This work begins with some brief historical comments to set the stage for a discussion of the long-term potential for land remote sensing technology. This is followed by comments about what is needed to accelerate the achievement of this potential. The discussion is concluded with what concomitant development is needed with regard to a hyperspectral data analysis system.

In this paper, we propose a cost-effective iterative semisupervised classifier based on a kernel concept. The proposed technique incorporates unlabeled data into the design of a binary classifier by introducing and optimizing a cost function in a feature space that maximizes the Rayleigh coefficient while minimizing the total cost associated with misclassified labeled samples. The cost assigned to misclassified labeled samples accounts for the number of misclassified labeled samples as well as the amount by which they are on the wrong side of the boundary, and this counterbalances any potential adverse effect of unlabeled data on the classifier performance. Several experiments performed with remotely sensed data demonstrate that using the proposed semisupervised classifier shows considerable improvements over the supervised-only counterpart.

In this paper, we propose a supervised classifier based on implementation of the Bayes rule with kernels. The proposed technique first proposes an implicit nonlinear transformation of the data into a feature space seeking to fit normal distributions having a common covariance matrix onto the mapped data. One requirement of this approach is the evaluation of posterior probabilities. We express the discriminant function in dot-product form, and then apply the kernel concept to efficiently evaluate the posterior probabilities. The proposed technique gives the flexibility required to model complex data structures that originate from a wide range of class-conditional distributions. Although we end up with piecewise linear decision boundaries in the feature space, these corresponds to powerful nonlinear boundaries in the original input space. For the data we considered, we have obtained some encouraging results.

In this paper, a new nonparametric feature extraction method is proposed for high-dimensional multiclass pattern recognition problems. It is based on a nonparametric extension of scatter matrices. There are at least two advantages to using the proposed nonparametric scatter matrices. First, they are generally of full rank. This provides the ability to specify the number of extracted features desired and to reduce the effect of the singularity problem. This is in contrast to parametric discriminant analysis, which usually only can extract L-1 (number of classes minus one) features. In a real situation, this may not be enough. Second, the nonparametric nature of scatter matrices reduces the effects of outliers and works well even for nonnormal datasets. The new method provides greater weight to samples near the expected decision boundary. This tends to provide for increased classification accuracy.

New Gaussian mixture classifiers are designed by replacing the maximum likelihood covariance estimator with regularized covariance estimator in both parameters estimation and model selection steps. The results of simulated and real data experiments suggested that nearest mean clustering and Bayesian information criterion with regularized covariance estimator is a better choice to build a Gaussian mixture classifier.

In this paper an adaptive Bayesian contextual classification procedure that utilizes both spectral and spatial interpixel dependency contexts in statistics estimation and classification is proposed. Essentially, this classifier is the constructive coupling of an adaptive classification procedure and a Bayesian contextual classification procedure. In this classifier, the joint prior probabilities of the classes of each pixel and its spatial neighbors are modeled by the Markov random field. Experiments with real hyperspectral data show that, starting with a small training sample set, this classifier can reach classification accuracies similar to that obtained by a pixelwise maximum likelihood classifier with a very large training sample set. Additionally, classification maps are produced which have significantly less speckle error.

In this paper, a new nonparametric feature extraction method is proposed for high dimensional multiclass pattern recognition problems. It is based on a nonparametric extension of scatter matrices. There are at least two advantages to using the proposed nonparametric scatter matrices. First, they are generally of full rank. This provides the ability to specify the number of extracted features desired and to reduce the effect of the singularity problem. This is in contrast to parametric discriminant analysis, which usually only can extract L-1 (number of classes minus one) features. In a real situation, this may not be enough. Second, the nonparametric nature of scatter matrices reduces the effects of outliers and works well even for non-normal data sets. The new method provides greater weight to samples near the expected decision boundary. This tends to provide for increased classification accuracy.

The main purpose of this work is to find an improved regularized covariance estimator of each class with the advantages of LOOC, and BLOOC, which are useful for high dimensional pattern recognition problems. The searching ranges of LOOC and BLOOC are between the linear combinations of three pair covariance estimators. The first proposed covariance estimator (mixed-LOOC1) extended the searching range and is a general case of LOOC and BLOOC. By observing that the optimal value of leave-one-out likelihood function of LOOC usually occurs at near the end point of the parameter domain, the second covariance estimator (mixed-LOOC2), which needs less computation, was proposed. Using the proposed covariance estimator to improve the linear feature extraction methods when the multivariate data are singular or nearly so is demonstrated.

It is well known that there is a strong relation between class definition precision and classification accuracy in pattern classification applications. In hyperspectral data analysis, usually classes of interest contain one or more components and may not be well represented by a single Gaussian density function. In this paper, a model-based mixture classifier, which uses mixture models to characterize class densities, is discussed. However, a key outstanding problem of this approach is how to choose the number of components and determine their parameters for such models in practice, and to do so in the face of limited training sets where estimation error becomes a significant factor. The proposed classifier estimates the number of subclasses and class statistics simultaneously by choosing the best model. The structure of class covariances is also addressed through a model-based covariance estimation technique introduced in this paper.

In this paper, a family of adaptive covariance estimators is proposed to mitigate the problem of limited training samples for application to hyperspectral data analysis in quadratic maximum likelihood classification. These estimators are the combination of adaptive classification procedures and regularized covariance estimators. In these proposed estimators, the semi-labeled samples (whose labels are determined by a decision rule) are incorporated in the process of determining the optimal regularized parameters and estimating those supportive covariance matrices that formulate final regularized covariance estimators. In all experiments with simulated and real remote sensing data, these proposed combined covariance estimators achieved significant improvement on statistics estimation and classification accuracy over conventional regularized covariance estimators and an adaptive maximum likelihood classifier (MLC). The degree of improvement increases with dimensions, especially for ill-posed or very ill-posed problems where the total number of training samples is smaller than the number of dimensions.

An adaptive Bayesian contextual classification procedure that utilizes both spectral and spatial interpixel dependency contexts in estimation of statistics and classification is proposed. Essentially, this classifier is the constructive coupling of an adaptive classification procedure and a Bayesian contextual classification procedure. In this classifier, the joint prior probabilities of the classes of each pixel and its spatial neighbors are modeled by the Markov random field. The estimation of statistics and classification are performed in a recursive manner to allow the establishment of the positive-feedback process in a computationally efficient manner. Experiments with real hyperspectral data show that, starting with a small training sample set, this classifier can reach classification accuracies similar to that obtained by a pixelwise maximum likelihood pixel classifier with a very large training sample set. Additionally, classification maps are produced that have significantly less speckle error.

A key to successful classification of multivariate data is the defining of an accurate quantitative model of each class. This is especially the case when the dimensionality of the data is high, and the problem is exacerbated when the number of training samples is limited. For the commonly used quadratic maximum-likelihood classifier, the class mean vectors and covariance matrices are required and must be estimated from the available training samples. In high dimensional cases, it has been found that feature extraction methods are especially useful, so as to transform the problem to a lower dimensional space without loss of information, however, here too class statistics estimation error is significant. Finding a suitable regularized covariance estimator is a way to mitigate these estimation error effects. The main purpose of this work is to find an improved regularized covariance estimator of each class with the advantages of Leave-One-Out Covariance Estimator (LOOC) and Bayesian LOOC (BLOOC). Besides, using the proposed covariance estimator to improve the linear feature extraction methods when the multivariate data is singular or nearly so is demonstrated. This work is specifically directed at analysis methods for hyperspectral remote sensing data.

There are many factors to consider in carrying out a hyperspectral data classification. Perhaps chief among them are class training sample size, dimensionality, and distribution separability. The intent of this study is to design a classification procedure that is robust and maximally effective, but which provides the analyst with significant assists, thus simplifying the analyst's task. The result is a quadratic mixture classifier based on Mixed-LOOC2 regularized discriminant analysis and nonparametric weighted feature extraction. This procedure has the advantage of providing improved classification accuracy compared to typical previous methods but requires minimal need to consider the factors mentioned above. Experimental results demonstrating these properties are presented.

Remote sensing data is collected and analyzed to enhance understanding of the terrestrial surface-in composition, in form, or in function. One approach for accomplishing this is to design the analysis process as an iterated composite of several analyst-directed modules. This paper proposes such a modular design for the data analysis. The proposed methodology was applied in a project to obtain the thematic map for a flightline over Washington, DC, with very satisfactory results-the qualification being in both the visual and the statistical sense. The project execution is presented as a case study in this paper.

Proposes a self-learning and self-improving adaptive classifier to mitigate the problem of small training sample size that can severely affect the recognition accuracy of classifiers when the dimensionality of the multispectral data is high. This proposed adaptive classifier utilizes classified samples (referred to as semilabeled samples) in addition to original training samples iteratively. In order to control the influence of semilabeled samples, the proposed method gives full weight to the training samples and reduced weight to semilabeled samples. The authors show that by using additional semilabeled samples that are available without extra cost, the additional class label information may be extracted and utilized to enhance statistics estimation and hence improve the classifier performance, and therefore the Hughes phenomenon (peak phenomenon) may be mitigated. Experimental results show this proposed adaptive classifier can improve the classification accuracy as well as representation of estimated statistics significantly.

In pattern recognition, when the ratio of the number of training samples to the dimensionality is small, parameter estimates become highly variable, causing the deterioration of classification performance. This problem has become more prevalent in remote sensing with the emergence of a new generation of sensors with as many as several hundred spectral bands. While the new sensor technology provides higher spectral and spatial resolution, enabling a greater number of spectrally separable classes to be identified, the needed labeled samples for designing the classifier remain difficult and expensive to acquire. Better parameter estimates can be obtained by exploiting a large number of unlabeled samples in addition to training samples, using the expectation maximization algorithm under the mixture model. However, the estimation method is sensitive to the presence of statistical outliers. In remote sensing data, miscellaneous classes with few samples are often difficult to identify and may constitute statistical outliers. Therefore, the authors propose to use a robust parameter-estimation method for the mixture model. The proposed method assigns full weight to training samples, but automatically gives reduced weight to unlabeled samples. Experimental results show that the robust method prevents performance deterioration due to statistical outliers in the data as compared to the estimates obtained from the direct EM approach.

It is well known that high-dimensional image data allows for the separation of classes that are spectrally very similar, i.e., possess nearly equal first-order statistics, provided that their second-order statistics differ significantly. The aim of this study is to contribute to a better understanding, from a more geometrically oriented point of view, of the role played by the second-order statistics in remote sensing digital image classification of natural scenes when the classes of interest are spectrally very similar and high dimensional multispectral image data is available. A number of the investigations that have been developed in this area deal with the fact that as the data dimensionality increases, so does the difficulty in obtaining a reasonably accurate estimate of the within-class covariance matrices from the number of available labeled samples, which is usually limited. Several approaches have been proposed to deal with this problem. This study aims toward a complementary goal. Assuming that reasonably accurate estimates for the within-class covariance matrices have been obtained, we seek to better understand what kind of geometrically-oriented interpretation can be given to them as the data dimensionality increases and also to understand how this knowledge can help the design of a classifier. In order to achieve this goal, the covariance matrix is decomposed into a number of parameters that are then analyzed separately with respect to their ability to separate the classes. Methods for image classification based on these parameters are investigated. Results of tests using data provided by the sensor system AVIRIS are presented and discussed.

This paper addresses a classification problem in which class definition through training samples or otherwise is provided a priori only for a particular class of interest. Considerable time and effort may be required to label samples necessary for defining all the classes existent in a given data set by collecting ground truth or by other means. Thus, this problem is very important in practice, because one is often interested in identifying samples belonging to only one or a small number of classes. The problem is considered as an unsupervised clustering problem with initially one known cluster. The definition and statistics of the other classes are automatically developed through a weighted unsupervised clustering procedure that keeps the known cluster from losing its identity as the "class of interest". Once all the classes are developed, a conventional supervised classifier such as the maximum likelihood classifier is used in the classification. Experimental results with both simulated and real data verify the effectiveness of the proposed method.

This paper proposes two decision fusion-based multitemporal classifiers, namely, the jointly likelihood and the weighted majority fusion classifiers, that are derived using two different definitions of the minimum expected cost. Without any overhead incurred by multitemporal processing, a user-selected conventional pixelwise classifier makes local class separately using each temporal data set, and the multitemporal classifiers make the global class decisions by optimally summarizing those local class decisions. The proposed weighted majority decision fusion classifier can handle not only the data set reliabilities but also the classwise reliabilities of each data set. Classification experiment using the jointly likelihood decision fusion with three remotely sensed Thematic Mapper (TM) data sets shows more than 10% overall classification accuracy improvement over the pixelwise maximum likelihood classifier.

As the number of spectral bands of high-spectral resolution data increases, the ability to detect more detailed classes should also increase, and the classification accuracy should increase as well. Often the number of labelled samples used for supervised classification techniques is limited, thus limiting the precision with which class characteristics can be estimated. As the number of spectral bands becomes large, the limitation on performance imposed by the limited number of training samples can become severe. A number of techniques for case-specific feature extraction have been developed to reduce dimensionality without loss of class separability. Most of these techniques require the estimation of statistics at full dimensionality in order to extract relevant features for classification. If the number of training samples is not adequately large, the estimation of parameters in high-dimensional data will not be accurate enough. As a result, the estimated features may not be as effective as they could be. This suggests the need for reducing the dimensionality via a preprocessing method that takes into consideration high-dimensional feature-space properties. Such reduction should enable the estimation of feature-extraction parameters to be more accurate. Using a technique referred to as projection pursuit (PP), such an algorithm has been developed. This technique is able to bypass many of the problems of the limitation of small numbers of training samples by making the computations in a lower-dimensional space, and optimizing a function called the projection index. A current limitation of this method is that, as the number of dimensions increases, it is likely that a local maximum of the projection index will be found that does not enable one to fully exploit hyperspectral-data capabilities.

This paper describes a covariance estimator formulated under an empirical Bayesian setting to mitigate the problem of limited training samples in the Gaussian maximum likelihood (ML) classification for remote sensing. The most suitable covariance mixture is selected by maximizing the average leave-one-out log likelihood. Experimental results using AVIRIS data are presented.

The recent development of more sophisticated remote-sensing systems enables the measurement of radiation in many more spectral intervals than was previously possible. An example of this technology is the AVIRIS system, which collects image data in 220 bands. The increased dimensionality of such hyperspectral data greatly enhances the data's information content, but provides a challenge to the current techniques for analyzing such data. Human experience in 3D space tends to mislead our intuition of geometrical and statistical properties in high-dimensional space, properties which must guide our choices in the data analysis process. Using Euclidean and Cartesian geometry, high-dimensional space properties are investigated in this paper, and their implication for high-dimensional data and its analysis is studied in order to illuminate the differences between conventional spaces and hyperdimensional space.

In this paper, we propose a new feature extraction method for feedforward neural networks. The method is based on the recently published decision boundary feature extraction algorithm which is based on the fact that all the necessary features for classification can be extracted from the decision boundary. The decision boundary feature extraction algorithm can take advantage of characteristics of neural networks which can solve complex problems with arbitrary decision boundaries without assuming underlying probability distribution functions of the data. To apply the decision boundary feature extraction method, we first give a specific definition for the decision boundary in a neural network. Then, we propose a procedure for extracting all the necessary features for classification from the decision boundary. Experiments show promising results.

We are developing a new graduate program at Purdue in Video and Image Systems Engineering (VISE). The project is comprised of three parts: a new curriculum centered around a degree option in VISE to be earned as part of the Masters or Ph.D. degrees; a state-of-the-art lecture/laboratory facility for instruction, laboratory experiments, and project and homework activities in VISE courses; and enhancement of existing courses and development of new courses in the VISE area.

A new covariance matrix estimator useful for designing classifiers with limited training data is developed. In experiments, this estimator achieved higher classification accuracy than the sample covariance matrix and common covariance matrix estimates. In about half of the experiments, it achieved higher accuracy than regularized discriminant analysis, but required much less computation.

This correspondence proposes a fast Parzen density estimation algorithm that would be especially useful in nonparametric discriminant analysis problems. By preclustering the data and applying a simple branch and bound procedure to the clusters, significant numbers of data samples that would contribute little to the density estimate can be excluded without detriment to actual evaluation via the kernel functions. This technique is especially helpful in the multivariant case, and does not require a uniform sampling grid. The proposed algorithm may also be used in conjunction with the data reduction technique of Fukunaga and Hayes (1989) to further reduce the computational load. Experimental results are presented to verify the effectiveness of this algorithm.>

The authors study the use of unlabeled samples in reducing the problem of small training sample size that can severely affect the recognition rate of classifiers when the dimensionality of the multispectral data is high. The authors show that by using additional unlabeled samples that are available at no extra cost, the performance may be improved, and therefore the Hughes phenomenon can be mitigated. Furthermore, by experiments, they show that by using additional unlabeled samples more representative estimates can be obtained. They also propose a semiparametric method for incorporating the training (i.e., labeled) and unlabeled samples simultaneously into the parameter estimation process.>

A novel approach to feature extraction for classification based directly on the decision boundaries is proposed. It is shown how discriminantly redundant features and discriminantly informative features are related to decision boundaries. A procedure to extract discriminantly informative features based on a decision boundary is proposed. The proposed feature extraction algorithm has several desirable properties: (1) it predicts the minimum number of features necessary to achieve the same classification accuracy as in the original space for a given pattern recognition problem; and (2) it finds the necessary feature vectors. The proposed algorithm does not deteriorate under the circumstances of equal class means or equal class covariances as some previous algorithms do. Experiments show that the performance of the proposed algorithm compares favorably with those of previous algorithms.>

Through a series of specific examples, some characteristics encountered in analyzing high-dimensional multispectral data are illustrated. The increased importance of the second-order statistics in analyzing high-dimensional data is shown, as is the shortcoming of classifiers such as the minimum distance classifier, which rely on first-order variations alone. It is also shown how inaccurate estimation of first- and second-order statistics, e.g., from use of training sets which are too small, affects the performance of a classifier. Recognizing the importance of second-order statistics on the one hand, but the increased difficulty in perceiving and comprehending information present in statistics derived from high-dimensional data on the other, the authors propose a method to aid visualization of high-dimensional statistics using a color coding scheme.>

A new feature extraction algorithm based on decision boundaries for nonparametric classifiers is proposed. It is noted that feature extraction for pattern recognition is equivalent to retaining discriminantly informative features, and a discriminantly informative feature is related to the decision boundary. Since nonparametric classifiers do not define decision boundaries in analytic form, the decision boundary and normal vectors must be estimated numerically. A procedure to extract discriminantly informative features based on a decision boundary for nonparametric classification is proposed. Experimental results show that the proposed algorithm finds effective features for the nonparametric classifier with Parzen density estimation.>

A contextual classifier which can utilize both spatial and temporal interpixel dependency contexts is investigated. After spatial and temporal neighbors are defined, a general form of maximum a posterior spatiotemporal contextual classifier is derived. This contextual classifier is simplified under several assumptions. Joint prior probabilities of the classes of each pixel and its spatial neighbors are modeled by the Gibbs random field. The classification is performed in a recursive manner to allow a computationally efficient contextual classification. Experimental results with bitemporal TM data show significant improvement of classification accuracy over noncontextual pixelwise classifiers. This spatiotemporal contextual classifier should find use in many applications of remote sensing, especially when the classification accuracy is important.>

To help better understand the problems of specifying data acquisition parameters and extracting desired information from the voluminous data, research has been focused on understanding the remote sensing process as a system and investigating the interrelated effects of various parameters. A system model is used to explore system parameter trade-offs for a model sensor based on the High-Resolution Imaging Spectrometer (HIRIS). Radiometric performance was studied, along with the effect on classification accuracy of several system parameters. The atmosphere and sensor have significant effects on the mean received signal and noise performance. The effect of random uncorrelated errors in the radiometric calibration of the detector array is discussed. Accurate pixel-to-pixel relative radiometric calibration and the use of the image motion compensation (IMC) option are seen to improve classification accuracy. The selection of feature sets based on combining spectral bands was studied under a variety of observational conditions.>

In applying pattern recognition methods in remote sensing problems, an inherent limitation is that there is almost always only a small number of training samples with which to design the classifier. A hybrid decision tree classifier design procedure that produces efficient and accurate classifiers for this situation is proposed. In doing so, several key questions are addressed, among them the question of the feature extraction techniques to be used and the mathematical relationship between sample size, dimensionality, and risk value. Empirical tests comparing the hybrid design classifier with a conventional single layered one are presented. They suggest that the hybrid design produces higher accuracy with fewer features. The need for fewer features is an important advantage, because it reflects favorably on both the size of the training set needed and the amount of computation time that will be needed in analysis.>

An adaptive image reconstruction system has been developed to analyze sequential images observed at regular time intervals. A least-squares linear prediction with escalator structure has been implemented in this system. Using the predictor, estimates of missing data or bad (possibly cloud-covered) data and spatial parameters at a specified time can be obtained from previous history. This algorithm recovers from observations which are contaminated due to blurring and correlated noise by using temporally adapted spatial parameters.>

A multistage classification that reduces the processing time substantially is proposed. This classification algorithm consists of several stages, and in each stage likelihood values of classes are calculated and compared. If a class has a likelihood value less than a threshold, the class is truncated at that stage as an unlikely class, thus reducing the number of classes for which likelihood values are to be calculated at the next stage. Thus a host of classes can be truncated by using a small portion of the total features at early stages, resulting in substantial reduction of computing time. Several truncation criteria are developed, and the relationship between thresholds and the error caused by the truncation is investigated. Experiments show that the proposed algorithm reduces the processing time by the factor of 3-7, depending on the number of classes and features, while maintaining essentially the same accuracies.>

The authors present a system model for the remote sensing process and some results that yield insight into the process. Key results include interrelations between the atmosphere, sensor noise, sensor view angle and scattered path radiance and their influence on classification accuracy of the ground cover type. Also included are results indicating the tradeoffs in ground cell size and surface spatial correlation and their effect on classification accuracy. >

A survey is presented of current methods for decision tree classifier (DTC) designs and the various existing issues. After considering potential advantages of DTCs over single-state classifiers, the subjects of tree structure design, feature selection at each internal node, and decision and search strategies are discussed. The relation between decision trees and neutral networks (NN) is also discussed.>

The authors examine several robust estimators of the mean and covariance matrix and their effect on the probability of error in classification. A simple and intuitive iterative approach which weighs each data point as a function of its distance (Mahalanobis distance) is given in the proposed algorithm, which showed good convergence behavior in simulation with artificial data. Some comments on alpha -ranked ( alpha -trimmed) estimators are presented.>

In remote sensing, because of physical properties of targets, sensor pixels in spatial proximity to one another are class conditionally correlated. Our main objective is to exploit this spatial correlation. Therefore, a two-dimensional causal first order Markov model was used to extract the spatial and spectral information and, based upon it, new object classifiers with improved performance were developed. First, the minimum distance (MT) and the maximum likelihood (ML) object classifiers are discussed. Then, based on the proposed model, these two classifiers are modified, and a linear object classifier is introduced. Finally, experimental results are presented.

Provides an overview of the technical articles and features presented in this issue.

Current implementation of probabilistic relaxation labeling (PRL) is based on stationary compatibility coefficients (SCC's). Such labeling frequently diverges from an achieved minimum labeling error. In this correspondence it is shown that by having nonstationary compatibility coefficients (NSCC's) the PRL stabilizes about the minimum error which is obtained during the early iterations. Also, a noniterative labeling algorithm which uses NSCC and has a performance similar to that of the modified PRL is suggested.

In this paper a criterion which measures the quality of the estimate of the covariance matrix of a multivariate normal distribution is developed. Based on this criterion, the necessary number of training samples is predicted. Experimental results which are used as a guide for determining the number of training samples are included.

A simple modification to existing probabilistic relaxation procedures is suggested which allows the information contained in initial labels to exert an influence on the direction of relaxation throughout the process. In this manner, the initial labels assume more importance than with conventional algorithms and are used in combination with the outcome of relaxation at each iteration to produce a cooperative estimate of the correct label for a particular object. Pixel labeling examples are presented which show the performance that can be obtained with the modified algorithm. The procedure is readily generalized to allow other data to influence the process.

Variance relationships among certain count estimators and posterior probability estimators of probability of correct classification are investigated. An estimator using posterior probabilities is presented for use in stratified sampling designs. A test case involving three normal classes is examined.