Dylan E. McNamara

Image processing with the radial Hilbert transform: theory and experiments.

The Hilbert transform is useful for image processing because it can select which edges of an input image are enhanced and to what degree the edge enhancement occurs. However, the transform operation is one dimensional and is not applicable for arbitrarily shaped two-dimensional objects. We introduce a radially symmetric Hilbert transform that permits two-dimensional edge enhancement. We implement one-dimensional, two-dimensional, and radial Hilbert transforms with a programmable phase-only liquid-crystal spatial light modulator. Experimental results are presented.

Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator.

We show how to two dimensionally encode the polarization state of an incident light beam using a parallel-aligned liquid-crystal spatial light modulator (LCSLM). Each pixel of the LCSLM acts as a voltage-controlled wave plate and can be programmed over a 2pi phase range at a wavelength of 514.5 nm. Techniques are reviewed for either rotating the major axis of elliptically polarized light or for converting an input linearly polarized beam into an arbitrary elliptically polarized beam. Experimental results are demonstrated in which we generate various two-dimensional spatial patterns of polarized light. Several potential applications are suggested. We also report an unexpected edge-enhancement effect that might be useful in image processing applications.

Analysis of the fractional Hilbert transform

The Hilbert transform is of interest for image-processing applications because it forms an image that is edge enhanced relative to an input object. Recently a fractional Hilbert transform was introduced that can select which edges are enhanced and to what degree the edge enhancement occurs. Although experimental results of this selective edge enhancement were presented, there was no explanation of this phenomenon. We analyze a one-dimensional fractional Hilbert transform acting on a one-dimensional rectangle function and show how it produces an output image that is selectively edge enhanced.

Spatial dynamics of benthic competition on coral reefs

The community structure of sedentary organisms is largely controlled by the outcome of direct competition for space. Understanding factors defining competitive outcomes among neighbors is thus critical for predicting large-scale changes, such as transitions to alternate states within coral reefs. Using a spatially explicit model, we explored the importance of variation in two spatial properties in benthic dynamics on coral reefs: (1) patterns of herbivory are spatially distinct between fishes and sea urchins and (2) there is wide variation in the areal extent into which different coral species can expand. We reveal that the size-specific, competitive asymmetry of corals versus fleshy algae highlights the significance of spatial patterning of herbivory and of coral growth. Spatial dynamics that alter the demographic importance of coral recruitment and maturation have profound effects on the emergent structure of the reef benthic community. Spatially constrained herbivory (as by sea urchins) is more effective than spatially unconstrained herbivory (as by many fish) at opening space for the time needed for corals to settle and to recruit to the adult population. Further, spatially unconstrained coral growth (as by many branching coral species) reduces the number of recruitment events needed to fill a habitat with coral relative to more spatially constrained growth (as by many massive species). Our model predicts that widespread mortality of branching corals (e.g., Acropora spp) and herbivorous sea urchins (particularly Diadema antillarum) in the Caribbean has greatly reduced the potential for restoration across the region.

Understanding Human–Landscape Interactions in the “Anthropocene”

This article summarizes the primary outcomes of an interdisciplinary workshop in 2010, sponsored by the U.S. National Science Foundation, focused on developing key questions and integrative themes for advancing the science of human–landscape systems. The workshop was a response to a grand challenge identified recently by the U.S. National Research Council (2010a)—“How will Earth’s surface evolve in the “Anthropocene?”—suggesting that new theories and methodological approaches are needed to tackle increasingly complex human–landscape interactions in the new era. A new science of human–landscape systems recognizes the interdependence of hydro-geomorphological, ecological, and human processes and functions. Advances within a range of disciplines spanning the physical, biological, and social sciences are therefore needed to contribute toward interdisciplinary research that lies at the heart of the science. Four integrative research themes were identified—thresholds/tipping points, time scales and time lags, spatial scales and boundaries, and feedback loops—serving as potential focal points around which theory can be built for human–landscape systems. Implementing the integrative themes requires that the research communities: (1) establish common metrics to describe and quantify human, biological, and geomorphological systems; (2) develop new ways to integrate diverse data and methods; and (3) focus on synthesis, generalization, and meta-analyses, as individual case studies continue to accumulate. Challenges to meeting these needs center on effective communication and collaboration across diverse disciplines spanning the natural and social scientific divide. Creating venues and mechanisms for sustained focused interdisciplinary collaborations, such as synthesis centers, becomes extraordinarily important for advancing the science.

Long-Term, Large-Scale Morphodynamic Effects of Artificial Dune Construction along a Barrier Island Coastline

Abstract Interactions between human manipulations and landscape processes can form a dynamically coupled system because landscape-forming processes affect humans, and humans increasingly manipulate landscape-forming processes. Despite the dynamic nature of sandy barrier islands, economic incentive and recreational opportunities attract humans and development. Storm-driven sediment-transport events that build barrier islands constitute hazards to humans and infrastructure, and manipulations aimed at preventing or mitigating such events link human actions and long-term island morphodynamics. To explore how the behavior of a natural barrier island differs from one in which humans are dynamic system constituents, we use a numerical model of storm-driven sediment redistributions within the shoreface/island/back-barrier system and human rearrangements of sediment within the subaerial barrier island. In a modeled natural system, periods of dune growth and island stability, initiated by stochastic lulls in storm activity, alternate with stormy periods, in which shoreline erosion and frequent overwash regulate dune heights. When humans are included in the model, overwash deposits are removed from the island, and artificially high dunes are rebuilt. These manipulations tend to filter moderate overwash events. However, with shoreline erosion and rising sea level, these manipulations promote lower and narrower islands in the long term, so that when dunes are overtopped, the sediment redistributions are more severe. Thus, the coupled human/barrier system exhibits wider swings between increased island stability and sudden island displacements. Increasing the height of artificially maintained dunes increases the rate of island narrowing and, therefore, infrastructure relocation, and increases the need for sediment to be imported from outside the system.

Fractional derivatives-analysis and experimental implementation.

The fractional derivative spatial-filtering operator is useful for image-processing applications, particularly for examination of phase objects. Experimental implementation is difficult because the mask function combines both amplitude and phase. We present a simple one-dimensional analysis of the fractional derivative operation and note similarities with the fractional Hilbert transform. We demonstrate how to encode these amplitude and phase masks using a phase-only liquid-crystal spatial light modulator and present experimental results. Finally, we introduce a radially symmetric extension of this operation that is more useful for objects having an arbitrary shape.

Climate adaptation and policy-induced inflation of coastal property value.

Human population density in the coastal zone and potential impacts of climate change underscore a growing conflict between coastal development and an encroaching shoreline. Rising sea-levels and increased storminess threaten to accelerate coastal erosion, while growing demand for coastal real estate encourages more spending to hold back the sea in spite of the shrinking federal budget for beach nourishment. As climatic drivers and federal policies for beach nourishment change, the evolution of coastline mitigation and property values is uncertain. We develop an empirically grounded, stochastic dynamic model coupling coastal property markets and shoreline evolution, including beach nourishment, and show that a large share of coastal property value reflects capitalized erosion control. The model is parameterized for coastal properties and physical forcing in North Carolina, U.S.A. and we conduct sensitivity analyses using property values spanning a wide range of sandy coastlines along the U.S. East Coast. The model shows that a sudden removal of federal nourishment subsidies, as has been proposed, could trigger a dramatic downward adjustment in coastal real estate, analogous to the bursting of a bubble. We find that the policy-induced inflation of property value grows with increased erosion from sea level rise or increased storminess, but the effect of background erosion is larger due to human behavioral feedbacks. Our results suggest that if nourishment is not a long-run strategy to manage eroding coastlines, a gradual removal is more likely to smooth the transition to more climate-resilient coastal communities.

Barrier Islands as Coupled Human–Landscape Systems

In recent decades, coastal development has transformed barrier systems around the world. The longest, most intensively developed chain of barriers extends along the Atlantic and Gulf Coasts of the U.S., where mean population density is the highest in the country. There are nearly 300 barrier islands between Maine and Texas, and of these, at least 70 are intensively built-up. Concentrated development exists and continues despite the fact that barrier islands are transient landscapes, not only over geologic time scales of millennia, but also within human and economic time scales of centuries to decades. Populated barrier islands are inherently vulnerable to natural hazards such as sea-level rise, cumulative erosion, and storm events; this vulnerability drives humans to actively modify barrier geometry and environments. The most common manipulations are beach nourishment, to mitigate shoreline erosion, and increases to dune height or seawall construction to prevent flooding and damage from overwash during storm events. Over time scales of years to decades, hazard-mitigation actions impact natural, spatio-temporal barrier processes such as washover deposition and planform transgression, which in turn affect future efforts to manage, control, or prevent changes to barrier morphology. Through their maintenance and persistence, interventions against coastal hazards represent a significant dynamical component of developed barrier-island system evolution, such that, within the past century, human actions and natural barrier-island processes have become dynamically coupled. This coupling leads to steady-state barrier-island behaviors that are new. A fundamental way to understand how developed barrier islands will respond to climate change over decadal time scales is to treat these settings as strongly coupled human–natural systems. Dynamical demonstration of coupled-system behavior suggests new avenues for less reactionary and more holistic coastal management perspectives for barrier systems and raises questions about whether and how society may adapt to coastal change. Over time scales longer than centuries, human interventions may be coupled only weakly to long-term barrier dynamics. Short of major technological advancements or sweeping decisions to transform these environments into comprehensively geoengineered terrains, high-density development on U.S. barrier islands will eventually have to change—perhaps radically—from its current configuration.

Decentralized Management Hinders Coastal Climate Adaptation: The Spatial-dynamics of Beach Nourishment

Climate change threatens to alter coastline erosion patterns in space and time and coastal communities adapt to these threats with decentralized shoreline stabilization measures. We model interactions between two neighboring towns, and explore welfare implications of spatial-dynamic feedbacks in the coastal zone. When communities are adjacent, the community with a wider beach loses sand to the community with a narrower beach through alongshore sediment transport. Spatial-dynamic feedbacks create incentives for both communities to nourish less, resulting in lower long-run beach width and lower property values in both communities, a result that parallels the classic prisoner’s dilemma. Intensifying erosion—consistent with accelerating sea level rise—increases the losses from failure to coordinate. Higher erosion also increases inequality in the distribution of benefits across communities under spatially coordinated management. This disincentive to coordinate suggests the need for higher-level government intervention to address a traditionally local problem. We show that a spatially targeted subsidy can achieve the first best outcome, and explore conditions under which a second-best uniform subsidy leads to small or large losses.