholding based on a recently developed meta-heuristic algorithm, Symbiotic Organisms Search (SOS). The SOS algorithm has been inspired by the symbiotic relationship among the organism in nature. This article has utilized the concept of the symbiotic relationship among the organisms to optimize three objective functions: Otsu's between class variance and Kapur's and Tsallis entropy for image segmentation. The performance of the SOS based image segmentation algorithm has been evaluated using a set of benchmark images and has been compared with four recent meta-heuristic algorithms. The algorithms are compared in terms of effectiveness and consistency. The quality of the algorithms has been estimated by some well-defined quality metrics such as peak signal-to-noise ratio (PSNR), structure similarity index (SSIM), and, feature similarity index (FSIM). The experimental results of the algorithms reveal that the balance of intensification and diversification of the SOS algorithm to achieve the global optima is better than others.

Improving image thresholding by the type II fuzzy entropy and a hybrid optimization algorithm

The segmentation of digital images is an open problem that has increasingly attracted the attention of researchers during the last years. Thresholding approaches are often used due to their independence from the resolution of the images and their speed. However, simple thresholding approaches usually generate low-quality images. To achieve a better balance between speed and quality, many criteria are used to select the thresholds that segment the image. The type II fuzzy entropy (TII-FE) was introduced to perform image thresholding by modeling the classes of an image as membership functions to avoid uncertainty on the selection of the thresholds leading to improvement regarding the quality of the segmented image. To maximize the TII-FE, an efficient optimizer should be used to converge quickly to the optimal. In this paper, a hybrid method based on the Paddy Field Algorithm (PFA) and the Plant Propagation Algorithm (PPA) with the disruption operator (HPFPPA-D) is presented for the maximization of the TII-FE. The hybridization of these algorithms is used to enhance the performance of each algorithm by introducing operators from other approaches. In this case, the PFA shows good exploitation features that are complemented by the exploration behavior of PPA and refined with the disruption operator. The synergy between those methods has led to an accurate methodology for TII-FE thresholding. The proposed HPFPPA-D for TII-FE is evaluated using a set of benchmark images regarding convergence and image quality. The results are compared against other state-of-the-art evolutionary algorithms providing evidence of a superior and significant performance.

Modified hybrid bat algorithm with genetic crossover operation and smart inertia weight for multilevel image segmentation

Multilevel thresholding is one of the most commonly used methods in image segmentation. However, the exhaustive search method is computationally expensive for selecting the optimal thresholds. Therefore, a hybrid bat algorithm with genetic crossover operation and smart inertia weight (SGA-BA) is proposed to choose the optimal thresholds. Furthermore, between-class variance (the Otsu method) and Kapur’s entropy are used as objective functions. In the novel SGA-BA, the smart inertia weight balances the SGA-BA’s exploration and exploitation based on the number of iterations and fitness values. Moreover, the local search capability of SGA-BA is strengthened by the crossover operation of the genetic algorithm. Meanwhile, the random vector is replaced by the beta distribution, which updates the frequency of bat in a smart way. The proposed SGA-BA was evaluated by a set of benchmark images with various levels of thresholds. Additionally, SGA-BA was compared with some well-known and recent heuristic algorithms, such as the genetic algorithm (GA), gravitational search algorithm (GSA), particle swarm optimization (PSO), whale optimization algorithm (WOA), improved salp swarm algorithm (LSSA) and basic bat algorithm (BA). The experimental results show that the proposed SGA-BA provides better outcomes than the other algorithms.

Combining information from thresholding techniques through an evolutionary Bayesian network algorithm

Segmentation is an important task in image processing because it could affect the performance of other steps in image analysis. One of the most used methods for segmentation is thresholding which can be formulated as an optimization problem, and evolutionary algorithms (EAs) are alternatives commonly applied to solve it. Estimation of Distribution Algorithms (EDAs) is a branch of EAs that explores the search space by building a probabilistic model, such as Bayesian Networks (BNs). In this article is proposed a BN-based EDA for multilevel image segmentation called BNMTH . The proposed approach iteratively selects the combination of thresholding techniques that permits to find the best configuration of thresholds for a digital image, exploring the inter-dependencies between the decision variables (thresholds) and the different techniques. BNMTH is applied over a set of benchmark images and the results of the segmentation are qualitatively analyzed by using the Peak Signal-to-Noise Ratio (PSNR), the Structure Similarity Index (SSIM) and the Feature Similarity Index (FSIM). Besides, a statistical analysis is provided to compare BNMTH with other state-of-the-art optimization algorithms. The results show that BNMTH is a competitive approach for image segmentation, providing accurate results in almost all the cases. Moreover, the segmented images and the histograms show that the classes are accurately generated even in complex conditions.

A multimodal particle swarm optimization-based approach for image segmentation

Color image segmentation is a fundamental challenge in the field of image analysis and pattern recognition. In this paper, a novel automated pixel clustering and color image segmentation algorithm is presented. The proposed method operates in three successive stages. In the first stage, a three-dimensional histogram of pixel colors based on the RGB model is smoothened using a Gaussian filter. This process helps to eliminate unreliable and non-dominating peaks that are too close to one another in the histogram. In the next stage, the peaks representing different clusters in the histogram are identified using a multimodal particle swarm optimization algorithm. Finally, pixels are assigned to the most appropriate cluster based on Euclidean distance. Determining the number of clusters to be used is often a manual process left for a user and represents a challenge for various segmentation algorithms. The proposed method is designed to determine an appropriate number of clusters, in addition to the actual peaks, automatically. Experiments confirm that the proposed approach yields desirable results, demonstrating that it can find an appropriate set of clusters for a set of well-known benchmark images.

Hyper-heuristic method for multilevel thresholding image segmentation

In digital image processing, one of the most relevant tasks is to classify pixels depending on their intensity level. To perform this process there exist different traditional methods as Otsu or Kapur, such methods are used to compute the thresholds that divide the histogram of the image into different groups. These methods are easy to implement for a single threshold; however, the computational effort is affected when more thresholds are required. Therefore, different meta-heuristic based approaches have been proposed, but each of them has its properties and limitations. So, this paper introduces an alternative concept to the image segmentation which is called hyper-heuristic that at each iteration determines the optimal execution sequence of meta-heuristic algorithms that provides the optimal thresholds. The proposed method consists of two layers, in the first layer, the genetic algorithm (GA) is used to determine the execution sequence of the meta-heuristic algorithms. While the second layer contains the set of four meta-heuristic algorithms that executed in a specific order, assigned by the current solution of GA, to update the threshold population. In order to evaluate the performance of the proposed approach, it has been tested over a set of benchmark images and the results provide a good performance in terms of quality of segmentation. Moreover, experimental comparisons support that the proposed hyper-heuristic is able to find more accurate solutions than other algorithms.

Multilevel thresholding by fuzzy type II sets using evolutionary algorithms

Abstract The image segmentation based on Multilevel thresholding has attracted more attention in recent years, they have been used in different applications. Therefore, several evolutionary computation methods have been proposed to determine the optimal threshold values. However, these approaches suffer from some limitations such as the stagnation point which leads to degradation the quality of the segmented image. In addition, most of them used either Otsu or Kapur as a fitness function, and the complexity of these methods is increased with increasing the threshold levels. Moreover, they don’t provide accurate results in all the cases. To overcome such situations, in this paper is proposed the use of evolutionary computation algorithms combined with the Type II Fuzzy Entropy as the objective function. Such methods are the Backtracking Search Optimization Algorithm (BSA) and the Salp Swarm Algorithm (SSA). The BSA and SSA are able to avoid the limitation of similar techniques for image threshold because the objective function removes the ambiguities helping to find more accurate results. The BSA and SSA are used to find the best parameters of the Type II Fuzzy Entropy that extracts the optimal thresholds that properly segment the histogram of a digital image. To evaluate the performance of the proposed two methods, a set of experiments are performed using a set of benchmark images which have different characteristics. Moreover, the experiments are also performed over medical images from blood cells. The experimental results indicate that the proposed two methods have a good performance. However, they provide better performance than other algorithms in terms of quality and accuracy.

Modified Firefly Algorithm for Vector Quantization Codebook Design in Image Compression

In the recent days, the importance of image compression techniques is exponentially increased due to the generation of massive amount of data which needs to be stored or transmitted. Numerous approaches have been presented for effective image compression by the principle of representing images in its compact form through the avoidance of unnecessary pixels. Vector quantization (VA) is an effective method in image compression and the construction of quantization table is an important process is an important task. The compression performance and the quality of reconstructed data are based on the quantization table, which is actually a matrix of 64 integers. The quantization table selection is a complex combinatorial problem which can be resolved by the evolutionary algorithms (EA). Presently, EA became famous to resolve the real world problems in a reasonable amount of time. This chapter introduces Firefly (FF) with Teaching and learning based optimization (TLBO) algorithm termed as FF-TLBO algorithm for the selection of quantization table and introduces Firefly with Tumbling algorithm termed as FF-Tumbling algorithm for the selection of search space. As the FF algorithm faces a problem when brighter FFs are insignificant, the TLBO algorithm is integrated to it to resolve the problem and Tumbling efficiently train the algorithm to explore all direction in the solution space. This algorithm determines the best fit value for every bock as local best and best fitness value for the entire image is considered as global best. When these values are found by FF algorithm, compression process takes place by efficient image compression algorithm like Run Length Encoding and Huffman coding. The proposed FF-TLBO and FF-Tumbling algorithm is evaluated by comparing its results with existing FF algorithm using a same set of benchmark images in terms of Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), Signal to Noise Ratio (SNR). The obtained results ensure the superior performance of FF-TLBO and FF-Tumbling algorithm over FF algorithm and make it highly useful for real time applications.

Multiple kernel dimensionality reduction based on linear regression virtual reconstruction for image set classification

In this paper, we propose a novel multiple kernel dimensionality reduction (DR) method based on linear regression reconstruction mechanism for image set based classification. The proposed method aims to learn an optimal kernel automatically from the multiple base kernels and a projection transformation such that in the projected low dimensional subspace, the between-class reconstruction error denoted by the distance of the between-class reconstructed virtual samples is maximized and the within-class reconstruction error denoted by the distance of the within-class reconstructed virtual samples is minimized. Therefore, the compactness of reconstructed within-class virtual samples is enhanced, and between-class reconstructed virtual samples are better separated. This feature extraction scheme can best work with the corresponding classification strategy, which will naturally enhance the classification performance. By employing the method of trace ratio maximization, we also develop a framework to solve the resulting nonconvex optimization problem efficiently. Extensive experiments on benchmark image set datasets well demonstrate the effectiveness of the proposed method compared with other set based methods.