Raster Map Monographs

Outline: This monograph serves to present novel methods for landscape pattern modeling and analysis. After an introductory chapter that provides ecological motivation for doing such work, then following chapters will develop theory and methods. Final chapters will apply the methods to actual analyses of watershed-delineated landscapes, whereby the power of using such methods with remotely-sensed landscape imagery for predicting different aspects of ecosystem condition are investigated.

The chapter titles are:

Introduction
Methods for Quantitative Characterization of Landscape Pattern
The Conditional Entropy Profile
Simulation with Neutral Stochastic Landscape Models
Categorizing Watersheds Based Only on Landscape Characteristics
Predictability of Surface Water Pollution Loading
Predictability of Bird Community-Based Ecological Integrity
Summary and Future Directions

Monograph 2: Understanding Surfaces: Echelon Analysis of Spatial Structure for Quantitative Geospatial Data

Authors: W. L. Myers and G. P. Patil

Outline: This monograph describes a recently developed echelon method of analyzing cellular data pertaining to surface variables and illustrates its applications in the context of environmental monitoring. The echelon approach is advantageous for elucidating spatial structure, determining critical areas, lending emphasis to areas of complexity, and mapping various aspects of surface organization. It is appropriate both for data consisting of actual measurements and for environmental indicators. A chapter outline of the monograph is as follows:

Nature of echelons.
Echelon orders and families.
Echelon trees, tables, and maps.
Echelon profiles.
Noise effects and filtering.
Echelon computations.
Echelons of landscape change.
Echelon comparatives.
Echelon stochastics.
Echelon topology.
Echelon advantage.

Monograph 3: Pattern-Based Compression of Multiband Image Data for
Landscape Analysis

Authors: W. L. Myers and G. P. Patil

Outline: This monograph describes an integrated approach to using remotely sensed data in conjunction with geographic information systems for landscape analysis. Remotely sensed data are compressed into an analytical image-map that is compatible with the most popular geographic information systems as well as freeware viewers. The approach is most effective for landscapes that exhibit a pronounced mosaic pattern of land cover. The image maps are much more compact than the original remotely sensed data, which enhances utility on the internet. As value-added products, distribution of image-maps is not affected by copyrights on original multiband image data. A chapter outline of the monograph is as follows:

Overview of multiband image data.
Landscape mosaics in relation to image segmentation.
Image segmentation and compression by cluster analysis.
Publicly available viewers for image maps.
Mapping relative accuracy of image maps.
Enhanced views of image maps.
Thematic classification and mapping from image maps.
Image maps as a basis for analysis of landscape change.
Synthetic image data.
Spatial analysis of image maps.
Constrictive analysis of landscape complexity.
Approximate restoration of image data.
Principal component analysis.
Higher-order pattern-based image compression.

Monograph 4: Modeling, Analysis and Simulation of Multicategorical Raster Maps

Authors: G. P. Patil and C. Taillie

Outline: This monograph develops statistical methods for analyzing raster maps when the responses are categorical instead of numerical. Spatial pattern is extracted through auto-association matrices which express the joint occurrence of pairs of categories at varying distances across the map. The collection of auto-association matrices is a categorical analogue of the variogram employed in geospatial analysis of numerical responses. A parametric stochastic model employing Markov transition matrices is developed for simulating categorical raster maps. There is a separate transition matrix for each level in the scaling hierarchy and these transition matrices can be estimated from the auto-association matrices. Model parameters, in the form of the eigenvalues and eigenvectors of the transition matrices, are used to characterize and compare spatial pattern in categorical maps. Model simulation is quite rapid and allows for Monte Carlo determination of the variability and other statistical properties of various landscape metrics. A tentative table of contents follows:

1. Multi-categorical Raster Maps

Clustering/Classification of remotely-sensed data

2. Summarizing Spatial Pattern in Multi-categorical Raster Maps

Auto-association matrices
Spatial transition matrices
4-tuple frequency tables
Typology of 4-tuples
Examples: Pennsylvania watersheds

3. Modeling Spatial Pattern in Multi-categorical Raster Maps

Hierarchical transition matrices
HMTM model
Identifiability of HMTM model
Model fitting
Eigen-structure of fitted models
Binary maps
Binary marginals of multi-categorical maps
Examples: Pennsylvania watersheds

4. Simulating Spatial Pattern in Multi-categorical Raster Maps

Alias-urn methods
Algorithms and computer programs
Binary maps
Examples

5. Analysis of Self-similarity in Multi-categorical Raster Maps

Self-similarity within the HMTM framework
Hypothesis formulation and statistical tests
Monte Carlo determination of null distributions
Examples

6. Patch Structure and Fragmentation Measures

Patch identification algorithms
Fragmentation and other landscape metrics
Fractals and perimeter-area exponents
Entropy profiles
Examples

7. Parametric HMTM submodels

Motivation: Near linearity of ordered eigenvalues
pqc models
Other parsimonious models
Fitting by minimum Kullback-Liebler distance
Examples

8. Comparison with Other Modeling Approaches

Multi-indicator kriging and co-kriging
Gibbs random Fields

9. Bivariate Raster Map Analysis (Tentative)

Bivariate HMTM modeling
Latent truth model
Regularization
Comparison of different classifications
Application to accuracy assessment
Application to change detection