Geometry

The process of measuring the exact location of points of interest on a plant in order to produce an accurate 3-D model is well developed (Godin et al. 1999). These use 3-D coordinate recording devices such as electromagnetic digitisers (Raab et al. 1979), photogrammetry (Innes and Koch 1998) or sonic digitisers (Mack and Pyke 1979) to manually record each coordinate along with the element type (trunk, leaf etc) so that little processing is needed after the data has been collected. Making such direct measurement of plant structure is a laborious and time consuming process, so is not suitable for creating the stand scale models necessary for remote sensing simulations (Godin

et al. (1999) took 24 worker days to digitise eight relatively small trees).

A much quicker method to build up a set of plant models required for a stand is to use mathematical models to “grow” them on a computer. This idea was pioneered by Lindenmeyer (1968a) (with the sister paper Lindenmeyer (1968b)) who showed that small adjustments of simple growth rules could lead to complex and vastly different structures that can mimic real organisms. A similar method of simple rules was used (seemingly independently) to produce 3-D tree-like structures (Honda 1971).

These early attempts were only plant-like as they were not based on real plants; just made to look similar. Gradually the methods were refined so that plants could be represented to a high degree of realism (Prusinkiewicz and Lindenmeyer 1990, Allen et al. 2005). Some take biological factors into account to predict how plants of the same species develop in different environments (Chelle 2005). As an interesting aside it has been found that the algorithms represent reality better if chosen to optimise light exposure (for light liking species (Honda 1978)) or mechanical strength (for exposed trees (Fisher 1992)), with slight randomisation, showing the optimisation process of evolution.

The growth rules needed to drive these models can be generated by measurement of relatively few plants, then tweaked to match local conditions. This technique has been employed to generate large scenes for remote sensing simulations (Disney et al. 2006) with some software available commercially (Onyx Computing Inc 2009).

An exciting recent development is the use of laser scanning to generate complete plant models. Laser scanners generate dense point clouds of targets rapidly (less than 10 minutes for a hemi- sphere). However, unlike a human interpreter in 3-D digitisation, the scanner does not know which points connect to which, much less what plant organs they represent. The conversion of a point cloud into a plant model is not trivial (Omasa et al. 2007) and explains the much slower pace of development compared to the comparatively simple building modelling. It has recently been shown that it is possible to use knowledge of plant structure (ie. a leaf must be connected to a branch which must be connected to trunk which must be connected to the ground) can be used to

generate a plant model from a point cloud (Cˆote et al. 2009) that looks the same and (through

Monte Carlo ray tracing) produces similar remote sensing signals based in the computer graphics method of Xu et al. (2007). This still requires some manual input to help connect the dots but it is a promising line of research.

Abstractions Completely explicit models with accurate element BRDFs do not rely any effective

parameters to simulate accurate signals (Widlowski et al. 2005), however such detail comes at a heavy computational price and requires an enormous amount of data to set up. In addition to the efficiency techniques given in section 2.2.3, some abstractions have been used to reduce the

computational burden and data requirements.

Having unique bidirectional reflectance and transmittance spectra for each element would re- quire either a set of look up tables or separate functions. These would most likely be wavelength dependent (for a leaf NIR reflectance is more specular than in the visible (Grant et al. 1993)) and so separate ray paths would be needed for each wavelength. If it is assumed that the bidirectional reflectance and transmittance are the same shape for all wavelengths (but not the same magni- tude) then a single ray tree can be used for all wavelengths (Lewis 1999). This greatly increases speed of multi-spectral simulations and the difference caused by brdf shapes has been shown to average out at the stand scale (Disney et al. 2006), although a comprehensive validation has not been performed at finer scales (such as lidar’s often centimetre scale). Typically reflection and transmission are assumed to be perfectly Lambertian, removing the need for look up tables or more complex functions.

In coniferous forests the vast majority of elements, and so intersection tests and computational expense, are made up of needles. Therefore abstracting a needle shoot to a single simple geometric primitive will make an enormous saving. It has been shown that such a model can reproduce stand and shoot scale brdfs (Rochdi et al. 2006) but care must be taken. Smolander and Stenberg (2003) showed that whilst using primitives with the same average projected area as needle shoots can recreate the single scattering reflectance accurately, it does not deal with internal multiple scat- tering and so to correct for this the parameters become effective rather than physical (Widlowski

et al. 2005). This suggests that the results of such models cannot be taken as entirely physically

accurate and so explicit models should be used were physical realism is important. There are moves towards faster methods that take scattering into account physically but these have not yet reached maturity (Smolander and Stenberg 2005, Rautiainen et al. 2009).

For complete realism all structures larger than the radiation’s wavelength should be explicitly modelled, including surface texture. For tree bark this would require many small facets, making ray tracing more computationally expensive. Using fewer large, smooth objects (such as cylinders) to represent these surfaces will miss this detail but be far faster to trace and requires far less memory to store. Various processes have been created in computer graphics to modify a simple geometric

primitive’s surface to emulate this small scale surface texture (Koenderink and van Doorn 1996). These work by a process of “bump mapping”, rotating local surface normals whenever a ray strikes to make the brdf more like that of a textured surface. This slightly increases the computational expense compared to geometric primitives alone (requiring a surface normal jitter value to be generated with each interaction) but this is more than made up for by the reduced number of objects to test for intersection. There are methods to deal various levels of detail, some simply rotating surface normals, others calculating how such rotations would shadow adjacent surfaces (Cabrel et al. 1987), but most remote sensing simulators do not go down to this level of detail, trusting that any such effects will average out on the scales of interest (pictures tend to be far higher resolution than remote sensing detectors). These techniques have been shown to produce realistic images of bark (Oppenheimer 1986) but, as far as the author is aware, the effect has not been quantified except for relatively simple scenes (Ulbricht et al. (2006) presents some results, mainly from architecture).

A method to reduce the memory requirements of objects is to use cloning. Rather then repre- senting many similar objects (such as leaves, pine shoots), each can be defined once, then copied to locations as required. These clones can be nested (clone leaves into shoots, shoots into whorls, whorls into trees, trees into stands, stands into forests) to make the scene model even more com- pact. This has no effect upon the computer processing requirements.

Some modern ray tracing models use turbid medium forests for computational speed (North 1996), whilst these are many hundreds of times faster than fully explicit models their reliance on effective parameters to explain clumping, multiple scattering and the hotspot limits their physical realism.