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Modern sidescan sonars provide the ability to image the seafloor with increasingly high resolution. With this comes a corresponding increase in complexity of determining the performance of the sensor, with focus shifting from simple signal detection theory to assess the capability for automatic target recognition (ATR) algorithms to discriminate between different objects based on the shape of the projected acoustic shadows on the seafloor. This paper uses information theory to place bounds on the performance of ATR algorithms which use features based on an object's shadow as a classification cue. Information is used to compute different bounds on the performance of any classification method. The technique is applied to a simple classification task namely to discriminate between circular and square shapes. The effect of sensor characteristics, such as contrast and resolution, are computed. An example is given where the bounds on performance for a sidescan sonar with given characteristics under some environmental conditions are computed. The performance is then analysed as a function of the shapes being classified by changing the circular shape to a superellipse. Although high-frequency imaging sonar is examined here, the method could be applied to other types of monochromatic imagery that contains multiplicative noise.