Stereo-video systems are used by marine ecologists to count and measure the size of aquatic organisms. Most marine ecologists are not experts in underwater photogrammetry and are not necessarily aware of some of the key design and implementation issues that influence the accuracy and precision of the measurements. Two factors that can influence the measurement accuracy and precision of a stereo-video system are the calibration strategy and the physical orientation of the system. We compare the accuracy and precision of length measurements made by systems calibrated using two regularly used calibration approaches. We also compare length measurements recorded from cameras with base separations of 150 mm, 400 mm, and 800 mm. A three-dimensional (3D), network calibration method using a purpose built calibration cube was used to determine key calibration and camera orientation parameters (e.g., base separation, focal length, and lens distortions) with much improved precision in comparison to a two-dimensional method using either an A3 or A4 planar calibration pattern. As a result, measurements made with a 3D cube displayed improved accuracy and precision compared to either the A3 or A4 planar calibration pattern across a range of typical operational distances. The distance between the cameras on the base bar (base separation) affects the accuracy and precision of measurements with the 800 mm system producing length estimates of improved accuracy and precision than the systems with narrower baselines. The 150 mm system resulted in measurements with poor precision and accuracy, especially for measurements made at distances greater than six meters.

Structurally complex habitats tend to contain more species and higher total abundances than simple habitats. This ecological paradigm is grounded in first principles: species richness scales with area, and surface area and niche density increase with three-dimensional complexity. Here we present a geometric basis for surface habitats that unifies ecosystems and spatial scales.The theory is framed by fundamental geometric constraints among three structure descriptors-surface height, rugosity and fractal dimension-and explains 98% of surface variation in a structurally complex test system: coral reefs. We then show how coral biodiversity metrics (species richness, total abundance and probability of interspecific encounter) vary over the theoretical structure descriptor plane, demonstrating the value of the theory for predicting the consequences of natural and human modifications of surface structure. Main textMost habitats on the planet are surface habitats-from the abyssal trenches to the tops of mountains, from coral reefs to the tundra. These habitats exhibit a broad range of structural complexities, from relatively simple, planar surfaces to highly complex three-dimensional structures. Currently, human and natural disturbances are changing the complexity of habitats faster than at any time in history [1][2][3][4] . Therefore, understanding and predicting the effects of habitat complexity changes on biodiversity is of paramount importance 5 . However, empirical relationships between commonly-used descriptors of structural complexity and biodiversity are .

AbstractStructurally complex habitats tend to contain more species and higher total abundances than simple habitats. This ecological paradigm is grounded in first principles: species richness scales with area, and surface area and niche density increase with three-dimensional complexity. Here we present a geometric basis for surface habitats that unifies ecosystems and spatial scales. The theory is framed by fundamental geometric constraints among three structure descriptors—surface height, rugosity and fractal dimension—and explains 98% of surface variation in a structurally complex test system: coral reefs. We then show how coral biodiversity metrics (species richness, total abundance and probability of interspecific encounter) vary over the theoretical structure descriptor plane, demonstrating the value of the theory for predicting the consequences of natural and human modifications of surface structure.