Hyperspectral Image Super-Resolution Network Based on Reinforcing Inter-Spectral Incremental Information

Hyperspectral images typically have high spectral resolution but low spatial resolution,which impacts the reliability and accuracy of subsequent applications,for example,remote sensingclassification and mineral identification.But in traditional methods via deep convolution neural net-works,indiscriminately extracting and fusing spectral and spatial features makes it challenging toutilize the differentiated information across adjacent spectral channels.Thus,we proposed a multi-branch interleaved iterative upsampling hyperspectral image super-resolution reconstruction net-work(MIIUSR)to address the above problems.We reinforce spatial feature extraction by integrat-ing detailed features from different receptive fields across adjacent channels.Furthermore,we pro-pose an interleaved iterative upsampling process during the reconstruction stage,which progres-sively fuses incremental information among adjacent frequency bands.Additionally,we add twoparallel three dimensional(3D)feature extraction branches to the backbone network to extractspectral and spatial features of varying granularity.We further enhance the backbone network’sconstruction results by leveraging the difference between two dimensional(2D)channel-groupingspatial features and 3D multi-granularity features.The results obtained by applying the proposednetwork model to the CAVE test set show that,at a scaling factor of×4,the peak signal to noiseratio,spectral angle mapping,and structural similarity are 37.310 dB,3.525 and 0.9438,respec-tively.Besides,extensive experiments conducted on the Harvard and Foster datasets demonstratethe superior potential of the proposed model in hyperspectral super-resolution reconstruction.

Batch Active Learning for Multispectral and Hyperspectral Image Segmentation Using Similarity Graphs

Graph learning,when used as a semi-supervised learning(SSL)method,performs well for classification tasks with a low label rate.We provide a graph-based batch active learning pipeline for pixel/patch neighborhood multi-or hyperspectral image segmentation.Our batch active learning approach selects a collection of unlabeled pixels that satisfy a graph local maximum constraint for the active learning acquisition function that determines the relative importance of each pixel to the classification.This work builds on recent advances in the design of novel active learning acquisition functions(e.g.,the Model Change approach in arXiv:2110.07739)while adding important further developments including patch-neighborhood image analysis and batch active learning methods to further increase the accuracy and greatly increase the computational efficiency of these methods.In addition to improvements in the accuracy,our approach can greatly reduce the number of labeled pixels needed to achieve the same level of the accuracy based on randomly selected labeled pixels.

Quantification of the adulteration concentration of palm kernel oil in virgin coconut oil using near-infrared hyperspectral imaging

The adulteration concentration of palm kernel oil(PKO)in virgin coconut oil(VCO)was quantified using near-infrared(NIR)hyperspectral imaging.Nowadays,some VCO is adulterated with lower-priced PKO to reduce production costs,which diminishes the quality of the VCO.This study used NIR hyperspectral imaging in the wavelength region 900-1,650 nm to create a quantitative model for the detection of PKO contaminants(0-100%)in VCO and to develop predictive mapping.The prediction equation for the adulteration of VCO with PKO was constructed using the partial least squares regression method.The best predictive model was pre-processed using the standard normal variate method,and the coefficient of determination of prediction was 0.991,the root mean square error of prediction was 2.93%,and the residual prediction deviation was 10.37.The results showed that this model could be applied for quantifying the adulteration concentration of PKO in VCO.The prediction adulteration concentration mapping of VCO with PKO was created from a calibration model that showed the color level according to the adulteration concentration in the range of 0-100%.NIR hyperspectral imaging could be clearly used to quantify the adulteration of VCO with a color level map that provides a quick,accurate,and non-destructive detection method.

Hyperspectral image super resolution using deep internal and self-supervised learning

By automatically learning the priors embedded in images with powerful modelling ca-pabilities,deep learning-based algorithms have recently made considerable progress in reconstructing the high-resolution hyperspectral(HR-HS)image.With previously collected large-amount of external data,these methods are intuitively realised under the full supervision of the ground-truth data.Thus,the database construction in merging the low-resolution(LR)HS(LR-HS)and HR multispectral(MS)or RGB image research paradigm,commonly named as HSI SR,requires collecting corresponding training triplets:HR-MS(RGB),LR-HS and HR-HS image simultaneously,and often faces dif-ficulties in reality.The learned models with the training datasets collected simultaneously under controlled conditions may significantly degrade the HSI super-resolved perfor-mance to the real images captured under diverse environments.To handle the above-mentioned limitations,the authors propose to leverage the deep internal and self-supervised learning to solve the HSI SR problem.The authors advocate that it is possible to train a specific CNN model at test time,called as deep internal learning(DIL),by on-line preparing the training triplet samples from the observed LR-HS/HR-MS(or RGB)images and the down-sampled LR-HS version.However,the number of the training triplets extracted solely from the transformed data of the observation itself is extremely few particularly for the HSI SR tasks with large spatial upscale factors,which would result in limited reconstruction performance.To solve this problem,the authors further exploit deep self-supervised learning(DSL)by considering the observations as the unlabelled training samples.Specifically,the degradation modules inside the network were elaborated to realise the spatial and spectral down-sampling procedures for transforming the generated HR-HS estimation to the high-resolution RGB/LR-HS approximation,and then the reconstruction errors of the observations were formulated for measuring the network modelling performance.By consolidating the DIL and DSL into a unified deep framework,the authors construct a more robust HSI SR method without any prior training and have great potential of flexible adaptation to different settings per obser-vation.To verify the effectiveness of the proposed approach,extensive experiments have been conducted on two benchmark HS datasets,including the CAVE and Harvard datasets,and demonstrate the great performance gain of the proposed method over the state-of-the-art methods.

Multiscale Fusion Transformer Network for Hyperspectral Image Classification

Convolutional neural network(CNN)has excellent ability to model locally contextual information.However,CNNs face challenges for descripting long-range semantic features,which will lead to relatively low classification accuracy of hyperspectral images.To address this problem,this article proposes an algorithm based on multiscale fusion and transformer network for hyperspectral image classification.Firstly,the low-level spatial-spectral features are extracted by multi-scale residual structure.Secondly,an attention module is introduced to focus on the more important spatialspectral information.Finally,high-level semantic features are represented and learned by a token learner and an improved transformer encoder.The proposed algorithm is compared with six classical hyperspectral classification algorithms on real hyperspectral images.The experimental results show that the proposed algorithm effectively improves the land cover classification accuracy of hyperspectral images.

A Spectral Convolutional Neural Network Model Based on Adaptive Fick’s Law for Hyperspectral Image Classification

Hyperspectral image classification stands as a pivotal task within the field of remote sensing,yet achieving highprecision classification remains a significant challenge.In response to this challenge,a Spectral Convolutional Neural Network model based on Adaptive Fick’s Law Algorithm(AFLA-SCNN)is proposed.The Adaptive Fick’s Law Algorithm(AFLA)constitutes a novel metaheuristic algorithm introduced herein,encompassing three new strategies:Adaptive weight factor,Gaussian mutation,and probability update policy.With adaptive weight factor,the algorithmcan adjust theweights according to the change in the number of iterations to improve the performance of the algorithm.Gaussianmutation helps the algorithm avoid falling into local optimal solutions and improves the searchability of the algorithm.The probability update strategy helps to improve the exploitability and adaptability of the algorithm.Within the AFLA-SCNN model,AFLA is employed to optimize two hyperparameters in the SCNN model,namely,“numEpochs”and“miniBatchSize”,to attain their optimal values.AFLA’s performance is initially validated across 28 functions in 10D,30D,and 50D for CEC2013 and 29 functions in 10D,30D,and 50D for CEC2017.Experimental results indicate AFLA’s marked performance superiority over nine other prominent optimization algorithms.Subsequently,the AFLA-SCNN model was compared with the Spectral Convolutional Neural Network model based on Fick’s Law Algorithm(FLA-SCNN),Spectral Convolutional Neural Network model based on Harris Hawks Optimization(HHO-SCNN),Spectral Convolutional Neural Network model based onDifferential Evolution(DE-SCNN),SpectralConvolutionalNeuralNetwork(SCNN)model,and SupportVector Machines(SVM)model using the Indian Pines dataset and PaviaUniversity dataset.The experimental results show that the AFLA-SCNN model outperforms other models in terms of Accuracy,Precision,Recall,and F1-score on Indian Pines and Pavia University.Among them,the Accuracy of the AFLA-SCNN model on Indian Pines reached 99.875%,and the Accuracy on PaviaUniversity reached 98.022%.In conclusion,our proposed AFLA-SCNN model is deemed to significantly enhance the precision of hyperspectral image classification.

Investigation on Physiological Status of Regional Vegetation Using Pushbroom Hyperspectral Imager Data

To extract vegetation pigment concentration and physiological status has been studied in two test areas covered with swamp and flourish vegetation using pushbroom hyperspectral imager (PHI) data which flied in September of 2000 at Daxing'anling district of Heilongjiang Province, China. The ratio analysis of reflectance spectra (RARS) indices, which were put forward by Chappelle et al (1992), are chosen in this paper owing to their effect and simpleness against both comparison with various methods and techniques for exploration of pigment concentration and characteristics of PHI data. The correlation coefficients between RARS indices and pigment concentration of vegetation were up to 0.8. The new RARS indices modes are established in the two test areas using both PHI data and spectra of different vegetations measured in the field. The indices' parameter images of chlorophyll a (Chl a), chlorophyll b (Chl b) and carotenoids (Cars) of the test areas covered with swamp and flourish vegetation are acquired by the new RARS indices modes. Furthermore, the regional concentration of Chl a and Chl b are extracted and quantified using regression equations between RARS indices and pigment concentrations, which were built by Blackburn (1998). The results showed the physiological status and variety clearly, and are in good agreement with the distribution of vegetation in the field.

Hyperspectral Image Super-Resolution Meets Deep Learning:A Survey and Perspective

Hyperspectral image super-resolution,which refers to reconstructing the high-resolution hyperspectral image from the input low-resolution observation,aims to improve the spatial resolution of the hyperspectral image,which is beneficial for subsequent applications.The development of deep learning has promoted significant progress in hyperspectral image super-resolution,and the powerful expression capabilities of deep neural networks make the predicted results more reliable.Recently,several latest deep learning technologies have made the hyperspectral image super-resolution method explode.However,a comprehensive review and analysis of the latest deep learning methods from the hyperspectral image super-resolution perspective is absent.To this end,in this survey,we first introduce the concept of hyperspectral image super-resolution and classify the methods from the perspectives with or without auxiliary information.Then,we review the learning-based methods in three categories,including single hyperspectral image super-resolution,panchromatic-based hyperspectral image super-resolution,and multispectral-based hyperspectral image super-resolution.Subsequently,we summarize the commonly used hyperspectral dataset,and the evaluations for some representative methods in three categories are performed qualitatively and quantitatively.Moreover,we briefly introduce several typical applications of hyperspectral image super-resolution,including ground object classification,urban change detection,and ecosystem monitoring.Finally,we provide the conclusion and challenges in existing learning-based methods,looking forward to potential future research directions.

Deep hybrid: Multi-graph neural network collaboration for hyperspectral image classification

With limited number of labeled samples,hyperspectral image(HSI)classification is a difficult Problem in current research.The graph neural network(GNN)has emerged as an approach to semi-supervised classification,and the application of GNN to hyperspectral images has attracted much attention.However,in the existing GNN-based methods a single graph neural network or graph filter is mainly used to extract HSI features,which does not take full advantage of various graph neural networks(graph filters).Moreover,the traditional GNNs have the problem of oversmoothing.To alleviate these shortcomings,we introduce a deep hybrid multi-graph neural network(DHMG),where two different graph filters,i.e.,the spectral filter and the autoregressive moving average(ARMA)filter,are utilized in two branches.The former can well extract the spectral features of the nodes,and the latter has a good suppression effect on graph noise.The network realizes information interaction between the two branches and takes good advantage of different graph filters.In addition,to address the problem of oversmoothing,a dense network is proposed,where the local graph features are preserved.The dense structure satisfies the needs of different classification targets presenting different features.Finally,we introduce a GraphSAGEbased network to refine the graph features produced by the deep hybrid network.Extensive experiments on three public HSI datasets strongly demonstrate that the DHMG dramatically outperforms the state-ofthe-art models.

Hyperspectral remote sensing identification of marine oil spills and emulsions using feature bands and double-branch dual-attention mechanism network

The accurate identification of marine oil spills and their emulsions is of great significance for emergency response to oil spill pollution.The selection of characteristic bands with strong separability helps to realize the rapid calculation of data on aircraft or in orbit,which will improve the timeliness of oil spill emergency monitoring.At the same time,the combination of spectral and spatial features can improve the accuracy of oil spill monitoring.Two ground-based experiments were designed to collect measured airborne hyperspectral data of crude oil and its emulsions,for which the multiscale superpixel level group clustering framework(MSGCF)was used to select spectral feature bands with strong separability.In addition,the double-branch dual-attention(DBDA)model was applied to identify crude oil and its emulsions.Compared with the recognition results based on original hyperspectral images,using the feature bands determined by MSGCF improved the recognition accuracy,and greatly shortened the running time.Moreover,the characteristic bands for quantifying the volume concentration of water-in-oil emulsions were determined,and a quantitative inversion model was constructed and applied to the AVIRIS image of the deepwater horizon oil spill event in 2010.This study verified the effectiveness of feature bands in identifying oil spill pollution types and quantifying concentration,laying foundation for rapid identification and quantification of marine oil spills and their emulsions on aircraft or in orbit.

Spatial-Spectral Joint Network for Cholangiocarcinoma Microscopic Hyperspectral Image Classification

Accurate histopathology classification is a crucial factor in the diagnosis and treatment of Cholangiocarcinoma(CCA).Hyperspectral images(HSI)provide rich spectral information than ordinary RGB images,making them more useful for medical diagnosis.The Convolutional Neural Network(CNN)is commonly employed in hyperspectral image classification due to its remarkable capacity for feature extraction and image classification.However,many existing CNN-based HSI classification methods tend to ignore the importance of image spatial context information and the interdependence between spectral channels,leading to unsatisfied classification performance.Thus,to address these issues,this paper proposes a Spatial-Spectral Joint Network(SSJN)model for hyperspectral image classification that utilizes spatial self-attention and spectral feature extraction.The SSJN model is derived from the ResNet18 network and implemented with the non-local and Coordinate Attention(CA)modules,which extract long-range dependencies on image space and enhance spatial features through the Branch Attention(BA)module to emphasize the region of interest.Furthermore,the SSJN model employs Conv-LSTM modules to extract long-range depen-dencies in the image spectral domain.This addresses the gradient disappearance/explosion phenom-ena and enhances the model classification accuracy.The experimental results show that the pro-posed SSJN model is more efficient in leveraging the spatial and spectral information of hyperspec-tral images on multidimensional microspectral datasets of CCA,leading to higher classification accuracy,and may have useful references for medical diagnosis of CCA.

Deep transformer and few‐shot learning for hyperspectral image classification

Recently,deep learning has achieved considerable results in the hyperspectral image(HSI)classification.However,most available deep networks require ample and authentic samples to better train the models,which is expensive and inefficient in practical tasks.Existing few‐shot learning(FSL)methods generally ignore the potential relationships between non‐local spatial samples that would better represent the underlying features of HSI.To solve the above issues,a novel deep transformer and few‐shot learning(DTFSL)classification framework is proposed,attempting to realize fine‐grained classification of HSI with only a few‐shot instances.Specifically,the spatial attention and spectral query modules are introduced to overcome the constraint of the convolution kernel and consider the information between long‐distance location(non‐local)samples to reduce the uncertainty of classes.Next,the network is trained with episodes and task‐based learning strategies to learn a metric space,which can continuously enhance its modelling capability.Furthermore,the developed approach combines the advantages of domain adaptation to reduce the variation in inter‐domain distribution and realize distribution alignment.On three publicly available HSI data,extensive experiments have indicated that the proposed DT‐FSL yields better results concerning state‐of‐the‐art algorithms.

Three-Stages Hyperspectral Image Compression Sensing with Band Selection

Compressed sensing(CS),as an efficient data transmission method,has achieved great success in the field of data transmission such as image,video and text.It can robustly recover signals from fewer Measurements,effectively alleviating the bandwidth pressure during data transmission.However,CS has many shortcomings in the transmission of hyperspectral image(HSI)data.This work aims to consider the application of CS in the transmission of hyperspectral image(HSI)data,and provides a feasible research scheme for CS of HSI data.HSI has rich spectral information and spatial information in bands,which can reflect the physical properties of the target.Most of the hyperspectral image compressed sensing(HSICS)algorithms cannot effectively use the inter-band information of HSI,resulting in poor reconstruction effects.In this paper,A three-stage hyperspectral image compression sensing algorithm(Three-stages HSICS)is proposed to obtain intra-band and inter-band characteristics of HSI,which can improve the reconstruction accuracy of HSI.Here,we establish a multi-objective band selection(Mop-BS)model,amulti-hypothesis prediction(MHP)model and a residual sparse(ReWSR)model for HSI,and use a staged reconstruction method to restore the compressed HSI.The simulation results show that the three-stage HSICS successfully improves the reconstruction accuracy of HSICS,and it performs best among all comparison algorithms.

Research on the detection of early caries based on hyperspectral imaging

Objective:We applied hyperspectral imaging(HSI)system to distinguish early caries from soundand pigmented areas.It will provide a theoretical basis and technical support,for research anddevelopment of an instrument that could be used for screening and detection of early dentalcaries.Methods:Eighteen extracted human teeth(molars and premolars),with varying degrees ofnatural pathology and no degree of decay involving dentin were obtained.HSI system with awavelength range from 400 to 1000nm was used to obtain images of all 18 teeth containingsound,carious and pigmented areas.We compared the spectra of the wavebands at both 500 nmand 780 nm from the different tooth states,and the reflectance diference bet ween sound versuscarious lesions and sound versus pigmented areas,respectively.Results:There was a slight diference in refectance bet ween carious areas and pigmented areas at500 nm.A substantial difference was additionally noted in refectance bet ween carious areas andpigmented areas at 780 nm.Conclusion:The results have shown that the interference of tooth surface pigment can be elim-inated in the near-infrared(NIR)waveband,and the caries can be effectively identifed from the pigmented areas.Thus,it could be used to detect carious areas of teeth in place of the traditionalvisual inspection method or white light endoscopy.Clinical significance:The NIR difused light signal enables the identification of early caries frompigment and other interference,providing a reasonable detection tool for early detection andearly treatment of teeth diseases.

Identification of Early Peach Aphid Infestation Based on Hyperspectral Imaging Technology

Peach aphid is a common pest and hard to detect.This study employs hyperspectral imaging technology to identify early damage in green cabbage caused by peach aphid.Through principal component transformation and multiple linear regression analysis,the correlation relation between spectral characteristics and infestation stage is analyzed.Then,four characteristic wavelength selection methods are compared and optimal characteristic wavelengths subset is determined to be input for modelling.One linear algorithm and two nonlinear modelling algorithms are compared.Finally,support vector machine(SVM)model based on the characteristic wavelengths selected by multi-cluster feature selection(MCFS)acquires the highest identification accuracy,which is 98.97%.These results indicate that hyperspectral imaging technology have the ability to identify early peach aphid infestation stages on green cabbages.

Differentiation of Wheat Diseases and Pests Based on Hyperspectral Imaging Technology with a Few Specific Bands

Hyperspectral imaging technique is known as a promising non-destructive way for detecting plants diseases and pests.In most previous studies,the utilization of the whole spectrum or a large number of bands as well as the complexity of model structure severely hampers the application of the technique in practice.If a detection system can be established with a few bands and a relatively simple logic,it would be of great significance for application.This study established a method for identifying and discriminating three commonly occurring diseases and pests of wheat,i.e.,powdery mildew,yellow rust and aphid with a few specific bands.Through a comprehensive spectral analysis,only three bands at 570,680 and 750 nm were selected.A novel vegetation index namely Ratio Triangular Vegetation Index(RTVI)was developed for detecting anomalous areas on leaves.Then,the Support Vector Machine(SVM)method was applied to construct the discrimination model based on the spectral ratio analysis.The validating results suggested that the proposed method with only three spectral bands achieved a promising accuracy with the Overall Accuracy(OA)of 83%.With three bands from the hyperspectral imaging data,the three wheat diseases and pests were successfully detected and discriminated.A stepwise strategy including background removal,damage lesions recognition and stresses discrimination was proposed.The present work can provide a basis for the design of low cost and smart instruments for disease and pest detection.

Hyperspectral Image Sharpening Based on Deep Convolutional Neural Network and Spatial-Spectral Spread Transform Models

In order to improve the spatial resolution of hyperspectral(HS)image and minimize the spectral distortion,an HS and multispectral(MS)image fusion approach based on convolutional neural network(CNN)is proposed.The proposed approach incorporates the linear spectral mixture model and spatial-spectral spread transform model into the learning phase of network,aiming to fully exploit the spatial-spectral information of HS and MS images,and improve the spectral fidelity of fusion images.Experiments on two real remote sensing data under different resolutions demonstrate that compared with some state-of-the-art HS and MS image fusion methods,the proposed approach achieves superior spectral fidelities and lower fusion errors.

Automated Deep Learning Driven Crop Classification on Hyperspectral Remote Sensing Images

Hyperspectral remote sensing/imaging spectroscopy is a novel approach to reaching a spectrum from all the places of a huge array of spatial places so that several spectral wavelengths are utilized for making coherent images.Hyperspectral remote sensing contains acquisition of digital images from several narrow,contiguous spectral bands throughout the visible,Thermal Infrared(TIR),Near Infrared(NIR),and Mid-Infrared(MIR)regions of the electromagnetic spectrum.In order to the application of agricultural regions,remote sensing approaches are studied and executed to their benefit of continuous and quantitativemonitoring.Particularly,hyperspectral images(HSI)are considered the precise for agriculture as they can offer chemical and physical data on vegetation.With this motivation,this article presents a novel Hurricane Optimization Algorithm with Deep Transfer Learning Driven Crop Classification(HOADTL-CC)model onHyperspectralRemote Sensing Images.The presentedHOADTL-CC model focuses on the identification and categorization of crops on hyperspectral remote sensing images.To accomplish this,the presentedHOADTL-CC model involves the design ofHOAwith capsule network(CapsNet)model for generating a set of useful feature vectors.Besides,Elman neural network(ENN)model is applied to allot proper class labels into the input HSI.Finally,glowworm swarm optimization(GSO)algorithm is exploited to fine tune the ENNparameters involved in this article.The experimental result scrutiny of the HOADTL-CC method can be tested with the help of benchmark dataset and the results are assessed under distinct aspects.Extensive comparative studies stated the enhanced performance of the HOADTL-CC model over recent approaches with maximum accuracy of 99.51%.

Automated Red Deer Algorithm with Deep Learning Enabled Hyperspectral Image Classification

Hyperspectral(HS)image classification is a hot research area due to challenging issues such as existence of high dimensionality,restricted training data,etc.Precise recognition of features from the HS images is important for effective classification outcomes.Additionally,the recent advancements of deep learning(DL)models make it possible in several application areas.In addition,the performance of the DL models is mainly based on the hyperparameter setting which can be resolved by the design of metaheuristics.In this view,this article develops an automated red deer algorithm with deep learning enabled hyperspec-tral image(HSI)classification(RDADL-HIC)technique.The proposed RDADL-HIC technique aims to effectively determine the HSI images.In addition,the RDADL-HIC technique comprises a NASNetLarge model with Adagrad optimi-zer.Moreover,RDA with gated recurrent unit(GRU)approach is used for the identification and classification of HSIs.The design of Adagrad optimizer with RDA helps to optimally tune the hyperparameters of the NASNetLarge and GRU models respectively.The experimental results stated the supremacy of the RDADL-HIC model and the results are inspected interms of different measures.The comparison study of the RDADL-HIC model demonstrated the enhanced per-formance over its recent state of art approaches.

A Novel Fuzzy Inference System-Based Endmember Extraction in Hyperspectral Images

Spectral unmixing helps to identify different components present in the spectral mixtures which occur in the uppermost layer of the area owing to the low spatial resolution of hyperspectral images.Most spectral unmixing methods are globally based and do not consider the spectral variability among its endmembers that occur due to illumination,atmospheric,and environmental conditions.Here,endmember bundle extraction plays a major role in overcoming the above-mentioned limitations leading to more accurate abundance fractions.Accordingly,a two-stage approach is proposed to extract endmembers through endmember bundles in hyperspectral images.The divide and conquer method is applied as the first step in subset images with only the non-redundant bands to extract endmembers using the Vertex Component Analysis(VCA)and N-FINDR algorithms.A fuzzy rule-based inference system utilizing spectral matching parameters is proposed in the second step to categorize endmembers.The endmember with the minimum error is chosen as the final endmember in each specific category.The proposed method is simple and automatically considers endmember variability in hyperspectral images.The efficiency of the proposed method is evaluated using two real hyperspectral datasets.The average spectral angle and abundance angle are used to analyze the performance measures.