Advantages of principal components analysis for land cover segmentation from SAR image series

Abstract

Two interrelated difficulties could hinder the widespread use of SAR imagery in land cover mapping and monitoring: speckle and georeferencing. Speckle poses problems for both scene segmentation and georeferencing: high-frequency, spatially random multiplicative noise hinders clustering algorithms and obscures landmarks. Most despeckling techniques trade spatial information for noise reduction. Using multiple image dates, noise can be reduced with little loss of spatial resolution. Furthermore, image time series enable assessment of land cover variation, whether due to seasonality or disturbance. Principal components analysis (PCA) on SAR image series can identify a landscape's dominant spatio-temporal modes of backscattering. The first principal component yields a very low noise image that contains information about temporally invariant terrain features (roads, rivers, slope/aspect), which can aid georeferencing. I illustrate the approach using a SAR image series for 12 sub-orbital repeats acquired during the 1995 growing season. PCA was performed on a scene containing Konza Prairie Research Natural Area, a scientific preserve for tallgrass ecology, and surrounding lands. The first four principal components held significant spatial information, while higher order components were dominated by speckle. A surprising result was the ability of PCA to pick out isolated riparian woodlands amidst a hilly prairie landscape. A kind of poor man's interferometry, this feature arises out of the differential backscattering caused by a 4 degree nominal shift in incidence angle between sub-orbital repeats.

Keywords: PCA; spatio-temporal analysis; speckle reduction; tallgrass prairie; Konza Prairie

Introduction

Principal components analysis (PCA) is an important tool for analysis of image time series. However, most applications have been to optical imagery (e.g., Townshend et al., 1985; Eklundh and Singh, 1993; Benedetti et al., 1994). The rare employment of PCA for SAR image studies likely arises for two reasons: (1) a general lack of availability of SAR image series until the past few years and (2) the presence of a well-defined scene model for most SAR applications. This last point merits some discussion.

A scene model can be broadly construed as some prior understanding of the spatio-temporal arrangement of stuff that interacts with the illuminating radiation (Strahler et al., 1986). What constitutes this "stuff" are the objects of interest in the imaged scene, e.g., agricultural fields, ice fields, geological lineaments. Given how few orbital SAR sensors had flown until 1990s and the technical requirements needed to understand and manipulate the data effectively, it is not surprising that the application domains for SAR data have been restricted until recently to disciplines where the scene objects were well-defined in advance of data acquisition. Land cover monitoring requires a rather loosely-defined prior scene model due to the typically heterogeneous mix of dynamic surfaces and textures. As a result, land cover segmentation and mapping involves aspects of data mining and statistical pattern recognition.

PCA of SAR image series has several advantages, most of which have been well demonstrated for optical data. PCA of a high temporal resolution image series can attenuate temporal autocorrelation, thereby increasing the suitability of the data for image segmentation and classification procedures (Benedetti et al., 1994). Furthermore, the principal components (PCs) are of intrinsic interest because they effectively summarize the dominant spatio-temporal modes of radiometric variation in the data in terms of linear combinations of image frames. The PC loadings, i.e., weights assigned to each image date, provide important information about what sort of thing each PC is summarizing, which points to its potential utility for land cover discrimination.

PCA has another potentially important use in the analysis of SAR image series: it could attenuate two interrelated difficulties that hinder the widespread use of SAR imagery in land cover mapping and monitoring -- speckle noise and georeferencing. Speckle noise poses problems for both scene segmentation and georeferencing: high-frequency, spatially random multiplicative noise hinders clustering algorithms and obscures landmarks. Most despeckling techniques trade spatial information for noise reduction. Using multiple image dates, noise can be reduced with PCA resulting in minimal loss of spatial resolution. Furthermore, image time series enable assessment of land cover variation, whether due to seasonality or disturbance.

Methods

A series of 11 ERS-1 SAR images (uncalibrated data in MLD format from CCRS) were acquired during the 1995 growing season (Table 1). I selected image subscenes to include Konza Prairie Research Natural Area, the City of Manhattan Airport, Kansas River floodplain, Interstate Highway 70, and neighboring grazing and agricultural lands. Using the Khoros warpimage program, scenes were coregistered to the 19MAY scene using between 50 and 80 tiepoints; the resulting areal extent used in the analysis was about 233 km2. I chose not to calibrate the data because terrain variation was very significant and no fine-resolution DEM exists for the entire study area, so calculation of local incidence angle was not feasible. (We are working to remedy this deficiency using SAR interferometry.) A datacube of 11 time-ordered scenes was then submitted to the PCA program in ERDAS Imagine; principal component images, eigenvalues, and eigenvectors (loadings) were received as the output.

Figure 1: Variance explained by principal components.

Figure 2: Loadings for first four principal components from PCA-11.

Results

The first PC (Figure 1). Radiometrically bright features are predominantly slopes with easterly aspects and some agricultural fields; dark features include airport runways, the Kansas River, highways I-70 and K-18, and terrain in radar shadows. Since these are persistent features in the scene, the loadings were nearly uniform across dates (Figure 2); PC1 summarized the stable scene elements.

Figure 3: First principal component from PCA-12.

The second PC (Figure 4) captured the distinction between burned and unburned prairie as well as some discrimination among agricultural fields. Burned areas are also typically grazed. Explaining about 9.5% of series variance (Figure 1), the loadings exhibited a definite seasonality (Figure 2).

Figure 4: Second principal component from PCA-12.

The third PC (Figure 5) revealed a surprising aspect of the image series: it captured look angle differences and thereby explained 8.3% of variance (Figure 1). The over-lapping orbital paths, 69 and 341, yielded different look angles, about 24.4^o and 20.2^o respectively, for this landscape. This difference translated into an enhanced sensitivity to local height variations. Riparian wooded areas were clearly distinguishable, even in complex upland drainages. Differences in river bank exposures are also captured. In addition to picking out ribbons of trees amid the grasslands, the look angle difference generated registration artifacts from hills with the brighter eastern aspect slopes. The alternating loadings confirm the association of PC3 with orbital path (Figure 2).

Figure 5: Third principal component from PCA-12.

The fourth PC (Figure 6), explaining 7.2% of datacube variance (Figure 1), captured the seasonality of agricultural production in the larger riparian landscapes. However, PC4 also exhibited a sensitivity, albeit weaker, to orbital path (Figure 2), which was manifested as additional registration artifacts adjacent to the artifacts in PC3.

Figure 6: Fourth principal component from PCA-12.

Higher order PCs exhibited little spatial localization and thus are attributable either to smaller patches of weaker radiometric change or to speckle noise (Figure 7). The total variance explained by the remaining 7 PCs is about 29%. Note the significant drop in explanatory power between PC4 and PC5 (Figure 1). Speckle noise is characterized by high spatial frequency and is usually treated as spatially random. The relatively slow decay of variance in the higher order PCs results from each PC skewering a high-dimensional cloud of effectively random points: every PC "skewer" explains some variance, just not very much. I have observed in optical image series this phenomenon of high-order PCs being dominated by noise elements and leading to slow variance decay (Henebry and Rieck, 1996).

Figure 7: Eleventh principal component from PCA-12.

The major consequence of the PCA pushing speckle into the higher order components is a greatly improved signal-to-noise ratio for the first PC. This low noise image has no significant of spatial resolution (although there is some negligible loss during coregistration). PCA speckle reduction is accomplished by sacrificing temporal resolution to maintain spatial resolution. PCA enables a time-for-space substitution to achieve a lower noise image that is well-suited for georeferencing. Crucial spatial detail needed for precisely locating ground control points is frequently obscured by speckle but can be recovered through PCA. In addition, the PC1 image provides a high resolution scene for multi-sensor fusion. All the low-order PCs provide important spatio-temporal information that can be exploited by segmentation and classification algorithms.

PCA uses a statistical decision rule to arrive at the components and these components are simply linear combinations of the variables -- here scenes from different dates. How robust are the PCs? Does their explanatory power extend beyond the particular dataset used to derive them? Clearly, particular sets of PCs will have limited extrapolatory power at best for different landscapes; but how well has a particular set captured the dominant spatio-temporal modes of backscattering in that landscape? One approach to this question is to increase or decrease the number of scenes submitted to the PCA and observe the changes in loading patterns and PC image structure. I guessed that adding a scene to the end or beginning of the growing season should have a marginal overall effect on the loadings but could give some indication of the robustness of particular PCs. Of particular interest are the first few PCs, since they are readily useful. To test for their robustness I added a twelfth image from late October to the datacube and reran the PCA.

To compare the results of the first PCA (PCA-11) with the second (PCA-12), I regressed the loadings for each corresponding principal component (Figure 8). The first three PCs were highly positively correlated; the fourth PC was highly negatively correlated; and the correlation of higher order components ranged from moderate to very low (Figure 9). The images produced by first four PCs of PCA-12 were virtually indistinguishable from those produced by PCA-11, except for the negative switch in PC4.

Figure 8: Comparison of principal components derived from PCA-11 and PCA-12.

Figure 9: Results of regression of PCA-11 and PCA-12.

Conclusions

Principal components analysis appears to have one fundamental use in land cover analysis of SAR image series: speckle reduction. From this perspective some significant advantages accrue: (1) identification of dominant spatio-temporal modes of backscattering within the scene; (2) partitioning of this variance into a set of discrete images that can be submitted to segmentation and classification algorithms; and (3) production of a high spatial resolution, low spatial noise image that can serve as a template for georeferencing and multi-sensor fusion.

There are limitations of PCA that relate to sampling rate relative to scene dynamics. In scenes with high intrinsic temporal variability, sampling frequency must at least meet the Nyquist criterion, but PCA works better when there is a high degree of temporal autocorrelation (Henebry and Rieck, 1996). In the absence of temporal oversampling in dynamic landscapes, PCA still segregates speckle to higher order components and lower order PCs tend more towards lower noise images of individual dates. (I have observed this in a seven date image series from the Brazilian Pantanal; see Henebry and Kux, this volume.) As SAR image series become more readily available over the next decade and as interest in land cover monitoring increases, there is a need for new approaches to spatio-temporal analysis. While not a new technique to remote sensing, PCA offers distinct advantages for SAR data analysis that should be further explored.

Acknowledgement

I gratefully acknowledge support from ESA through project AO2.USA126 and from NSF through grant DEB-9696229. Thanks to Shawn Hutchinson for assistance with image coregistration.

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Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry