PLUMB model unifies perception of vertical and eye level in one formula

A new paper from A. Y. Shavit at Hunter College (CUNY) presents PLUMB—a compact, image-computable model that reduces decades of experimental findings on visual vertical perception to a single orientation order parameter. The model treats orientation as a director (θ ≡ θ+π), forcing a doubled-angle domain for circular-mean readout. In that domain, the perceived vertical is simply half the argument of the first circular moment. This automatically reproduces the three Li-Matin regularities (linear tracking with roll-tilted peripheral lines, linear combination of two lines, and cancellation of symmetric tilts) without any per-configuration free parameters.

The model also explains why lines tilted at 45° produce no bias (null), and how combining lines across hemifields yields sub-additive effects—exactly as Shavit, Li, and Matin reported in 2013 from 30-observer trials. The same order parameter, read as a sum and a difference across the two hemifields, simultaneously predicts perceived vertical and eye level. All parameters are stimulus-side: a single mass-action length function (three constants) governs magnitude. The paper refutes complete summation but is indistinguishable from simple averaging for long lines; the decisive tests are short-line regimes and the |cos 2θ| strength law.

Implications extend beyond vision science. Since the model is image-computable and links to classical orientation descriptors (structure tensors, population vectors), it can be integrated into computer vision pipelines for spatial orientation estimation. Applications could improve VR/AR headsets that need to know a user’s subjective vertical, or robots that must orient themselves in cluttered environments. The closed-form nature also makes it suitable for real-time inference with minimal compute.