Spatial Statistics and Digital Image Analysis (1991) / Chapter Skim
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3. Oceanographic and Atmospheric Applications of Spatial Statistics and Digital Image Analysis
3. Oceanographic and Atmospheric Applications of Spatial Statistics and Digital Image Analysis
Pages 37-70
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From page 37... ...
The hyclrologic cycle, the biogeochemical cycle, and climate processes are the fundamental processes that integrate the earth as a system, and thus each of these cycles must be examined in detail and on a global scale if meaningful progress is to be made on the problems cited above. I,arge-scaTe, synoptic observations of a winkle variety of phenomena (e.g., sea surface temperature, sea level, winct stress, ozone concentration, radi37
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From page 38... ...
The magnitude of the data set, however, may preclude understanding unless it can be distilled and synthesized into organized patterns that can be related meaningfully to the underlying governing physics, chemistry, or biology of these global cycles and processes. Spatial statistics and mathematical methods of digital image analysis provide mechanisms for such a synthesis.
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From page 39... ...
, and agriculture (e.g., rainfall, Browning, 1986~. The PCT can be used with multispectral image data to robustly segment clouds from natural images.
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pure hierarchical methods impose a taxonomic structure on the data (Anderberg, 1973) , which is not characteristic of cloud-containing AVHRR imagery; (4)
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In this panel, the coastline is black. The segmented image produced by the PCTSMC algorithm is shown in Plate 3.1c and the final cloud-masked sea surface temperature is shown in Plate 3.16.
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From page 42... ...
More recent studies in oceanography and atmospheric science (e.g., Barnett and Patzert, 1980) prefer to use EOFs with the same units as the original data for easier interpretation of the spatial patterns of variance resulting from the EOF analysis (method I)
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Theoretical Basis. The objective of EOF analysis is to represent a given matrix of data D by the product F A
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The empirical orthogonal functions can be computed from a singular value decomposition (SVD) of the data D
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Example. The purpose of this example is to show that EOF analysis can be useful for determining the dominant patterns of spatial variance in a sequence of images.
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Care must be taken to ensure that the composite time scale is very much less than the time step between images in the sequence undergoing EOF analysis. Other interpolation schemes (e.g., kriging)
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These gradients are defined as normal in direction to contours of constant brightness (or sea surface temperature [SST] for the case of the Advanced Very High Resolution Radiometer [AVHRR]
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48 Total Flow Fielc! From Pattern Matching Consider a pair of real, discrete, two-dimensional random functions, sum, n)
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. Velocities obtained from the pattern matching technique and proper choice of correlation threshold show good correspondence with observations.
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These methods are computationally very expensive but win perform well in the presence of curvature in the motion field of the pattern. Only translational techniques were used herein because they are sufficient to determine the general flow pattern in the image sequence under consideration.
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51 The Normal Component of Flow Marr and UlIman (MU) Method.
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52 where the subscript represents differentiation with respect to time, and the unit normal vector n is in the direction of the gradient V]
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that the estimate of the total flow field may be very far from the actual velocity field, depending on various factors influencing the time series of images. Given the material derivative constraint (3.31)
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was solved for the normal component of velocity using the singular value decomposition to obtain the solution of minimum norm (hereafter referred to as MN) at every point in the given image subsection (Wah!
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An Indirect Solution. Given the total flow field computed on a rectangular grid from the pattern matching method mentioned previously, one can take the normal component of flow and perform a vector subtraction to obtain the tangential component.
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The image is stored as a matrix where, by tradition in image analysis, the row index is referred to as a line and the column index is referred to as a sample. Co-registration is the process of mapping images observed in the line and sample domain to the same latitude and longitude domain using an appropriate map projection (e.g., Brush, 1985; Jezclhing and Jain, 1989~.
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3.2.3 Ice Floe Iclentification ant} Principal Curves Overview of Banfield and Raftery Algorithm Knowledge of the spatial distribution, size, and shape of ice floes is critical to understanding physical processes in polar regions and the potential role of these processes in studies of global warming. Moreover, in high-latitude zones, shipping, naval operations, fishing, and the successful deployment of offshore structures are all strongly influenced by the distribution of the polar ice pack.
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They further noted that the final result is relatively insensitive to the precise value of the threshold chosen. The erosion part of the EP algorithm identifies potential edge elements by using standard concepts from mathematical morphology (Serra, 1982)
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From page 59... ...
3.3.1 Storage Considerations The primary archive of satellite data is generally the raw digitized telemetry stream directly received from the satellite. For multispectral images, the data are usually band interleaved rather than band sequential, usually contain embedded calibration information, and often include other data needed for proper Earth location of the scene.
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Data compression techniques and optical disc storage technology clearly are required if the data storage issue is to be adequately addressed. (Data compression is the process of reducing the number of bits required to store a given amount of information without loss of information.)
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From page 61... ...
Quadtrees have proved to be useful data structures for dithering algorithms, computing geometric properties of images, implementation of linear image transformations, development of hierarchical hidden-surface algorithms, and ray tracing. The quadtree is only one of several digital data structures useful in spatial statistics and digital image analysis.
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From page 62... ...
The examples cited herein included princinal component analyses, which are useful for image segmentation and for determining spatial patterns of variance in large data sets; edge (letection; pattern matching; optical flow methods, which are useful for determining fields of motion from sequences of image data; and principal curves, which are useful for determining the spatial distribution, size, and shape of ice floes observed from spacecraft data. Atmospheric correction algorithms, sensor calibration algorithms, and earth location algorithms generally are required as pre-processes to digital image analysis of remotely-sensed images.
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From page 63... ...
E Raft ery, Ice Floe Identification in Satellite Images using Mathematical Morphology and Clustering about Principal Curves, Technical Report No.
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E., Predictability of sea surface temperature and sea level pressure anomalies over the North Pacific Ocean, '7.
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J Simpson, Seasonal and non-seasonal variability in sea surface temperature off Punta Eugenia, to be submitted to Remote Sensing Environ.
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R., Introductory Digital Image Processing, Prentice Hall, Englewood Cliffs, N.J., 1986.
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A., Remote Sensing Digital Image Analysis: An Introduction, Springer-VerIag, New York, 1986.
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J., Image segmentation using recursive polygon fill operations, Remote Sensing Environ., submitted (1991~.
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From page 69... ...
REC Run length coding used in data compression algorithms. SST Sea surface temperature.
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