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NASA NTRS2003

A Fast Implementation of the ISOCLUS Algorithm

Unsupervised clustering is a fundamental building block in numerous image processing applications. One of the most popular and widely used clustering schemes for remote sensing applications is the ISOCLUS algorithm, which is based on the ISODATA method. The algorithm is given a set of n data points in d-dimensional space, an integer k indicating the initial number of clusters, and a number of additional parameters. The general goal is to compute the coordinates of a set of cluster centers in d-space, such that those centers minimize the mean squared distance from each data point to its nearest center. This clustering algorithm is similar to another well-known clustering method, called k-means. One significant feature of ISOCLUS over k-means is that the actual number of clusters reported might be fewer or more than the number supplied as part of the input. The algorithm uses different heuristics to determine whether to merge lor split clusters. As ISOCLUS can run very slowly, particularly on large data sets, there has been a growing .interest in the remote sensing community in computing it efficiently. We have developed a faster implementation of the ISOCLUS algorithm. Our improvement is based on a recent acceleration to the k-means algorithm of Kanungo, et al. They showed that, by using a kd-tree data structure for storing the data, it is possible to reduce the running time of k-means. We have adapted this method for the ISOCLUS algorithm, and we show that it is possible to achieve essentially the same results as ISOCLUS on large data sets, but with significantly lower running times. This adaptation involves computing a number of cluster statistics that are needed for ISOCLUS but not for k-means. Both the k-means and ISOCLUS algorithms are based on iterative schemes, in which nearest neighbors are calculated until some convergence criterion is satisfied. Each iteration requires that the nearest center for each data point be computed. Naively, this requires O(kn) time, where k denotes the current number of centers. Traditional techniques for accelerating nearest neighbor searching involve storing the k centers in a data structure. However, because of the iterative nature of the algorithm, this data structure would need to be rebuilt with each new iteration. Our approach is to store the data points in a kd-tree data structure. The assignment of points to nearest neighbors is carried out by a filtering process, which successively eliminates centers that can not possibly be the nearest neighbor for a given region of space. This algorithm is significantly faster, because large groups of data points can be assigned to their nearest center in a single operation. Preliminary results on a number of real Landsat datasets show that our revised ISOCLUS-like scheme runs about twice as fast.

Memarsadeghi, Nargess↗
NASA NTRS2003

A Fast Implementation of the ISOCLUS Algorithm

Unsupervised clustering is a fundamental tool in numerous image processing and remote sensing applications. For example, unsupervised clustering is often used to obtain vegetation maps of an area of interest. This approach is useful when reliable training data are either scarce or expensive, and when relatively little a priori information about the data is available. Unsupervised clustering methods play a significant role in the pursuit of unsupervised classification. One of the most popular and widely used clustering schemes for remote sensing applications is the ISOCLUS algorithm, which is based on the ISODATA method. The algorithm is given a set of n data points (or samples) in d-dimensional space, an integer k indicating the initial number of clusters, and a number of additional parameters. The general goal is to compute a set of cluster centers in d-space. Although there is no specific optimization criterion, the algorithm is similar in spirit to the well known k-means clustering method in which the objective is to minimize the average squared distance of each point to its nearest center, called the average distortion. One significant feature of ISOCLUS over k-means is that clusters may be merged or split, and so the final number of clusters may be different from the number k supplied as part of the input. This algorithm will be described in later in this paper. The ISOCLUS algorithm can run very slowly, particularly on large data sets. Given its wide use in remote sensing, its efficient computation is an important goal. We have developed a fast implementation of the ISOCLUS algorithm. Our improvement is based on a recent acceleration to the k-means algorithm, the filtering algorithm, by Kanungo et al.. They showed that, by storing the data in a kd-tree, it was possible to significantly reduce the running time of k-means. We have adapted this method for the ISOCLUS algorithm. For technical reasons, which are explained later, it is necessary to make a minor modification to the ISOCLUS specification. We provide empirical evidence, on both synthetic and Landsat image data sets, that our algorithm's performance is essentially the same as that of ISOCLUS, but with significantly lower running times. We show that our algorithm runs from 3 to 30 times faster than a straightforward implementation of ISOCLUS. Our adaptation of the filtering algorithm involves the efficient computation of a number of cluster statistics that are needed for ISOCLUS, but not for k-means.

Memarsadeghi, Nargess↗
NASA NTRS1981

Comparison of wheat classification accuracy using different classifiers of the image-100 system

Classification results using single-cell and multi-cell signature acquisition options, a point-by-point Gaussian maximum-likelihood classifier, and K-means clustering of the Image-100 system are presented. Conclusions reached are that: a better indication of correct classification can be provided by using a test area which contains various cover types of the study area; classification accuracy should be evaluated considering both the percentages of correct classification and error of commission; supervised classification approaches are better than K-means clustering; Gaussian distribution maximum likelihood classifier is better than Single-cell and Multi-cell Signature Acquisition Options of the Image-100 system; and in order to obtain a high classification accuracy in a large and heterogeneous crop area, using Gaussian maximum-likelihood classifier, homogeneous spectral subclasses of the study crop should be created to derive training statistics.

Dejesusparada, N.↗
NASA NTRS1972

Unsupervised classification of remote multispectral sensing data

The new unsupervised classification technique for classifying multispectral remote sensing data which can be either from the multispectral scanner or digitized color-separation aerial photographs consists of two parts: (a) a sequential statistical clustering which is a one-pass sequential variance analysis and (b) a generalized K-means clustering. In this composite clustering technique, the output of (a) is a set of initial clusters which are input to (b) for further improvement by an iterative scheme. Applications of the technique using an IBM-7094 computer on multispectral data sets over Purdue's Flight Line C-1 and the Yellowstone National Park test site have been accomplished. Comparisons between the classification maps by the unsupervised technique and the supervised maximum liklihood technique indicate that the classification accuracies are in agreement.

Su, M. Y.↗
NASA NTRS1972

Mapping of terrain by computer clustering techniques using multispectral scanner data and using color aerial film

Two clustering techniques were used for terrain mapping by computer of test sites in Yellowstone National Park. One test was made with multispectral scanner data using a composite technique which consists of (1) a strictly sequential statistical clustering which is a sequential variance analysis, and (2) a generalized K-means clustering. In this composite technique, the output of (1) is a first approximation of the cluster centers. This is the input to (2) which consists of steps to improve the determination of cluster centers by iterative procedures. Another test was made using the three emulsion layers of color-infrared aerial film as a three-band spectrometer. Relative film densities were analyzed using a simple clustering technique in three-color space. Important advantages of the clustering technique over conventional supervised computer programs are (1) human intervention, preparation time, and manipulation of data are reduced, (2) the computer map, gives unbiased indication of where best to select the reference ground control data, (3) use of easy to obtain inexpensive film, and (4) the geometric distortions can be easily rectified by simple standard photogrammetric techniques.

Smedes, H. W.↗
NASA NTRS1972

The composite sequential clustering technique for analysis of multispectral scanner data

The clustering technique consists of two parts: (1) a sequential statistical clustering which is essentially a sequential variance analysis, and (2) a generalized K-means clustering. In this composite clustering technique, the output of (1) is a set of initial clusters which are input to (2) for further improvement by an iterative scheme. This unsupervised composite technique was employed for automatic classification of two sets of remote multispectral earth resource observations. The classification accuracy by the unsupervised technique is found to be comparable to that by traditional supervised maximum likelihood classification techniques. The mathematical algorithms for the composite sequential clustering program and a detailed computer program description with job setup are given.

Su, M. Y.↗
NASA NTRS1972

Unsupervised classification of earth resources data.

A new clustering technique is presented. It consists of two parts: (a) a sequential statistical clustering which is essentially a sequential variance analysis and (b) a generalized K-means clustering. In this composite clustering technique, the output of (a) is a set of initial clusters which are input to (b) for further improvement by an iterative scheme. This unsupervised composite technique was employed for automatic classification of two sets of remote multispectral earth resource observations. The classification accuracy by the unsupervised technique is found to be comparable to that by existing supervised maximum liklihood classification technique.

Su, M. Y.↗
NASA NTRS1973

An unsupervised classification technique for multispectral remote sensing data.

Description of a two-part clustering technique consisting of (a) a sequential statistical clustering, which is essentially a sequential variance analysis, and (b) a generalized K-means clustering. In this composite clustering technique, the output of (a) is a set of initial clusters which are input to (b) for further improvement by an iterative scheme. This unsupervised composite technique was employed for automatic classification of two sets of remote multispectral earth resource observations. The classification accuracy by the unsupervised technique is found to be comparable to that by traditional supervised maximum-likelihood classification techniques.

Su, M. Y.↗
NASA NTRS1975

Design data collection with Skylab microwave radiometer-scatterometer S-193, volume 2

The author has identified the following significant results. Skylab S-193 radiometer/scatterometer produced terrain responses with various polarizations and observation angles for cells of 100 to 400 sq km area. Classification of the observations into natural categories was achieved by K-means and spatial clustering algorithms. Microwave data acquired over the Great Salt Lake Desert area by sensors aboard Skylab and Nimbus 5 indicate that the microwave emission and backscatter were strongly influenced by contributions from subsurface layers of sediment saturated with brine. Correlations were noted between microwave backscatter response at approximately 33 deg from scatterometer (operating at 13.9 GHz) and the configuration of ground targets in Brazil as discerned from coarse scale maps. With limited, available ground truth, these correlations were sufficient to permit the production of image-like displays which bear a marked resemblance to known terrain features in several instances.

Moore, R. K.↗
NASA NTRS1984

Assessment of computer techniques for processing digital LANDSAT MSS data for lithological discrimination of Serra do Ramalho, State of Bahia

Enhancement techniques and thematic classifications were applied to the metasediments of Bambui Super Group (Upper Proterozoic) in the Region of Serra do Ramalho, SW of the state of Bahia. Linear contrast stretch, band-ratios with contrast stretch, and color-composites allow lithological discriminations. The effects of human activities and of vegetation cover mask and limit, in several ways, the lithological discrimination with digital MSS data. Principal component images and color composite of linear contrast stretch of these products, show lithological discrimination through tonal gradations. This set of products allows the delineations of several metasedimentary sequences to a level superior to reconnaissance mapping. Supervised (maximum likelihood classifier) and nonsupervised (K-Means classifier) classification of the limestone sequence, host to fluorite mineralization show satisfactory results.

Paradella, W. R.↗
NASA NTRS1993

Applications of wavelet-based compression to multidimensional Earth science data

A data compression algorithm involving vector quantization (VQ) and the discrete wavelet transform (DWT) is applied to two different types of multidimensional digital earth-science data. The algorithms (WVQ) is optimized for each particular application through an optimization procedure that assigns VQ parameters to the wavelet transform subbands subject to constraints on compression ratio and encoding complexity. Preliminary results of compressing global ocean model data generated on a Thinking Machines CM-200 supercomputer are presented. The WVQ scheme is used in both a predictive and nonpredictive mode. Parameters generated by the optimization algorithm are reported, as are signal-to-noise (SNR) measurements of actual quantized data. The problem of extrapolating hydrodynamic variables across the continental landmasses in order to compute the DWT on a rectangular grid is discussed. Results are also presented for compressing Landsat TM 7-band data using the WVQ scheme. The formulation of the optimization problem is presented along with SNR measurements of actual quantized data. Postprocessing applications are considered in which the seven spectral bands are clustered into 256 clusters using a k-means algorithm and analyzed using the Los Alamos multispectral data analysis program, SPECTRUM, both before and after being compressed using the WVQ program.

Bradley, Jonathan N.↗
NASA NTRS1993

Vision based obstacle detection and grouping for helicopter guidance

Electro-optical sensors can be used to compute range to objects in the flight path of a helicopter. The computation is based on the optical flow/motion at different points in the image. The motion algorithms provide a sparse set of ranges to discrete features in the image sequence as a function of azimuth and elevation. For obstacle avoidance guidance and display purposes, these discrete set of ranges, varying from a few hundreds to several thousands, need to be grouped into sets which correspond to objects in the real world. This paper presents a new method for object segmentation based on clustering the sparse range information provided by motion algorithms together with the spatial relation provided by the static image. The range values are initially grouped into clusters based on depth. Subsequently, the clusters are modified by using the K-means algorithm in the inertial horizontal plane and the minimum spanning tree algorithms in the image plane. The object grouping allows interpolation within a group and enables the creation of dense range maps. Researchers in robotics have used densely scanned sequence of laser range images to build three-dimensional representation of the outside world. Thus, modeling techniques developed for dense range images can be extended to sparse range images. The paper presents object segmentation results for a sequence of flight images.

Sridhar, Banavar↗
NASA NTRS1994

Unsupervised texture image segmentation by improved neural network ART2

We here propose a segmentation algorithm of texture image for a computer vision system on a space robot. An improved adaptive resonance theory (ART2) for analog input patterns is adapted to classify the image based on a set of texture image features extracted by a fast spatial gray level dependence method (SGLDM). The nonlinear thresholding functions in input layer of the neural network have been constructed by two parts: firstly, to reduce the effects of image noises on the features, a set of sigmoid functions is chosen depending on the types of the feature; secondly, to enhance the contrast of the features, we adopt fuzzy mapping functions. The cluster number in output layer can be increased by an autogrowing mechanism constantly when a new pattern happens. Experimental results and original or segmented pictures are shown, including the comparison between this approach and K-means algorithm. The system written in C language is performed on a SUN-4/330 sparc-station with an image board IT-150 and a CCD camera.

Wang, Zhiling↗
NASA NTRS1993

Radial basis function neural networks applied to NASA SSME data

This paper presents a brief report on the application of Radial Basis Function Neural Networks (RBFNN) to the prediction of sensor values for fault detection and diagnosis of the Space Shuttle's Main Engines (SSME). The location of the Radial Basis Function (RBF) node centers was determined with a K-means clustering algorithm. A neighborhood operation about these center points was used to determine the variances of the individual processing notes.

Wheeler, Kevin R.↗
NASA NTRS1995

Bayes classification of interferometric TOPSAR data

We report the Bayes classification of terrain types at different sites using airborne interferometric synthetic aperture radar (INSAR) data. A Gaussian maximum likelihood classifier was applied on multidimensional observations derived from the SAR intensity, the terrain elevation model, and the magnitude of the interferometric correlation. Training sets for forested, urban, agricultural, or bare areas were obtained either by selecting samples with known ground truth, or by k-means clustering of random sets of samples uniformly distributed across all sites, and subsequent assignments of these clusters using ground truth. The accuracy of the classifier was used to optimize the discriminating efficiency of the set of features that was chosen. The most important features include the SAR intensity, a canopy penetration depth model, and the terrain slope. We demonstrate the classifier's performance across sites using a unique set of training classes for the four main terrain categories. The scenes examined include San Francisco (CA) (predominantly urban and water), Mount Adams (WA) (forested with clear cuts), Pasadena (CA) (urban with mountains), and Antioch Hills (CA) (water, swamps, fields). Issues related to the effects of image calibration and the robustness of the classification to calibration errors are explored. The relative performance of single polarization Interferometric data classification is contrasted against classification schemes based on polarimetric SAR data.

Michel, T. R.↗
NASA NTRS1997

On the Implementation of a Land Cover Classification System for SAR Images Using Khoros

The Synthetic Aperture Radar (SAR) sensor is widely used to record data about the ground under all atmospheric conditions. The SAR acquired images have very good resolution which necessitates the development of a classification system that process the SAR images to extract useful information for different applications. In this work, a complete system for the land cover classification was designed and programmed using the Khoros, a data flow visual language environment, taking full advantages of the polymorphic data services that it provides. Image analysis was applied to SAR images to improve and automate the processes of recognition and classification of the different regions like mountains and lakes. Both unsupervised and supervised classification utilities were used. The unsupervised classification routines included the use of several Classification/Clustering algorithms like the K-means, ISO2, Weighted Minimum Distance, and the Localized Receptive Field (LRF) training/classifier. Different texture analysis approaches such as Invariant Moments, Fractal Dimension and Second Order statistics were implemented for supervised classification of the images. The results and conclusions for SAR image classification using the various unsupervised and supervised procedures are presented based on their accuracy and performance.

Medina Revera, Edwin J.↗
NASA NTRS2002

Using Clustering to Establish Climate Regimes from PCM Output

A multivariate statistical clustering technique--based on the k-means algorithm of Hartigan has been used to extract patterns of climatological significance from 200 years of general circulation model (GCM) output. Originally developed and implemented on a Beowulf-style parallel computer constructed by Hoffman and Hargrove from surplus commodity desktop PCs, the high performance parallel clustering algorithm was previously applied to the derivation of ecoregions from map stacks of 9 and 25 geophysical conditions or variables for the conterminous U.S. at a resolution of 1 sq km. Now applied both across space and through time, the clustering technique yields temporally-varying climate regimes predicted by transient runs of the Parallel Climate Model (PCM). Using a business-as-usual (BAU) scenario and clustering four fields of significance to the global water cycle (surface temperature, precipitation, soil moisture, and snow depth) from 1871 through 2098, the authors' analysis shows an increase in spatial area occupied by the cluster or climate regime which typifies desert regions (i.e., an increase in desertification) and a decrease in the spatial area occupied by the climate regime typifying winter-time high latitude perma-frost regions. The patterns of cluster changes have been analyzed to understand the predicted variability in the water cycle on global and continental scales. In addition, representative climate regimes were determined by taking three 10-year averages of the fields 100 years apart for northern hemisphere winter (December, January, and February) and summer (June, July, and August). The result is global maps of typical seasonal climate regimes for 100 years in the past, for the present, and for 100 years into the future. Using three-dimensional data or phase space representations of these climate regimes (i.e., the cluster centroids), the authors demonstrate the portion of this phase space occupied by the land surface at all points in space and time. Any single spot on the globe will exist in one of these climate regimes at any single point in time. By incrementing time, that same spot will trace out a trajectory or orbit between and among these climate regimes (or atmospheric states) in phase (or state) space. When a geographic region enters a state it never previously visited, a climatic change is said to have occurred. Tracing out the entire trajectory of a single spot on the globe yields a 'manifold' in state space representing the shape of its predicted climate occupancy. This sort of analysis enables a researcher to more easily grasp the multivariate behavior of the climate system.

Oglesby, Robert↗
NASA NTRS2004

Automatic Generation of Algorithms for the Statistical Analysis of Planetary Nebulae Images

Analyzing data sets collected in experiments or by observations is a Core scientific activity. Typically, experimentd and observational data are &aught with uncertainty, and the analysis is based on a statistical model of the conjectured underlying processes, The large data volumes collected by modern instruments make computer support indispensible for this. Consequently, scientists spend significant amounts of their time with the development and refinement of the data analysis programs. AutoBayes [GF+02, FS03] is a fully automatic synthesis system for generating statistical data analysis programs. Externally, it looks like a compiler: it takes an abstract problem specification and translates it into executable code. Its input is a concise description of a data analysis problem in the form of a statistical model as shown in Figure 1; its output is optimized and fully documented C/C++ code which can be linked dynamically into the Matlab and Octave environments. Internally, however, it is quite different: AutoBayes derives a customized algorithm implementing the given model using a schema-based process, and then further refines and optimizes the algorithm into code. A schema is a parameterized code template with associated semantic constraints which define and restrict the template s applicability. The schema parameters are instantiated in a problem-specific way during synthesis as AutoBayes checks the constraints against the original model or, recursively, against emerging sub-problems. AutoBayes schema library contains problem decomposition operators (which are justified by theorems in a formal logic in the domain of Bayesian networks) as well as machine learning algorithms (e.g., EM, k-Means) and nu- meric optimization methods (e.g., Nelder-Mead simplex, conjugate gradient). AutoBayes augments this schema-based approach by symbolic computation to derive closed-form solutions whenever possible. This is a major advantage over other statistical data analysis systems which use numerical approximations even in cases where closed-form solutions exist. AutoBayes is implemented in Prolog and comprises approximately 75.000 lines of code. In this paper, we take one typical scientific data analysis problem-analyzing planetary nebulae images taken by the Hubble Space Telescope-and show how AutoBayes can be used to automate the implementation of the necessary anal- ysis programs. We initially follow the analysis described by Knuth and Hajian [KHO2] and use AutoBayes to derive code for the published models. We show the details of the code derivation process, including the symbolic computations and automatic integration of library procedures, and compare the results of the automatically generated and manually implemented code. We then go beyond the original analysis and use AutoBayes to derive code for a simple image segmentation procedure based on a mixture model which can be used to automate a manual preproceesing step. Finally, we combine the original approach with the simple segmentation which yields a more detailed analysis. This also demonstrates that AutoBayes makes it easy to combine different aspects of data analysis.

Fischer, Bernd↗