ABSTRACT

Objective

We investigated the role of Perrone’s algorithm in the Black Hole Illusion (BHI). After analyzing the algorithm and identifying two of its predictions, we empirically tested them with two on-line experiments.

Background

In 1983, Perrone proved that in daylight conditions it is possible to compute the descent angle using a ratio of retinal distances corresponding to the runway and surrounding context. Using the algorithm in nighttime conditions, with just the visible runway, pilots would overestimate the descent angle, leading to the BHI.

Method

Mathematical analysis indicates the algorithm predicts a large BHI; perhaps too large if there are no mitigating factors. As Perrone noted, the BHI illusion magnitude should be affected by runway width; we also found that some conditions predict a reverse BHI (pilots should underestimate their descent angle). In our experiments, participants observed a cockpit view of a runway during five seconds of steady approach. In a subsequent still image, participants indicated where they believed the plane would land if it continued its flight path. We measured the accuracy of the landing positions for various runway widths and various background contexts.

Results

The experiments did not show a BHI for any conditions; so the experiments do not validate the model predictions.

Conclusion

Based on our analyses, Perrone’s algorithm does not provide an adequate explanation of the Black Hole Illusion.

中文翻译：

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研究黑洞错觉的计算解释

摘要

客观的

我们研究了 Perrone 算法在黑洞错觉 (BHI) 中的作用。在分析了算法并确定了其中的两个预测之后，我们通过两个在线实验对它们进行了经验性测试。

背景

1983 年，Perrone 证明，在日光条件下，可以使用与跑道和周围环境相对应的视网膜距离比率来计算下降角。在夜间条件下使用该算法，只有可见的跑道，飞行员会高估下降角，导致 BHI。

方法

数学分析表明该算法预测的 BHI 较大；如果没有缓解因素，可能会太大。正如 Perrone 所指出的，BHI 错觉幅度应该受到跑道宽度的影响；我们还发现，某些条件会预测反向 BHI（飞行员应该低估他们的下降角）。在我们的实验中，参与者在 5 秒的稳定进近过程中观察了跑道的驾驶舱视图。在随后的静止图像中，参与者指出如果飞机继续其飞行路径，他们认为飞机将降落在哪里。我们测量了各种跑道宽度和各种背景环境下着陆位置的准确性。

结果

实验没有显示任何条件下的 BHI；所以实验不能验证模型的预测。

结论

根据我们的分析，Perrone 的算法没有提供对黑洞错觉的充分解释。