Mapping Continuous Distributions of Land Cover: A Comparison of Maximum-Likelihood Estimation and Artificial Neural Networks

Both maximum-likelihood and neural network classifiers can be used to characterize land cover as continuous fields that represent either class proportions or classification certainty. We compared these two approaches by examining the correspondence between their output values and photointerpreted class proportions of 39 test regions within a heterogeneous study area in southern California. The neural network models consistently produced stronger correlations (1) between output values for a given class and the proportions of that class for all test regions combined and (2) between output values and proportions for all classes and test regions combined. However, due to the discrete nature of the response surface relative to the maximum-likelihood classifier, maps produced using the neural networks did not represent significant variability in the certainty of class labeling. Conversely, the maximum-likelihood classifier produced membership likelihood surfaces that varied considerably across the study areas. Differences between the response functions of the two methods relate to the parametric versus nonparametric nature of the maximumlikelihood and neural network models, respectively Wsualization of the results from continuous classifiers can be accomplished in several ways which help illustrate the nature and spatial distribution of classification certainty. Introduction Remote sensing classification typically involves the use of spectral samples at a fixed spatial resolution to discriminate a fixed set of classes whose spectral and spatial characteristics are variable. If the spatial resolution is small relative to the objects of interest, then classification error will occur primarily along the boundaries of objects, presuming that objects are homogeneous and spectral discrimination is adequate (Strahler et al., 1986). In this case, a "hard" classifier that assigns one class label to each pixel may be appropriate. However, if the spatial resolution is large relative to the scene objects, then individual pixels will contain multiple objects, and error will occur due to spatial mixing if each pixel is labeled with a single class (Cracknell, 1998). The spatial mixing within pixels reflects a mismatch between the scale of the phenomenon of interest, and the resolution of the data used to measure it. This case is common, however, due to choice limitations in sensor characteristics, difficulty identifying the proper resolution for a given application, and a tendency to push the limits of remote sensing technology. There are three basic methods to reduce the impact of spatial mixing on land-cover classification results. Mixture models can provide estimates of subpixel composition, assuming Department of Geography, University of North Carolina, 203 Saunders Hall, Chapel Hill, NC 27599-3220 (aaronm@ PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING that linear or other mixing assumptions are valid, that classes are spectrally separable, and that pure class spectra can be estimated (Adams et al., 1986; Roberts et al., 1993; Oleson et al., 1995). Alternatively, calibrated post-classification models can improve area estimates from remote sensing, assuming that the relationship between true and estimated proportions can be modeled (Mayaux and Lambin, 1995; Kalkhan et al., 1995; Moody, 1998). Athird approach is to map continuous gradients of membership certainty for each class, rather than using a binary class representation (DeFries et al., 1995). We present an empirical comparison of a modified maximum-likelihood classifier (MLC) and a feedforward backpropagation artificial neural network (ANN) for producing continuous land-cover surfaces using Landsat Thematic Mapper (TM) data. These methods are first applied to a small (55km2) agricultural site in the San Joaquin Valley, California (Plate 1). This site permits an evaluation of the two methods for an area where class transitions are spatially abrupt, and scene objects are large relative to the pixel size, spectrally separable, and spectrally homogeneous. The methods are then applied to the main study site, a 700-km2 area near Santa Barbara, California (Plate 1). The main site contains varying degrees of landcover heterogeneity and is composed of land-cover types that are generally representative of vegetation in the region at large. Background In remote sensing classification, homogeneity in land cover relative to the spatial resolution of the data is often assumed (Foody and Arora, 1996). However, vegetation distributions often exhibit gradual changes in community composition across the landscape (Brown and Lomolino, 1998). Given the absence of discrete boundaries, vegetation units are often spatially indefinite (Poulter, 1996; Usery, 1996). In addition, heterogeneous mosaics of land cover can produce a mixture of cover types within image pixels (Fisher, 1996). Even if a landscape does happen to consist of large, homogeneous units of land cover with discrete boundaries between classes, mixing still occurs where pixels overlap class boundaries (Foody, 1997). Despite these known effects, analysts commonly use "hard" classification methods, producing a discrete map in which each pixel belongs to only one class. As with conventional ("hard") classifiers, continuous ("soft") classifiers operate by comparing the spectral signature of each pixel to the distribution of the training data for each Photogrammetric Engineering & Remote Sensing Vol. 67, No. 6, June 2001, pp. 693-705. 0099-1112/01/6706-693$3.00/0 O 2001 American Society for Photogrammetry and Remote Sensing class. However, while conventional classifiers employ a discriminant function for assigning a single class label to each pixel, continuous classifiers do not assume subpixel homogeneity, and membership values (MVS) for each class are retained on a per-pixel basis. Information is thus available regarding the certainty with which each pixel is assigned to each possible class (Wang, 1990). Given this information, a data user can visualize the spatial distribution of classification certainty, apply need-specific rules for the creation of hard classifications, sample land-cover data within specific certainty ranges, map zones of class transition, or characterize the landscape in terms of cover-type dominance and co-dominance. In addition to the above advantages, continuous classifiers can provide improved parameter estimates for ecosystem, climate, and biogeochemical cycle models by capturing functionally important variation within and between vegetation types (DeFries et al., 1995; Coughlan and Dungan, 1997). Continuous classifiers can also support improved area estimation for monitoring land cover and land-cover change (Palubinskas et al., 1995; Moody et al., 1996; Mayaux and Lambin, 1997), and provide a means for remote analysis of ecotones, which sometimes host unique ecological communities, and can be particularly sensitive to disturbance and climate change (Forman and Godron, 1986). The maximum-likelihood classifier (MLC) is a parametric method that assumes a normal distribution of data within each class (Strahler, 1980). The membership values produced by the MLC represent probabilities of class membership. Typically, the class for which a pixel has the highest probability of membership is used to label the pixel, and the probability values for the remaining classes are discarded. The elimination of these values may constitute a loss of information regarding the composition of the pixel (Strahler, 1980; Wang, 1990). The MLC classifier can be modified to retain class membership values for each class. For example, Foody et al. (1992) used this approach to extract information on subpixel proportions. Artificial neural networks (ANN) are nonparametric models that are increasingly used for classifying remotely sensed data (Hepner et al., 1990; Benediktsson et al., 1990; Kanellopoulos et al., 1992; Key, 1994; Leung, 1997; Paoloa and Schowengerdt, 1997). The most common type of ANN applied in this context is a supervised model called a feedforward backpropagation neural network (Atkinson and Tatnall, 1997), which belongs to a class of ANNS called multilayer perceptrons (Rumelhart et al., 1986). This type of network is composed of layers of "neurons" that are interconnected through weighted synapses. All nodes in a given layer are connected to each node in the subsequent layer of the network. Each internode connection has an associated weight that can be excitatory or inhibitory. The first layer contains a single node for each input variable. The last layer contains a node for each of the possible output classes. Intermediate "hidden" layers provide an internal structure of pathways through which input data are processed to arrive at output values. The output signals are linear combinations of input signals and the weights. In the learning phase, input patterns from training data are fed forward through a network initiated with random synapse weights. The root-mean-square error (RMSE) is calculated between the network outputs and the desired outputs. The errors are backpropagated through the network and the synapse weights are adjusted in order to reduce the total RMSE. This process continues until a convergence criterion is satisfied (Rumelhart et al., 1986) Once the network is trained, it can be used to classify new input data. Upon presentation of an input pattern, the trained network will produce an output signal for each class. Typically, the class that receives the largest output signal is used to label the pixel. However, as with the MLC, discarding the output signals for the remaining classes constitutes a loss of information regarding their potential membership (Civco, 1993). By evaluating the full vector of network output values, information is retained regarding each pixel's potential membership in each possible class. Similar approaches have been demonstrated in a range of contexts by Civco (1993), Moody et al. (1996), Foody (1997), Atkinson et al. (1997), and Warner and Shank (1997). Study Area The main study area is located 50 krn north-northeast of Santa Barbara, California (Plate 1). The southern portion of the site lies in the Los Padres National Forest and the northern portion contains the Bitter Creek National Wildlife Refuge and part of the Caliente Mountain Range. The northern third of the study TABLE 1. LANDCOVER CLASSES FOR THE MAIN STUDY AREA (SITE 1) Class Description Common Species