The two-alternative forced choice (2AFC) experimental setup is popular in the visual perception literature, where practitioners aim to understand how human observers perceive distances within triplets that consist of a reference image and two distorted versions of that image. In the past, this had been conducted in controlled environments, with a tournament-style algorithm dictating which images are shown to each participant to rank the distorted images. Recently, crowd-sourced perceptual datasets have emerged, with no images shared between triplets, making ranking impossible. Evaluating perceptual distances using this data is non-trivial, relying on reducing the collection of judgements on a triplet to a binary decision -- which is suboptimal and prone to misleading conclusions. Instead, we statistically model the underlying decision-making process during 2AFC experiments using a binomial distribution. We use maximum likelihood estimation to fit a distribution to the perceptual judgements, conditioned on the perceptual distance to test and impose consistency and smoothness between our empirical estimates of the density. This way, we can evaluate a different number of judgements per triplet, and can calculate metrics such as likelihoods of judgements according to a set of distances -- key ingredients that neural network counterparts lack.

翻译：二选一强制选择(2AFC)实验范式在视觉感知研究领域广泛应用，研究者旨在理解人类观察者如何感知由参考图像及其两个失真版本构成的三元组内的距离。传统上，这类实验在受控环境中进行，采用锦标赛式算法确定向每位参与者展示的图像顺序以完成失真图像的排序。然而，近期涌现的众包感知数据集不再共享三元组间的图像，导致排序方法失效。利用此类数据评估感知距离颇具挑战性，现有方法将三元组评判结果简化为二元决策——这种做法存在次优性且易产生误导性结论。为此，我们采用二项分布对2AFC实验中的决策过程进行统计建模，通过最大似然估计拟合感知判断的分布函数。该方法以感知距离为条件，对密度函数的经验估计施加一致性与平滑性约束。由此，我们可处理每个三元组中不同数量的判断数据，并基于距离集计算判断似然度等指标——这些关键要素正是神经网络模型所欠缺的。