Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

Belowground decomposition of mangrove roots in Florida coastal everglades

Mangrove root decomposition rates were measured by distributing mesh bags containing fine root material across six sites with different soil fertility and hydroperiod to compare ambient differences to substrate quality. Roots from a site with lower soil phosphorus concentration were used as a reference and compared to ambient roots at five other sites with increased phosphorus concentration. Four mesh bags of each root type (ambient versus reference), separated into four 10-cm replicate intervals, were buried up to 42 cm depth at each site and incubated for 250 d (initiation in May 2004). Mass loss of ambient mangrove roots was significant at all study sites and ranged from 17% to 54%; there was no significant difference with depth at any one site. Reference decomposition constants (−k) ranged from 0.0012 to 0.0018 d−1 among Taylor Slough sites compared to 0.0023–0.0028 d−1 among Shark River sites, indicating slower decomposition rates associated with lower soil phosphorous and longer flood duration. Reference roots had similar decomposition rates as ambient roots in four of the six sites, and there were no significant correlations between indices of root substrate quality and decomposition rates. Among these distinct landscape gradients of south Florida mangroves, soil environmental conditions have a greater effect on belowground root decomposition than root substrate quality.

Changes in mass and nutrient content of wood during decomposition in a south Florida mangrove forest

1. Large pools of dead wood in mangrove forests following disturbances such as hurricanes may influence nutrient fluxes. We hypothesized that decomposition of wood of mangroves from Florida, USA (Avicennia germinans, Laguncularia racemosa and Rhizophora mangle), and the consequent nutrient dynamics, would depend on species, location in the forest relative to freshwater and marine influences and whether the wood was standing, lying on the sediment surface or buried. 2. Wood disks (8–10 cm diameter, 1 cm thick) from each species were set to decompose at sites along the Shark River, either buried in the sediment, on the soil surface or in the air (above both the soil surface and high tide elevation). 3. A simple exponential model described the decay of wood in the air, and neither species nor site had any effect on the decay coefficient during the first 13 months of decomposition. 4. Over 28 months of decomposition, buried and surface disks decomposed following a two-component model, with labile and refractory components. Avicennia germinans had the largest labile component (18 ± 2% of dry weight), while Laguncularia racemosa had the lowest (10 ± 2%). Labile components decayed at rates of 0.37–23.71% month−1, while refractory components decayed at rates of 0.001–0.033% month−1. Disks decomposing on the soil surface had higher decay rates than buried disks, but both were higher than disks in the air. All species had similar decay rates of the labile and refractory components, but A. germinans exhibited faster overall decay because of a higher proportion of labile components. 5. Nitrogen content generally increased in buried and surface disks, but there was little change in N content of disks in the air over the 2-year study. Between 17% and 68% of total phosphorus in wood leached out during the first 2 months of decomposition, with buried disks having the greater losses, P remaining constant or increasing slightly thereafter. 6. Newly deposited wood from living trees was a short-term source of N for the ecosystem but, by the end of 2 years, had become a net sink. Wood, however, remained a source of P for the ecosystem. 7. As in other forested ecosystems, coarse woody debris can have a significant impact on carbon and nutrient dynamics in mangrove forests. The prevalence of disturbances, such as hurricanes, that can deposit large amounts of wood on the forest floor accentuates the importance of downed wood in these forests.