Line drawings can effectively convey the 3D shape of objects despite the absence of most conventional depth cues. The 3D percept can be especially clear when drawings include internal contours and T-junctions as well as outer bounding contours. Early work that focused on cataloguing and analyzing various junction types (Huffman, 1971; Clowes, 1971; Waltz, 1972; Mackworth, 1973; Charkravarty, 1979; Malik, 1987) was limited by a dependence on deterministic junction interpretation rules. We revisit the study of T-junctions and related contour cues to depth, but now in a probabilistic framework. We hypothesized that the interpretation of surface shape in line drawings including T-junctions involves a process of probabilistic estimation of depth, based on both local and non-local cues. This formulation incorporates default (traditional) depth interpretations of junctions into a likelihood function, and can thus accommodate non-default (non-traditional) interpretations with other constraints when they are required to maximize the posterior. Moreover, the probabilistic framework allows us to quantitatively model the contribution of local and non-local depth cues, including the "propagation" of the influence of a T-junction at points various distances from it. We measured depth order for pairs of points (Koenderink et al., 1996; Koenderink et al., 2011) inside line drawings constructed so as to modulate the presence and location of critical depth cues. Observers reported the depth order of the dots, with the responses indicating the apparent 3D surface structure of the inferred shape. We found systematic effects of the location of dots with respect to the T-junctions, with systematic changes in the way depth order was interpreted as a result of the local and global structure of the contours. The findings shed light on how the local depth information drawn from T-junctions propagates and interacts with cues derived from other contours to yield a percept of the 3D surface.
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