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Keywords:

  • canopy texture;
  • French Guiana;
  • submetric images;
  • two-dimensional spectral analysis

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  • 1
    Predicting stand structure parameters for tropical forests from remotely sensed data has numerous important applications, such as estimating above-ground biomass and carbon stocks and providing spatial information for forest mapping and management planning, as well as detecting potential ecological determinants of plant species distributions. As an alternative to direct measurement of physical attributes of the vegetation and individual tree crown delineation, we present a powerful holistic approach using an index of canopy texture that can be extracted from either digitized air photographs or satellite images by means of two-dimensional spectral analysis by Fourier transform.
  • 2
    We defined an index of canopy texture from the ordination of the Fourier spectra computed for 3545 1-ha square images of an undisturbed tropical rain forest in French Guiana. This index expressed a gradient of coarseness vs. fineness resulting from the relative importance of small, medium and large spatial frequencies in the Fourier spectra.
  • 3
    Based on 12 1-ha control plots, the canopy texture index showed highly significant correlations with tree density (R2 = 0·80), diameter of the tree of mean basal area (R2 = 0·71), distribution of trees into d.b.h. classes (R2 = 0·64) and mean canopy height (R2 = 0·57), which allowed us to produce reasonable predictive maps of stand structure parameters from digital aerial photographs.
  • 4
    Synthesis and applications. Two-dimensional Fourier analysis is a powerful method for obtaining quantitative characterization of canopy texture, with good predictive ability on stand structure parameters. Forest departments should use routine forest inventory operations to set up and feed regional databases, featuring both tree diameter figures and digital canopy images, with the ultimate aims of calibrating robust regression relationships and deriving predictive maps of stand structure parameters over large areas of tropical forests. Such maps would be particularly useful for forest classification and to guide field assessment of tropical forest resources and biodiversity.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Retrieving tropical forest stand structure parameters from remotely sensed data is of primary importance for estimating global carbon stocks in above-ground biomass (Houghton et al. 2001; Grace 2004) as well as for obtaining large-scale information required by regional biodiversity studies and forest type classification and mapping (Tuomisto et al. 1995). Indeed, stand structure parameters such as tree density, basal area and canopy height not only allow predictions of forest biomass (Chave et al. 2003) but may also provide spatial information on potential determinants of plant species’ distributions (Couteron et al. 2003), such as the gap-phase regeneration stages (Riéra, Pélissier & Houllier 1998) and the variations in substratum conditions and soil fertility (Ashton & Hall 1992; Paget 1999).

Thanks to the various kinds of satellite and airborne remotely sensed data that are available, for example Landsat™ (Lu et al. 2004), SPOT (De Wasseige & Defourny 2002), Laser Vegetation Imaging Sensor (Drake et al. 2002) and Synthetic Aperture Radar JERS-1 (Santos et al. 2002), predicting stand structure parameters over large areas with a spatial resolution of a dozen to several dozen metres may be achievable. It is, however, surprising that fine spatial resolution techniques capable of detecting small-scale variation in physical signals have only been of limited applicability for the study of tropical forest structure, and therefore of limited use for both ecological research and operational management/conservation (Read 2003). In fact, small-footprint laser altimeters have proven to be of limited efficiency in dense tropical forests because of inconsistent ground returns (Nelson, Oderwald & Gregoire 1997; Dubayah & Drake 2000; Drake et al. 2003; but see Clark, Clark & Roberts 2004). Recent metric and submetric resolution optical data, such as IKONOS and QuickBird panchromatic images, have mostly been used in tropical forests for visual tree crown delineation (Asner et al. 2002; Read et al. 2003; Clark et al. 2004a, 2004b), although Asner & Warner (2003) used an automatic quantification of shadowing while Hurtt et al. (2003) reported preliminary investigations on automatic crown delineation. However, tropical foresters have more than half a century of tradition of delineating and mapping forest types by visual interpretation of aerial photographs (see Table 1 in Polidori et al. 2004), a practice that could easily be extended to modern very-high resolution (VHR) satellite imagery. Furthermore, aerial photographs, when digitized at metric spatial resolution, have enabled numerical extraction of textural information in temperate forest (Sommerfeld, Lundquist & Smith 2000) and semi-arid vegetation (Couteron & Lejeune 2001; Couteron 2002). Such techniques could thus also be applied to satellite images. The present study aimed to demonstrate that texture analysis of digitized aerial photographs by two-dimensional Fourier transform (Mugglestone & Renshaw 1998), as adapted by Couteron (2002), is a valuable approach to characterizing tropical rain forest canopies and obtaining reasonable predictions of tropical forests stand structure parameters.

Table 1.  Stand structure parameters measured for 12 1-ha ground-truth plots in the study area of the DIME project near the Petit-Saut reservoir dam, French Guiana. Dg, the diameter of the tree of mean basal area; R, standard deviation of Hm; CA1, plot scores along axis 1 of the correspondence analysis carried out on diameter distributions (see text)
PlotsDensity D (trees ha−1)Basal area G (m2 ha−1)Mean tree Dg diameter (cm)Mean canopy Hm tree height (m)Canopy R roughnessDiametric CA1 structure
145537·4532·330·48·28   0·236
245828·4128·127·57·45   0·020
348138·5731·926·07·37   0·134
474637·0825·226·86·36−0·098
580239·4425·026·35·02−0·107
654839·2630·228·16·48   0·156
798932·9620·621·15·28−0·284
846142·3834·229·98·44   0·337
946136·5531·827·59·25   0·184
1054737·1633·229·05·57   0·058
1147635·1430·629·56·66   0·168
1286133·0322·124·44·56−0·208

Materials and methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

study site

The study was conducted as part of the DIME ‘Diversité Multi-échelles (multiscale diversity)’ project, within an area of 65 km2 of undisturbed lowland evergreen rain forest, located at about 10 km east of the Petit-Saut reservoir dam in French Guiana (5°00′N, 52°55′W). A small river (Crique Plomb) running along a geological boundary divides the area into a hilly landscape (hilltops from 80 to 210 m a.s.l.) lying on sedimentary rocks (pelite) to the north, and the Montagne Plomb volcano-sedimentary massif that reaches its highest point at 332 m a.s.l. to the south (Delor et al. 2003). The varied geomorphology of the site results in contrasted textural aspects of the forest canopy, which are apparent on aerial photographs.

digitized aerial photographs

A set of black and white aerial photographs at 1 : 25000 scale (numbers 379–383, 397–401 and 456–460 of coverage 1992-GUF-91/250) were obtained from the Institut Géographique National (IGN, Saint-Mandé, France). Each image was digitized into 256 grey levels with a Nikon® Scantouch 210 flatbed scanner (Nikon Corp., Tokyo, Japan) using a resolution of 600 dots per inch (d.p.i.), corresponding to a pixel size of 1 m in the field. On images, the fully sunlit crowns of canopy trees appeared in white or light grey, while shadowed intercrown gaps were dark-grey or black. A monotonic relationship between grey-level scale and canopy height can thus be assumed as long as there is no substantial relief-induced shadowing. Contact numbers 399 and 401 were separately submitted for spectral analysis (see below) without any prior correction. In each photograph we only analysed the central part, i.e. a 4·8 × 4-km block (1920 ha) in which convex deformation as a result of the camera lens is of minor importance (Avery & Berlin 1992). For field navigation, a copy of the digitized images was assembled, georeferenced and superimposed on a digitized 1 : 50 000 topographical map (sheets Kourou S-O NB-22-VIII-1a and Haut Kourou NO NB-22-II-3c; IGN) using ArcGIS (ArcGIS™ Version 8.3; ESRI Inc., Redlands, CA).

spectral analysis by fourier transform

Only broad outlines of two-dimensional spectral analysis by Fourier transform are provided here, as detailed presentations (Ripley 1981) as well as applications to digital images (Mugglestone & Renshaw 1998; Couteron 2002) are already available. For simplicity, only square images were considered although the method also applies to rectangular images. A digital image is defined here as an n by n array of grey-scale values in the range 0–255 expressing the panchromatic radiance of each pixel. Spectral analysis aims at modelling such data as a weighted sum of cosine and sine waveforms of varying travelling direction and spatial frequency. For a particular geographical direction, the wavenumber, p, quantifies spatial frequency and corresponds to the number of times a waveform repeats itself within the image. The two-dimensional Fourier periodogram features the decomposition of the total image variance according to all possible integer pairs (p, q), of wavenumbers along the two Cartesian geographical directions (with 1 ≤ p≤ n/2 and 1 ≤ q ≤ n/2). When expressed in polar form (Mugglestone & Renshaw 1998), periodogram values, Irθ, are portions of image variance accounted for by a waveform having spatial frequency r and travelling direction θ, with inline image and θ = tan−1(p/q).

For each spatial frequency, summing values on all possible travelling directions yields an azimuthally cumulated ‘radial’ spectrum, I(r), that provides a convenient way to quantify coarseness-related textural properties by studying the decomposition of variance among spatial frequencies. Images with a coarse texture will yield a radial spectrum that is skewed towards small wavenumbers, whilst fine-textured images are expected to produce more balanced spectra (for a schematic illustration see fig. 3 in Couteron 2002). An image in which each pixel takes a random value independent of the value taken by any other pixel will have the finest possible texture and a virtually flat spectrum.

ordination of radial spectra

We carried out a systematic textural analysis that started by partitioning the canopy photographs into square windows of 1 ha, at which scale radial spectra were computed. A general table was built in which each row was the radial spectrum of a given window, while each column contained I(r) values, i.e. the portions of the grey-level variance explained by a given spatial frequency or wavenumber, r. This table of spectra was submitted to a principal component analysis (PCA; Manly 1994), which means that windows were considered as statistical observations characterized by their spectral profiles, i.e. the way in which the grey-level variance was broken down in relation to spatial frequencies. Conversely, spatial frequencies were seen as quantitative variables that were to be linearly combined to yield principal components. We used standardized PCA, so that principal components were defined from the eigenvector analysis of the correlation matrix between spatial frequencies. Note that our method of textural analysis, which fully relies on Fourier spectra, is totally distinct from the approach of Sommerfeld, Lundquist & Smith (2000), who only use the Fourier transform to filter an image before identifying trees by applying a binary threshold.

ground control data

Twelve 1-ha control plots were laid out to serve as ground-truth for the textural analysis. We used a Magellan SporTrak Color hand-held GPS unit (Magellan Systems Corp., San Dimas, CA) to locate the plots in the field, link them to the aerial photographs, and extract the corresponding digital images using GIS. Each plot was a 100 × 100-m square in which we measured diameter at breast height (d.b.h.), or above the buttresses if present, of all the trees greater than 10 cm d.b.h. We also sampled 49 canopy trees (i.e. trees with estimated Dawkin's (1958) crown index of 4 or 5) for total height measurement using a calibrated optical telemeter (Birnbaum 2001). These canopy trees were selected systematically and regardless of their size as the closest to the nodes of a 15 × 15-m grid covering the entire plot. We computed from these data five simple structural characteristics of the forest stands (Table 1): density (D), basal area (G), diameter of the tree of mean basal area (Dg), mean canopy height (Hm) and the standard deviation of mean canopy height as an index of canopy roughness (R). All measured trees were also classified into eight d.b.h. classes of 10 cm width, plus an additional class in which all the trees 90 cm d.b.h. were pooled. The table crossing plots with d.b.h. classes was submitted to correspondence analysis (CA; Manly 1994) to summarize diameter distributions. The first CA axis that was prominent (73% of the variance of the table) ranked d.b.h. classes in their natural order and expressed a gradient from the smallest class (10–20 cm) to the largest (≥ 50 cm). Plot scores on this axis were then used as a latent variable summarizing the diameter distributions (CA1 in Table 1). Subsequent CA axes proved difficult to interpret and were not considered further.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

textural analysis

A preliminary PCA analysis dealing with all the 3840 windows of 1 ha highlighted that a limited number of windows (about 7·5% of the total) was strongly differentiated from the remainder. These windows, which displayed large features (at the scale of 1 ha) such as forest roads or stream valleys and so could not be adequately assessed for forest canopy, were excluded from subsequent analyses. A second PCA was run on the 3545 remaining windows, yielding a first factorial plane (Fig. 1, top) that reflected a progressive transition from spectra dominated by the first wavenumber (r = 1, positive part of PCA axis 2) to spectra characterized by the relative importance of small (r = 2–3, negative part of axis 1), intermediate (r = 4–8, negative part of axis 2) and large wavenumbers (r > 8, positive part of axis 1). Accordingly, we found windows displaying coarse-grained canopy aspects (Fig. 1b) on the negative extremity of axis 1, while fine-grained canopy textures were found on the positive extremity (Fig. 1f). Windows of intermediate texture were located all around the axes origin, although the best illustrations of these textural types (Fig. 1c,d) were found around the negative extremity of axis 2. The textural properties of the canopy frequently resulted from size and spatial distributions of gaps and aggregates of crowns rather than from size distribution of individual crowns. This was particularly the case for the coarser textural types (Fig. 1b).

image

Figure 1. Results of the multidimensional comparison of spectral profiles for 3545 forest canopy windows of 1 ha in the study area of the DIME project near the Petit-Saut reservoir dam, French Guiana. The five textural classes (T1–T5) identified by k-means clustering (see text) are plotted against the two main axes yielded by the PCA of the spectra table. The envelopes of classes delineate twice the standard deviation of PCA scores of the constituting windows. Windows (a) to (g) have been automatically selected as the most illustrative (largest distance from axes origin) with regards to successive angular directions in the PCA plane and, thus, to the relative importance of the corresponding ranges of wavenumbers. Top-left inset, distribution of relative eigenvalues. Top-right inset, correlations of wavenumbers (some of the wavenumbers above 10 are omitted for legibility) with PCA axes 1 and 2; each radial direction in the PCA plane corresponds to the relative importance in the spectrum of particular ranges of wavenumbers.

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All windows having high positive scores along axis 2 displayed heterogeneity mostly as a result of the influence of relief on sun illumination; for example, on Fig. 1a–g about one half of the window appeared sunlit and the other half in shadow. Most of those windows encompassed a prominent relief feature such as a ridge or a pronounced valley. Some of those windows displayed either a coarse-grained or a complex canopy texture (e.g. Fig. 1a) while others had a fine-grained canopy (Fig. 1g). In this latter case, the spectrum was characterized by the simultaneous dominance of first and large wavenumbers.

relationships between canopy texture and stand structure

We used coordinates of the plots on the textural ordination axis 1 as an index of canopy texture (PCA1), while explanatory power regarding stand structure parameters of Table 1 was tested using ordinary linear regressions (Fig. 2). It is noteworthy that while PCA1 was a good predictor of the mean stem density (R2 = 0·80, P < 0·0001), the regression against mean basal area displayed almost no slope. This was because of the limited variability of basal area across the reference plots. Good predictions were also obtained for stand structure parameters such as the diameter of the tree of mean basal area (R2 = 0·71, P < 0·001) and plot coordinates along axis 1 of the correspondence analysis summarizing the size (d.b.h.) distribution of trees (R2 = 0·64, P < 0·01). The relationship with mean canopy height was weaker but statistically significant (R2 = 0·57, P < 0·01), as with standard deviation of canopy heights (R2 = 0·55, P < 0·01), a proxy for stand canopy roughness.

image

Figure 2. Stand structure parameters (see Table 1) as a function of scores of the ground-truth plots along PCA axis 1 used as an index of canopy texture (see Fig. 1). Study site of the DIME project near the Petit-Saut reservoir dam, French Guiana.

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predictive maps of stand structure parameters

To complement the textural analysis, we submitted the table of the radial spectra to k-means clustering (Manly 1994) using the Euclidean distance after prior standardization by column standard deviations in order to remain consistent with results of standardized PCA. In this example, clustering using five classes yielded the most meaningful results. Textural classes T2 (coarse-grained canopy) to T5 (fine-grained) were ordinated along PCA axis 1 of the textural analysis (Fig. 1). Class T1 differentiated from other coarse-grained classes along PCA axis 2, on the basis of image macro-heterogeneity as a result of relief-induced illumination discrepancy. Class T5 encompassed all fine-grained canopy windows whatever the level of illumination heterogeneity.

Although allocating canopy windows to an arbitrary number of classes provides less objective information than ordination scores, it is very convenient for mapping. For instance, Fig. 3 presents a map of the canopy texture based on the five classes for contact number 399 while Table 2 shows predictions of the most significant mean stand structure parameters of these classes, as inferred from the above regressions (Sokal & Rohlf 1995). Figure 3 reveals a clear spatial partition between: (i) coarse- to intermediate-grained canopies (T2–3; red and green squares), which were observed on volcano sedimentary materials on the slopes of Montagne Plomb in the southern part of the study site, corresponding to tall stands (Ĥm c. 29–30 m) with a low density (D̂c. 400–500 trees ha−1) of large trees (D̂g c. 32–34 cm d.b.h.); and (ii) intermediate- to fine-grained canopies (T4–5; yellow and light-blue squares) on pelitic formations in the northern hilly part of the site, corresponding to low stands (Ĥm c. 26–28 m) with a high density (D̂c. 600–700 trees ha−1) of small trees (D̂g c. 26–29 cm d.b.h.). In this northern part, fine-grained windows were intermixed with coarse-grained windows (T1; dark-blue squares) containing sharp relief features such as ridges and deep valleys (Fig. 1a–g). These features, while fairly well detected by the textural analysis (Fig. 3), were infrequent on the smooth slopes of Montagne Plomb but frequent in the hilly northern part. Furthermore, it was on steep slopes in this northern part, where unfavourable substratum conditions (virtually no soil on the alterite) determine dense stands of small trees, that frequent occurrence of the finest-grained windows (Fig. 1g) was observed.

image

Figure 3. (a) Central part of contact image number 399 (coverage 1992-GUF-91/250; IGN, France) in the study area of the DIME project, near the Petit-Saut reservoir dam, French Guiana. (b) The same area with coloured squares corresponding to 1-ha forest canopy windows coded in five classes of canopy texture (see Fig. 1, Table 2 and text): dark-blue, T1 (coarse-grained texture for windows marked by relief-induced illumination discrepancy); red, T2 (coarse-grained canopy texture); green, T3 (coarse- to intermediate-grained canopy texture); yellow, T4 (intermediate- to fine-grained canopy texture); light-blue, T5 (fine-grained canopy texture).

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Table 2.  Predictions of mean stand structure parameters (with standard error) for the five classes of canopy texture (see Fig. 2 and text). Study site of the DIME project, near the Petit-Saut reservoir dam, French Guiana
Textural classesPredicted density D̂ (trees ha−1)Predicted mean tree diameter D̂g (cm)Predicted mean canopy tree height, Ĥm (m)
T1453·2 (35·2)32·2 (1·0)29·0 (0·7)
T2382·0 (43·7)33·8 (1·3)29·8 (0·9)
T3482·2 (32·3)31·6 (0·9)28·7 (0·7)
T4583·2 (25·9)29·3 (0·7)27·5 (0·5)
T5738·2 (32·9)25·8 (0·9)25·7 (0·7)

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Two-dimensional Fourier analysis is a powerful method for obtaining both quantitative characterization of canopy texture and reasonable estimations of stand structure parameters from VHR optical images. This conclusion, drawn from the use of digitized aerial photographs, is likely to hold regarding submetric pixel satellite images, which are easier to use with respect to georeferencing and assembling into large maps. But the availability of such images at affordable cost is still problematic if the aim is to document large areas of tropical rain forest. In addition, frequent cloud coverage limits the acquisition of satellite scenes of good quality. Visual interpretation is not only time consuming but also of limited spatiotemporal consistency, and this is probably why it has not been widely applied in the tropics even though extensive air coverage has been available for as long as in the temperate zone. Indeed, only an automatic or a semi-automatic approach can deal with the subtle and spatially intricate variations that characterize tropical evergreen forest stands. Most examples of visual interpretation quoted by Polidori et al. (2004) dealt with contrasted and spatially segregated forest types, for example deciduous vs. evergreen.

Automatic recognition and delineation of individual tree crowns has been attempted in homogeneous, even-aged tree stands from VHR optical data at the price of complex algorithms and heavy computation (Gougeon 1995; Pouliot et al. 2002). Automatic delineation is also under investigation for heterogeneous natural stands (Hurtt et al. 2003). There are, however, good reasons why automatic delineation of individual crowns should be perceived as a difficult task in tropical stands, because of the frequent crown merging between adjacent trees. Asner et al. (2002), who performed a thorough manual delineation of tree crowns, acknowledged situations for which deciding between single crowns vs. merged crowns is virtually impossible and reported a serious positive bias on crown size estimation from VHR satellite imagery. Hence, broad-scale applicability of individual tree approaches to tropical stand characterization cannot be considered in the near future. On the other hand, our more holistic approach, which considers canopy texture as a whole, presents good prospects of immediate large-scale applicability. From this point of view, it represents a promising alternative to direct measurement of physical attributes of the vegetation, such as canopy tree height estimates from LIDAR (light detection and ranging), which require complex algorithms to separate ground returns from overlying vegetation returns, a process remaining subject to increased random errors in dense, multilayered evergreen forests (Clark, Clark & Roberts 2004).

However, as for every regression-based parameter retrieval technique, there is a need for both calibration and validation, because values of the canopy texture index are relative to a particular set of images and also because the ecological relationship between canopy texture and stand parameters has remained up to now poorly investigated. The need to measure additional field plots to recalibrate regression coefficients, for each new study area and each new set of images, may, at first sight, appear a serious hindrance to a wide-scale implementation of the method. However, it is not unrealistic to think that large data sets featuring both tree diameter data and digitized canopy images for many 1-ha plots could be efficiently set up by forest departments as part of their routine field operations of forest monitoring and inventory. From such databases, textural indices and regression coefficients with broad regional validity could be easily derived to yield automatic estimates of forest stand structure parameters over vast areas of tropical forests. This would be particularly useful to guide preparation of field prospects for consistent resource inventory, forest classification and management planning.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

This research has been carried out in the framework of the DIME project supported by the French Ministère de l’écologie et du développement durable (MEDD) through grant CV02000074. We thank C. François, J.-F. Molino, M.-F. Prévost, D. Sabatier and J.-L. Smock along with the students of the ENGREF ‘FTH-2002’ training stay for their contribution to the collection of field data, and F. Lokonadinpoullé for assistance with GIS. We also thank Ch. Proisy, D. Lo Seen, D.B. Clark and one anonymous referee for comments on an earlier draft of the paper.

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  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
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