426 H.-E. Andersen

measured position (Cxˆ k ). The Kalman gain (K) incorporates the measurement error such that when the measurement error (i.e. GPS error in our case) is large, the gain K is small, and the measured GPS position (yk+1) will not have as much influence on the estimated position xˆ k+1 [50].

Although differential post-processing of the GPS data previously required base station data, even these requirements are now disappearing with the advent of processing techniques such as precise point positioning (PPP), which can provide accurate GPS coordinates without base station data [37]. These developments could dramatically reduce the cost of aerial photo acquisitions, especially in remote, unpopulated areas.

10.2.2 Tree Height Measurement Using Forest Photogrammetry

In this section, we first consider manual and then automatic methods of forest photogrammetry.

10.2.2.1Manual Forest Measurements Using Large-Scale Aerial Photogrammetry

The ability to accurately identify and measure individual tree crowns using aerial photographs is heavily dependent on scale and image quality [23]. Scale is a function of focal length of the camera lens and the flying height, while image quality is determined by many factors, including film characteristics and processing, camera lens design, atmospheric and lighting conditions, image motion compensation (blur), resolution (pixel size), color balance, etc.

The other important consideration in determining the efficacy of tree height measurement using forest photogrammetry is image geometry and radial displacement. Many newer digital imaging systems have significantly shorter effective focal lengths than older film mapping cameras, leading to severe layover of trees throughout most of the image area (see Fig. 10.3). Layover (radial displacement) can make it very difficult to view forested scenes in stereo, leading to difficulties in tree height measurement. For this reason, relatively long lenses (e.g. 305 mm) were usually used on mapping cameras in forest photogrammetry applications [23].

Image motion, or blurring due to movement of the aircraft during the time that the camera shutter is open, is another significant concern when acquiring largescale photography for forestry applications. Before the advent of Forward Motion Compensation (FMC) technology in the late 1980s, image motion with film cameras could only be minimized through the use of a short exposure time, which in turn required a fast film with larger grain size [39]. FMC technology actually involved moving the film plate a minute amount during the time that the shutter is open, thereby reducing image blurring. In the case of modern digital imaging systems, a technology called Time Delayed Integration (TDI) is used. In TDI, the image is

read continuously by the detector and the accumulated images are digitally shifted in such a way as to correct for the movement of the aircraft during the time that the shutter is open [39].

The accuracy of manual tree height measurements using photogrammetry usually depends upon the ability of the interpreter to see both the base and top of the tree. Due to the characteristics of the tree crown and in particular, the size of the crown apex, the species of tree will influence the accuracy of photogrammetric tree height measurements. For example, Kovats [23] found that with large-scale photographs measured under an analytical stereo plotter instrument, lodge pole pine tree tops were larger and could be measured more accurately than relatively small Douglas-fir tree tops [13]. This study found that when tree tops were visible, tree heights could be measured very accurately (0.05 ± 0.59 m (mean error ± standard deviation (SD))) with large scale (1 : 1200) photography. In dense, closed canopy forests on mountainous terrain it is often impossible to see through the forest canopy and therefore the base of trees cannot be accurately measured. This leads to increasing tree height error as forest canopy closure and terrain roughness increase. Other studies have shown that large scale non-metric (i.e. non-mapping) 35-mm camera could be used to accurately measure stem counts and determine species in a loblolly pine plantation in Virginia [38].

In general, the process to obtain individual tree measurements and attributes from digital aerial images within a digital photogrammetric workstation consists of the following steps:

1.Obtain overlapping aerial stereo imagery (using digital camera or scanned film imagery)

2.Carry out interior orientation using camera calibration information

3.Carry out exterior orientation using either direct georeferencing (obtained using airborne GPS and IMU) or ground control points

4.Manually measure tree dimensions and digitize features using collinearity condition and space forward intersection (Fig. 10.2).

5.Export coordinates and attributes of trees for further analysis within a geographical information system (GIS).

10.2.2.2 Automated Methods in Forest Photogrammetry

To a large extent, acquisition of accurate individual tree measurements from digital aerial photographs requires the use of manual techniques. Given the complexity and irregularity of imaged forest scenes, which are composed of various vegetation and ground surface components with differing textures, spectral signatures, shadow patterns, as well as the fact that every image represents a different perspective on these complex and irregular features, it is very difficult to efficiently automate the acquisition of forest photogrammetric measurements. However, this has been an active area of research over the last 10–15 years, and progress has been made.

Several studies in the 1990s and early 2000s investigated the possibility of automatically extracting individual tree-level measurements from high resolution imagery in a two-dimensional space. Gougeon developed a shadow-following technique that effectively delineated individual tree crowns in both aerial photographs and high resolution satellite images [17]. Brandtberg and Walter used multiple scale analysis to extract individual tree crowns from aerial images [9]. Both Larsen and Rudemo [24] and Pollock [42] used template-matching techniques to detect individual trees in aerial images. Lund and Rudemo [27] developed a probabilistic approach to identifying individual tree crown tops in digital imagery based on a stochastic point process model. Larsen and Rudemo [24] have since extended this model to a three-dimensional point pattern using multiple image views, although the technique is still largely theoretical in nature. Gong et al. [15] developed a semi-automated method to extract tree measurements using a three-dimensional generalized ellipsoid model for tree crown shape. Culvenor [10] developed a technique called the tree identification and delineation algorithm (TIDA) based on (1) identification of local maxima, (2) identification of local minima, and (3) clustering of crown pixels, where local maxima are used as seed points for the clustering and local minima are used to constrain the clustering. Due to the difficulty of finding individual tree crown positions, however, this method relied on manual determination of tree top and base.

Other approaches have concentrated on the automated measurement of canopy surface models from digital stereo imagery, instead of direct extraction of individual tree crowns. This approach involves the automated identification of conjugate points (image points corresponding to the same object on the ground) in the overlapping areas of stereo imagery, and then uses the collinearity equations (described above) to calculate the elevation of each surface point throughout the overlap area. The process of locating conjugate points throughout the overlap area is called image matching. Although this approach does not attempt to isolate individual tree crowns, image matching in a forested area is also complicated by many of the same factors as the individual tree methods, including (1) occlusions, (2) repetitive patterns, (3) shadows, perspective differences, (4) semi-transparent surfaces, and (5) rough, discontinuous surfaces [25]. Although most digital photogrammetric software packages provide image matching and surface generation capabilities, these systems are usually designed to generate digital terrain models in relatively unvegetated areas and usually yield disappointing results over forests. That being said, attempts have been made to develop image matching algorithms that are more effective in forested areas. For example, Li and Gruen [25] developed an approach that matches both grid points, textural and edge features, uses geometric constraints to limit the search space, and employs two different matching techniques (sum of modified cross-correlation and least-squares matching) to improve the accuracy of matching results in complex forested scenes. The technique combines both area-based matching (ABM) and feature-based matching (FBM) approaches, and employs a hierarchical approach moving from coarse to finer resolutions in the matching process. A triangular irregular network (TIN) surface is generated at each level of the resolution hierarchy, and a modified multi-photo geometrically constrained (MPGC) matching algorithm