**2.1 Notion of canopy grain**

The notion of canopy grain needs to be clarified. In the context of this study, it refers to the aspect of the uppermost layer of the forest, i.e. the top canopy. It emerges from the images as soon as the contrast between sunlit and shadowed tree crowns becomes perceptible. This property increases with the fineness of image spatial resolution (Fig. 1) that explains why, in VHR images, the tropical forest no longer appears as a continuous homogenous layer, or 'red carpet', as it is the case on medium resolution images with pixel size greater than 5 meters (Fig. 1). Intuitively, the canopy grain depends on both the spatial distribution of trees within a scene and the shapes and dimensions of their crowns. The question is then how to derive quantitative measurements of such canopy grain texture. Following Rao and Lohse (1993), who explained that repetitiveness is the most important dimension of human perception for structural textures, our idea is to measure the degree of repetitiveness expressed in canopy grain within a forest scene. Two dimensional (2D) Fourier or wavelet transforms proved to be well adapted for this purpose (e.g. Couteron, 2002; Ouma et al., 2006) because they allow shifting canopy grain properties from the spatial domain to the frequency domain. Though of larger potential application, we focus in this paper on the 2D Fourier-based frequency spectra as a mean for relating tropical forest canopy grain to aboveground biomass (AGB).

#### **2.2 The FOTO method**

60 Remote Sensing of Biomass – Principles and Applications

pixel size greater than 4 meters, VHR imagery greatly improves thematic information on forest canopies. Indeed, the contrast between sunlit and shadowed trees crowns as visible on such images (Fig. 1) is potentially informative on the structure of the forest canopy. Furthermore, new promising methods now exist for analyzing these fine scale satellite observations (e.g. Bruniquel-Pinel & Gastellu-Etchegorry, 1998; Malhi & Roman-Cuesta, 2008; Rich et al. 2010). In addition, we believe that there is also a great potential in similarly using historical series of digitized aerial photographs that proved to be useful in the past for mapping large extents of unexplored forest (Le Touzey, 1968; Richards, 1996) for quantifying AGB changes through time. This book chapter presents the advancement of a research program undertaken by our team for estimating above ground biomass of mangrove and *terra firme* forests of Amazonia using canopy grain from VHR images (Couteron et al. 2005; Proisy et al. 2007; Barbier et al., 2010; 2011). We present in a first section, the canopy grain notion and the fundamentals of the Fourier-based Textural Ordination (FOTO) method we developed. We then introduce a dual experimental-theoretical approach implemented to understand how canopy structure modifies the reflectance signal and produces a given texture. We discuss, for example, the influence of varying sun-view acquisition conditions on canopy grain characteristics. A second section assesses the potential and limits of the canopy grain approach to predict forest stand structure and more specifically above ground biomass. Perspectives for a better

understanding of canopy grain-AGB relationships conclude this work.

Fig. 1. Differences of canopy grain perception between two 300 m square subset images of different spatial resolution over a mixed savanna forest-inhabited area, French Guiana. Left: a 2.5-m SPOT5 Fusion image acquired in October 2010. Right: a 20-cm aerial photograph

The notion of canopy grain needs to be clarified. In the context of this study, it refers to the aspect of the uppermost layer of the forest, i.e. the top canopy. It emerges from the images

acquired in July 2010 (© L'Avion Jaune).

**2. The canopy grain approach** 

**2.1 Notion of canopy grain** 

#### **2.2.1 Workflow up to forest AGB prediction**

The well-known Fourier transform is highly suitable for analyzing repetitiveness of canopy grain as it breaks down an intensity signal into sinusoidal components with different frequencies. We built on this principle the development of the Fourier-based Textural Ordination (FOTO) method to primarily explore the potential of digitized aerial photographs and VHR satellite images for predicting tropical forest stand structure parameters including AGB (Couteron et al., 2005; Proisy et al. 2007). We summarize, hereafter, the flow of operations that yield AGB predictions from FOTO outputs.

A prerequisite of the method is to mask non-forest areas, such as clouds and their shadows, water bodies, savannas, crops and civil infrastructures areas (Fig. 2, step 1). The method then proceeds with the specification of a square window size in which 2D-Fourier spectra are computed (Fig. 2, step 2). To be clear, the window size *WS* is expressed in meters as:

$$\text{WS} = \text{N.A} \mathbf{S} \tag{1}$$

where N is the number of pixels in the *X* or Y direction of the image and *S* is the pixel size in meters. *WS* may influence the FOTO results as discussed in the following sub-section. Using large *WS* also means that spatial resolution of the FOTO outputs and subsequent biomass maps will be *N* times coarser than the spatial resolution of the source image(s). Although the use of a sliding window is computationally intensive, it can attenuate the effects of both spatial resolution degradation and study areas fringe erosion.

After windowing the forest images, Fourier radial spectra (or r-spectra) are computed and give for each window, the frequency vs. amplitude of a sinusoidal signal that fits the spatial arrangement of pixels grey levels (Fig. 2, step 3) as described in the next paragraph. The rspectra may be then stacked into a common matrix in which each row corresponds to the rspectrum of a given window, whereas each column contains amplitude values. This table is then submitted to multivariate analysis techniques (ordinations/classifications). With this approach, the study can concern as many images as necessary, providing they have the same spatial resolution. The resulting table can, for instance, be submitted to a standardized principal component analysis (PCA; Fig. 2, step 4). Window scores on the 3 most prominent

Biomass Prediction in Tropical Forests: The Canopy Grain Approach 63

axes are used as texture indices (the so-called FOTO indices) that are mapped by composing red–green–blue (RGB) images expressing window scores values against first, second and third axes, respectively. Such FOTO maps have a spatial resolution equal to the window size *WS*. The final step (Fig. 2, step 5) is to relate ground truth forest plot biomass to FOTO

> GB a a T *c*

where *a0* and *ac* are the coefficients of the multiple regression of *AGB* onto the texture indices

The computation of radial spectra has to be detailed because such frequency signatures are essential components of the canopy grain analysis. It is to note that the calculation of rspectra is also possible for any single image extract centered on one forest plot as illustrated

Each image extract is subjected to the two dimensional discrete fast Fourier transform algorithm implemented in most of the technical computing software. Image intensity expressed in spatial *XY* Cartesian referential domain is transposed to the frequency domain. Power spectrum decomposing the image variance into frequency bins along the two Cartesian axes is then obtained for each square window (Fig. 2, step 3, right). This latter was demonstrated as an efficient way to quantify pattern scale and intensity (Couteron et al. 2006) from images of various vegetation types (Couteron et al. 2002; 2006). Assuming that images of tropical forest have isotropic properties, the radial spectra are then obtained after azimuthally averaging over all travelling directions (Fig. 2, step 3, left). Frequencies are expressed in cycles per kilometer, i.e. the number of repetitions over a 1 km distance. The discrete set of spatial frequencies *f* can be also transformed into sampled wavelengths (in meters) as *λ*=1000/*f*. For example, a frequency of 200 cycles per kilometre corresponds to a wavelength of 5 metres.

Standardized principal component analysis of the spectra table created by the stacking of all r-spectra is a mean to perform regional analysis of canopy grain variations through one or several image scenes. For illustration, a 0.5-m panchromatic Geoeye image covering (after masking non-forest areas) 11271 hectares of mangroves is analyzed (Fig. 3). The three first factorial axes of the PCA accounted for more than 81% of the total variability. The first PCA axis opposes coarse and fine canopy grain that correspond to spatial frequencies of less than 100 cycles/km (=10 m) and more than 250 cycles/km (=4 m), respectively. Intermediate

From this analysis, we coded window scores on the three main PCA axes as RGB real values (Fig. 4). Pioneer and young stages of mangroves are characterized by red–i.e. high scores on PC1 only– whereas intergrades between blue and cyan corresponded to areas with adult trees (low positive scores on PC1 and negative scores on PC2). Green color maps mature and decaying stages of mangrove with high PC2 and very low PC1 scores. Hence, coarseness/fineness gradients of thousands of unexplored hectares of mangrove can be mapped and allow to capture, at a glance, the overall spatial organization presented in the

spatial frequencies are found with high negative loadings on the second axis.

*A*

3 0 cc 1

(2)

indices using a linear model of the form:

*T* obtained from the first three PCA axes.

**2.2.2 Computing radial spectra of forest plots** 

in the numerous examples provided hereafter.

**2.2.3 Principal component analysis for regional analysis** 

Fig. 2. Flow of operations involved in the FOTO analysis up to biomass prediction

Fig. 2. Flow of operations involved in the FOTO analysis up to biomass prediction

axes are used as texture indices (the so-called FOTO indices) that are mapped by composing red–green–blue (RGB) images expressing window scores values against first, second and third axes, respectively. Such FOTO maps have a spatial resolution equal to the window size *WS*. The final step (Fig. 2, step 5) is to relate ground truth forest plot biomass to FOTO indices using a linear model of the form:

$$\text{AGB} = \mathbf{a}\_0 + \sum\_{c=1}^{3} \mathbf{a}\_c \text{ T}\_c \tag{2}$$

where *a0* and *ac* are the coefficients of the multiple regression of *AGB* onto the texture indices *T* obtained from the first three PCA axes.

#### **2.2.2 Computing radial spectra of forest plots**

The computation of radial spectra has to be detailed because such frequency signatures are essential components of the canopy grain analysis. It is to note that the calculation of rspectra is also possible for any single image extract centered on one forest plot as illustrated in the numerous examples provided hereafter.

Each image extract is subjected to the two dimensional discrete fast Fourier transform algorithm implemented in most of the technical computing software. Image intensity expressed in spatial *XY* Cartesian referential domain is transposed to the frequency domain. Power spectrum decomposing the image variance into frequency bins along the two Cartesian axes is then obtained for each square window (Fig. 2, step 3, right). This latter was demonstrated as an efficient way to quantify pattern scale and intensity (Couteron et al. 2006) from images of various vegetation types (Couteron et al. 2002; 2006). Assuming that images of tropical forest have isotropic properties, the radial spectra are then obtained after azimuthally averaging over all travelling directions (Fig. 2, step 3, left). Frequencies are expressed in cycles per kilometer, i.e. the number of repetitions over a 1 km distance. The discrete set of spatial frequencies *f* can be also transformed into sampled wavelengths (in meters) as *λ*=1000/*f*. For example, a frequency of 200 cycles per kilometre corresponds to a wavelength of 5 metres.

#### **2.2.3 Principal component analysis for regional analysis**

Standardized principal component analysis of the spectra table created by the stacking of all r-spectra is a mean to perform regional analysis of canopy grain variations through one or several image scenes. For illustration, a 0.5-m panchromatic Geoeye image covering (after masking non-forest areas) 11271 hectares of mangroves is analyzed (Fig. 3). The three first factorial axes of the PCA accounted for more than 81% of the total variability. The first PCA axis opposes coarse and fine canopy grain that correspond to spatial frequencies of less than 100 cycles/km (=10 m) and more than 250 cycles/km (=4 m), respectively. Intermediate spatial frequencies are found with high negative loadings on the second axis.

From this analysis, we coded window scores on the three main PCA axes as RGB real values (Fig. 4). Pioneer and young stages of mangroves are characterized by red–i.e. high scores on PC1 only– whereas intergrades between blue and cyan corresponded to areas with adult trees (low positive scores on PC1 and negative scores on PC2). Green color maps mature and decaying stages of mangrove with high PC2 and very low PC1 scores. Hence, coarseness/fineness gradients of thousands of unexplored hectares of mangrove can be mapped and allow to capture, at a glance, the overall spatial organization presented in the

Biomass Prediction in Tropical Forests: The Canopy Grain Approach 65

Fig. 4. Panchromatic-derived FOTO map obtained from a Geoeye panchromatic image acquired in September 2009. RGB channels code for windows scores on PCA axes. A large part of the mangrove area is masked because either under clouds or with bare mud.

The 3D Discrete Anisotropic Radiative Transfer (DART) model is a ray-tracing model that can simulate, simultaneously in several wavelengths of the optical domain, remotely sensed images of heterogeneous natural and urban landscapes with or without relief, using 3D generic representations of these landscapes for any sun direction, any view direction or any atmosphere (Gastellu-Etchegorry et al., 2004). The model is freely downloadable from *http://www.cesbio.ups-tlse.fr/fr/dart.html* for scientific studies, after signing a charter of use. In the case of forests, a DART scene, namely a 'maket', is a three-dimensional representation of a forest stand within a voxel space. Transmittance and phase functions (the optical properties) associated to each voxel depend on the voxel type (leaves, trunk, soil, etc.). Leaves cells are modelled as turbid media with volume interaction properties whereas others voxel types are taken as solid media with surface properties. Others structural characteristics within the cell (e.g. LAI, leaf and branches angle distribution) can be taken into account. The scattering of rays from each cell is simulated iteratively in a discrete number of directions. We keep the maket size 10% larger than the FOTO window or the forest plot sizes in order to avoid border effects. The final DART image is a sub-scene of

**2.3.1 Basic principles** 

equal dimensions as the reference window or plot.

image. An equivalent result was also obtained using a 1-m panchromatic Ikonos image (Proisy et al. 2007). The FOTO analysis is confirmed of prime interest for mangrove monitoring studies and for highlighting coastal processes in French Guiana (Fromard et al. 2004) through the mapping of forest growth stages.

Fig. 3. Principal component analysis of Fourier spectra obtained from the FOTO analysis of a Geoeye panchromatic image covering 11271 hectares of mangroves in French Guiana. Correlation between PCA axes and spatial frequencies are shown in the left graph.

#### **2.3 The DART modelling method**

Large-scale validation of the FOTO method is highly desirable, to study both the method's sensitivity to complex variations in forest structure and to instrumental perturbations. However, it is notoriously difficult to obtain both detailed forest structure information in inaccessible tropical environments and cloudless imagery over field plots. It was therefore necessary to develop a modeling framework for testing FOTO sensitivity, in simplified but controlled conditions (Barbier et al. 2010; 2011; in press).

Fig. 4. Panchromatic-derived FOTO map obtained from a Geoeye panchromatic image acquired in September 2009. RGB channels code for windows scores on PCA axes. A large part of the mangrove area is masked because either under clouds or with bare mud.

#### **2.3.1 Basic principles**

64 Remote Sensing of Biomass – Principles and Applications

image. An equivalent result was also obtained using a 1-m panchromatic Ikonos image (Proisy et al. 2007). The FOTO analysis is confirmed of prime interest for mangrove monitoring studies and for highlighting coastal processes in French Guiana (Fromard et al.

Fig. 3. Principal component analysis of Fourier spectra obtained from the FOTO analysis of a Geoeye panchromatic image covering 11271 hectares of mangroves in French Guiana. Correlation between PCA axes and spatial frequencies are shown in the left graph.

Large-scale validation of the FOTO method is highly desirable, to study both the method's sensitivity to complex variations in forest structure and to instrumental perturbations. However, it is notoriously difficult to obtain both detailed forest structure information in inaccessible tropical environments and cloudless imagery over field plots. It was therefore necessary to develop a modeling framework for testing FOTO sensitivity, in simplified but

2004) through the mapping of forest growth stages.

**2.3 The DART modelling method** 

controlled conditions (Barbier et al. 2010; 2011; in press).

The 3D Discrete Anisotropic Radiative Transfer (DART) model is a ray-tracing model that can simulate, simultaneously in several wavelengths of the optical domain, remotely sensed images of heterogeneous natural and urban landscapes with or without relief, using 3D generic representations of these landscapes for any sun direction, any view direction or any atmosphere (Gastellu-Etchegorry et al., 2004). The model is freely downloadable from *http://www.cesbio.ups-tlse.fr/fr/dart.html* for scientific studies, after signing a charter of use. In the case of forests, a DART scene, namely a 'maket', is a three-dimensional representation of a forest stand within a voxel space. Transmittance and phase functions (the optical properties) associated to each voxel depend on the voxel type (leaves, trunk, soil, etc.). Leaves cells are modelled as turbid media with volume interaction properties whereas others voxel types are taken as solid media with surface properties. Others structural characteristics within the cell (e.g. LAI, leaf and branches angle distribution) can be taken into account. The scattering of rays from each cell is simulated iteratively in a discrete number of directions. We keep the maket size 10% larger than the FOTO window or the forest plot sizes in order to avoid border effects. The final DART image is a sub-scene of equal dimensions as the reference window or plot.

Biomass Prediction in Tropical Forests: The Canopy Grain Approach 67

In this work, we only simulated mono-spectral images in the visible domain on flat topography without taking into account atmospheric effects (Fig. 5). Standard optical profiles of reflectance for soil, trunks and leaves are selected from the DART database using, for instance, '2D soil-vegetation', '2D bark\_spruce' and '3D leaf\_decidous' files. Such oversimplified images of virtual forest stands composed of trees with 'lollipop-shaped' crowns produce homogeneous texture dominated by few frequencies. The FOTO analysis of 330 DART images however demonstrated their potential for benchmarking textural gradient

Large windows may include features characterizing landforms such as relief variations rather than canopy grain (Couteron et al., 2006) whereas small windows may be unable to adequately capture large canopy features observable in mature growth stages. However, whatever the window size taken within a reasonable range of variations, i.e. 75 to 150 m for tropical forest, spatial frequencies should display more or less the same patterns of contribution to PCA axes (Couteron et al. 2006). The influence of spatial resolution on the sensitivity of r-spectra to capture canopy grain of different forest types was highlighted using 1-m panchromatic and 4-m near infrared (NIR) Ikonos images in

of real forest canopies throughout the Amazon basin (cf. Fig. 3 in Barbier et al. 2010).

Fig. 6. Radial spectra of 2 different mangrove growth stages using 0.5-m and 2-m

panchromatic and near infrared Geoeye channels.

**2.3.3 Virtual canopy images** 

Proisy et al. (2007).

**2.4 Influence of instrumental characteristics 2.4.1 Window size and spatial resolution** 
