According to recognition-by-components theory, object recognition relies on a specific subset of three-dimensional shapes called geons. In particular, these configurations are a powerful cue to a three dimensional object reconstruction because their two dimensional projection remains viewpoint-invariant. While a large body of literature has demonstrated sensitivity to changes in these so-called non-accidental configurations, it remains unclear what information is used in establishing such sensitivity. In this study, we explored a possibility that non-accidental configurations can already be inferred from the basic constituents of objects, namely, their edges. We constructed a set of stimuli composed of two lines corresponding to various non-accidental properties and configuration of geons, including collinearity, alignment, curvature of contours, curvature of configuration axis, expansion, cotermination, and junction type. Using a simple visual search paradigm, we demonstrated that participants were faster at detecting targets that differed from distractors in a non-accidental configuration than in a metric one. Given that such sensitivity emerged from a configuration of only two lines, our results open a possibility that non-accidental configurations could be encoded at the earliest stages of the visual information processing.