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Distributed signal processing techniques for classification of objects are studied assuming knowledge of sensor measurement statistics. The spatio-temporal signal field generated by an object is modeled as a bandlimited stationary ergodic Gaussian field. The model suggests a simple abstraction of correlation between node measurements: it partitions the network into disjoint spatial coherence regions over which the signal remains strongly correlated, whereas the signal in distinct coherence regions is approximately uncorrelated. The size of coherence regions is determined by spatial signal bandwidths. It is shown that this partitioning imposes a structure on optimal distributed classification algorithms that is naturally suited to the communication constraints of the network: local high-bandwidth exchange of feature vectors within each coherence region to improve the measurement signal-to-noise ratio (SNR), and global low-bandwidth exchange of local decisions across coherence regions to stabilize the inherent variability in the signal. Classifier performance is analyzed for both soft and hard decision fusion across coherence regions assuming noise-free, as well as noisy communication links between nodes. Under mild conditions, the probability of error of all classification schemes (soft, hard, noisy) decays exponentially to zero with the number of independent node measurements-the error exponent depends on both the measurement and communication SNRs and decreases from soft to hard to noisy fusion. Numerical results based on real data illustrate the remarkable advantage of multiple sensor measurements in distributed decision making.