Assume that we are trying to build a visual recognizer for a particular class of objects - chairs, for example - using existing induction methods. Assume the assistance of a human teacher who can label an image of an object as a positive or a negative example. As positive examples, we can obviously use images of real chairs. It is not clear, however, what types of objects we should use as negative examples. This is an example of a common problem where the concept we are trying to learn represents a small fraction of a large universe of instances. In this work we suggest learning with the help of near misses - negative examples that differ from the learned concept in only a small number of significant points, and we propose a framework for automatic generation of such examples. We show that generating near misses in the feature space is problematic in some domains, and propose a methodology for generating examples directly in the instance space using modification operators - functions over the instance space that produce new instances by slightly modifying existing ones. The generated instances are evaluated by mapping them into the feature space and measuring their utility using known active learning techniques. We apply the proposed framework to the task of learning visual concepts from range images.