Robert Ehrlich

Bio: Robert Ehrlich is an academic researcher from University of South Carolina. The author has contributed to research in topics: Shape analysis (digital geometry) & Impact crater. The author has an hindex of 24, co-authored 88 publications receiving 6488 citations.

An Exact Method for Characterization of Grain Shape

Abstract: Grain shape may be described as precisely as needed by Fourier series expansion of the radius about the center of mass utilizing coordinates of peripheral points. Empirical results of grains from typical samples indicate that the series contains, in partitioned form, a large amount of geologically interesting information. Consequently, previous subjective evaluations of the worth of shape variations in the solution of geologic problems are justified. The shape variable is amenable to semiquantitative graphical evaluation or may be used as data for multivariate analytical schemes. Illustrative examples show that the shape variables easily discriminate grain differences arising from geographic, stratigraphic, and process factors.

Petrographic image analysis; I, Analysis of reservoir pore complexes

Abstract: There exists a need to relate the petrology of reservoirs (pore geometry, surface areas of mineral phases and pores) to geophysical and petrophysical data. The end result is improved assessment of reservoir quality as well as better interpretation of well logs and seismic data. Petrographic Image Analysis (PIA) was developed from the beginning to interface with petrophysical/geophysical data. PIA relies upon computer-based image analysis using pattern recognition/classification programs, and so information can be obtained very rapidly--the rate simply tied to sophistication of the computer in use. PIA consists of a critical mix of hardware and software which perform four separate functions: 1) image acquisition; 2) image digitization; 3) image segmentation; and 4) image analysis. A sp cial effort has been made to characterize the geometry of the pore complex. Separate spectra related to pore size and pore roughness are generated from each image. In addition, surface area per unit volume of pore can be estimated. Pore spectra can be decomposed and classified using pattern recognition/ classification algorithms or used directly to estimate physical parameters.

Petrography and reservoir physics I: Objective classification of reservoir porosity

Abstract: Porosity observed in thin section can be objectively classified using a combination of digital acquisition procedures and pattern recognition algorithms. Pore types are derived from the frequency distributions of sizes and shapes of patches of porosity exposed in thin section. Each pore type is represented by a characteristic distribution of sizes and shapes found in thin section. Most sandstone reservoirs contain fewer than six pore types. Much of the intersample variability in reservoir physics is associated with changes in pore type abundance. The advantages of this approach to porosity classification are (1) the criteria for classification are objectively defined, (2) classification procedure is rapid, accurate, and precise, (3) pore types are understood easily in ter s of conventional genetic classification schemes, and (4) pore type data are related strongly to petrophysical properties.

EXTENDED QMODEL—objective definition of external end members in the analysis of mixtures

Abstract: Analysis of empirical data considered to be mixtures of a finite number of end members has been a topic of increasing interest recently. The algorithms EXTENDED CABFAC and QMODEL by Klovan and Miesch (1976) represent a satisfactory solution to this problem if pure end members are captured within the data set or if the composition of “true” end members are known a priori. Where neither condition is satisfied, the composition of “external” end members can, under certain conditions, be deduced from the structure of the data. Described herein is an algorithm termed EXTENDED QMODEL which defines feasible end members which are “closest” to the data envelope.

On Clustering Validation Techniques

Abstract: Cluster analysis aims at identifying groups of similar objects and, therefore helps to discover distribution of patterns and interesting correlations in large data sets. It has been subject of wide research since it arises in many application domains in engineering, business and social sciences. Especially, in the last years the availability of huge transactional and experimental data sets and the arising requirements for data mining created needs for clustering algorithms that scale and can be applied in diverse domains. This paper introduces the fundamental concepts of clustering while it surveys the widely known clustering algorithms in a comparative way. Moreover, it addresses an important issue of clustering process regarding the quality assessment of the clustering results. This is also related to the inherent features of the data set under concern. A review of clustering validity measures and approaches available in the literature is presented. Furthermore, the paper illustrates the issues that are under-addressed by the recent algorithms and gives the trends in clustering process.

Remote sensing, models, and methods for image processing

Abstract: The Nature of Remote Sensing: Introduction. Remote Sensing. Information Extraction from Remote-Sensing Images. Spectral Factors in Remote Sensing. Spectral Signatures. Remote-Sensing Systems. Optical Sensors. Temporal Characteristics. Image Display Systems. Data Systems. Summary. Exercises. References. Optical Radiation Models: Introduction. Visible to Short Wave Infrared Region. Solar Radiation. Radiation Components. Surface-Reflected. Unscattered Component. Surface-Reflected. Atmosphere-Scattered Component. Path-Scattered Component. Total At-Sensor. Solar Radiance. Image Examples in the Solar Region. Terrain Shading. Shadowing. Atmospheric Correction. Midwave to Thermal Infrared Region. Thermal Radiation. Radiation Components. Surface-Emitted Component. Surface-Reflected. Atmosphere-Emitted Component. Path-Emitted Component. Total At-Sensor. Emitted Radiance. Total Solar and Thermal Upwelling Radiance. Image Examples in the Thermal Region. Summary. Exercises. References. Sensor Models: Introduction. Overall Sensor Model. Resolution. The Instrument Response. Spatial Resolution. Spectral Resolution. Spectral Response. Spatial Response. Optical PSFopt. Image Motion PSFIM. Detector PSFdet. Electronics PSFel. Net PSFnet. Comparison of Sensor PSFs. PSF Summary for TM. Imaging System Simulation. Amplification. Sampling and Quantization. Simplified Sensor Model. Geometric Distortion. Orbit Models. Platform Attitude Models. Scanner Models. Earth Model. Line and Whiskbroom ScanGeometry. Pushbroom Scan Geometry. Topographic Distortion. Summary. Exercises. References. Data Models: Introduction. A Word on Notation. Univariate Image Statistics. Histogram. Normal Distribution. Cumulative Histogram. Statistical Parameters. Multivariate Image Statistics. Reduction to Univariate Statistics. Noise Models. Statistical Measures of Image Quality. Contrast. Modulation. Signal-to-Noise Ratio (SNR). Noise Equivalent Signal. Spatial Statistics. Visualization of Spatial Covariance. Covariance with Semivariogram. Separability and Anisotropy. Power Spectral Density. Co-occurrence Matrix. Fractal Geometry. Topographic and Sensor Effects. Topography and Spectral Statistics. Sensor Characteristics and Spectral Stastistics. Sensor Characteristics and Spectral Scattergrams. Summary. Exercises. References. Spectral Transforms: Introduction. Feature Space. Multispectral Ratios. Vegetation Indexes. Image Examples. Principal Components. Standardized Principal Components (SPC) Transform. Maximum Noise Fraction (MNF) Transform. Tasseled Cap Tranformation. Contrast Enhancement. Transformations Based on Global Statistics. Linear Transformations. Nonlinear Transformations. Normalization Stretch. Reference Stretch. Thresholding. Adaptive Transformation. Color Image Contrast Enhancement. Min-max Stretch. Normalization Stretch. Decorrelation Stretch. Color Spacer Transformations. Summary. Exercises. References. Spatial Transforms: Introduction. An Image Model for Spatial Filtering. Convolution Filters. Low Pass and High Pass Filters. High Boost Filters. Directional Filters. The Border Region. Characterization of Filtered Images. The Box Filter Algorithm. Cascaded Linear Filters. Statistical Filters. Gradient Filters. Fourier Synthesis. Discrete Fourier Transforms in 2-D. The Fourier Components. Filtering with the Fourier Transform. Transfer Functions. The Power Spectrum. Scale Space Transforms. Image Resolution Pyramids. Zero-Crossing Filters. Laplacian-of-Gaussian (LoG) Filters. Difference-of-Gaussians (DoG) Filters.Wavelet Transforms. Summary. Exercises. References. Correction and Calibration: Introduction. Noise Correction. Global Noise. Sigma Filter. Nagao-Matsuyama Filter. Local Noise. Periodic Noise. Distriping 359. Global,Linear Detector Matching. Nonlinear Detector Matching. Statistical Modification to Linear and Nonlinear Detector. Matching. Spatial Filtering Approaches. Radiometric Calibration. Sensor Calibration. Atmospheric Correction. Solar and Topographic Correction. Image Examples. Calibration and Normalization of Hyperspectral Imagery. AVIRIS Examples. Distortion Correction. Polynomial Distortion Models. Ground Control Points (GCPs). Coordinate Transformation. Map Projections. Resampling. Summary. Exercises References. Registration and Image Fusion: Introduction. What is Registration? Automated GCP Location. Area Correlation. Other Spatial Features. Orthrectification. Low-Resolution DEM. High-Resolution DEM. Hierarchical Warp Stereo. Multi-Image Fusion. Spatial Domain Fusion. High Frequency Modulation. Spectral Domain Fusion. Fusion Image Examples. Summary. Exercises. References. Thematic Classification: Introduction. The Importance of Image Scale. The Notion of Similarity. Hard Versus Soft Classification. Training the Classifier. Supervised Training. Unsupervised Training. K-Means Clustering Algorithm. Clustering Examples. Hybrid Supervised/Unsupervised Training. Non-Parametric Classification Algorithms. Level-Slice. Nearest-Mean. Artificial Neural Networks (ANNs). Back-Propagation Algorithm. Nonparametric Classification Examples. Parametric Classification Algorithms. Estimation of Model-Parameters. Discriminant Functions. The Normal Distribution Model. Relation to the Nearest-Mean Classifier. Supervised Classification Examples and Comparison to Nonparametric Classifiers. Segmentation. Region Growing. Region Labeling. Sub-Pixel Classification. The Linear Mixing Model. Unmixing Model. Hyperspectral Image Analysis. Visualization of the Image Cube. Feature Extraction. Image Residuals. Pre-Classification Processing and Feature Extraction. Classification Algorithms. Exercises. Error Analysis. Multitemporal Images. Summary. References. Index.

Spectral unmixing

Abstract: Spectral unmixing using hyperspectral data represents a significant step in the evolution of remote decompositional analysis that began with multispectral sensing. It is a consequence of collecting data in greater and greater quantities and the desire to extract more detailed information about the material composition of surfaces. Linear mixing is the key assumption that has permitted well-known algorithms to be adapted to the unmixing problem. In fact, the resemblance of the linear mixing model to system models in other areas has permitted a significant legacy of algorithms from a wide range of applications to be adapted to unmixing. However, it is still unclear whether the assumption of linearity is sufficient to model the mixing process in every application of interest. It is clear, however, that the applicability of models and techniques is highly dependent on the variety of circumstances and factors that give rise to mixed pixels. The outputs of spectral unmixing, endmember, and abundance estimates are important for identifying the material composition of mixtures.