A border-ownership model based on computational electromagnetism

The mathematical relation between a vector electric field and its corresponding scalar potential field is useful to formulate computational problems of lower/middle-order visual processing, specifically related to the assignment of borders to the side of the object: so-called border ownership (BO). BO coding is a key process for extracting the objects from the background, allowing one to organize a cluttered scene. We propose that the problem is solvable simultaneously by application of a theorem of electromagnetism, i.e., “conservative vector fields have zero rotation, or “curl.” We hypothesize that (i) the BO signal is definable as a vector electric field with arrowheads pointing to the inner side of perceived objects, and (ii) its corresponding scalar field carries information related to perceived order in depth of occluding/occluded objects. A simple model was developed based on this computational theory. Model results qualitatively agree with object-side selectivity of BO-coding neurons, and with perceptions of object order. The model update rule can be reproduced as a plausible neural network that presents new interpretations of existing physiological results. Results of this study also suggest that T-junction detectors are unnecessary to calculate depth order

初期視覚野における遮蔽・被遮蔽物体知覚に関する計算理論

Humans can distinguish the order of mutually overlapping objects in a visual scene. The border between an occluding object and the occluded object is “owned” by the occluding object. How the brain assigns these borders, or Border-ownership (BO) assignment, determines the perception of object depth order. Findings from physiological experiments reveal that some neurons in area V2 of the brain respond selectively when the object which “owns” the edge in its receptive field is located on a specific side. Several models have been proposed in existing studies to reproduce this phenomenon. However, these models are not based on a clear computational theory. This study is the first to approach BO assignment from a computational viewpoint by treating it as a well-defined problem. I propose that the direction of BO　assignment can be defined as a conservative vector field E(x,y) with arrowheads pointing towards the occluding object, and that information pertaining to depth order can be defined as its corresponding scalar field Φ(x,y). By using a theorem in electromagnetics which states that the gradient of electric potential is its electric field E(x,y) = ∇Φ(x,y), I demonstrate that the BO assignment problem can be　solved by updating an initial vector field until its rotation, or “curl”, is zero. A model developed on this computational theory can simultaneously reproduce BO assignment and perceived depth order. Results of numerical simulations agree qualitatively with the response of object-side selective neurons in V2 to stimuli containing occlusion with simple geometry. Neural networks can be deduced from the update rule curl using only one parameter for adjusting the scale of neural connections. This study also presents new interpretations of existing models in addition to insight into a possible method for calculation of depth order.外界には奥行きが異なる物体が多数存在し，これら物体の視覚情報は重なりあっている場合が多い．このとき「遮蔽物体と被遮蔽物体を隔てる境界（Border）は遮蔽物体に帰属する」．Border Ownership（BO）問題は，物体の重なり順序を計算するための基盤的問題である．本研究の具体的な成果として，境界のOwnerが存在する方向であるBO信号をベクトル場E(x,y)，重なり順序をスカラー場Φ(x,y)として見なせば，電磁気学の電位と電場に関する定理（電場は電位の勾配， E(x,y) = ∇Φ(x,y)である）を用いることで問題の定式化ができることを発見した．数値シミュレーション結果から，提案モデルは様々な遮蔽状況や形状の変化に対して頑健に，BO問題と重なり順序計算問題が解けることを見出した．電気通信大学201