This paper introduces a new method for acquiring and interpreting data on cognitive (or perceptual) networks. The proposed method involves the collection of multiple reports on randomly chosen pairs of individuals, and statistical means for aggregating these reports into data of conventional sociometric form. We refer to the method as "perceptual tomography" to emphasize that it aggregates multiple 3rd-party data on the perceived presence or absence of individual properties and pairwise relationships. Key features of the method include its low respondent burden, flexible interpretation, as well as its ability to find "robust intransitive" ties in the form of perceived non-edges. This latter feature, in turn, allows for the application of conventional balance clustering routines to perceptual tomography data. In what follows, we will describe both the method and an example of the implementation of the method from a recent community study among Alaska Natives. Interview data from 170 community residents is used to ascribe 4446 perceived relationships (2146 perceived edges, 2300 perceived non-edges) among 393 community members, and to assert the perceived presence (or absence) of 16 community-oriented helping behaviors to each individual in the community. Using balance theory-based partitioning of the perceptual network, we show that people in the community perceive distinct helping roles as structural associations among community members. The fact that role classes can be detected in network renderings of "tomographic" perceptual information lends support to the suggestion that this method is capable of producing meaningful new kinds of data about perceptual networks.