Needless to say, large, high-contrast targets are more easily recognized than small, low-contrast targets. But at what size and contrast does recognition begin? The question is important when specifying the resolution and contrast requirements for a new imaging system, or when assessing the range of an existing system beyond which worsening resolution and contrast ruin serviceable performance. The question is addressed here, in a general way, under the assumption that recognition depends on the agent's ability to draw a line (extract an edge) around distinctive target features. If the target is small, moreover, with its recognizable facets occupying few pixels, and if line rendering suffers mainly due to noise or image speckle, then neither human or complex automatic target recognition systems have a clear advantage, one above the other, or above more tractable, statistically optimized pattern recognition algorithms. Thus a theory of optimal linear edge detection is proposed here as a plausible model for estimating the recognition limits of both human and automatic agents, making it possible to estimate when the line-rendering process, and hence, recognition, fails due to insufficient contrast for small targets. The method is used to estimate the shadow-background contrasts needed for the recognition of sea mines in sidescan sonar images.