# VSS 2015: Rejecting probability summation for RF patterns, not so Quick!

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**Alex S. Baldwin**, Gunnar Schmidtmann, Frederick A. A. Kingdom & Robert. F. Hess

Investigations of shape processing frequently use radial frequency (RF) patterns. An RF pattern is a circular contour with a periodic modulation applied to its radius. The way in which the visual system detects these patterns has been studied in several previous summation experiments. Typically data is compared to predictions from a model that detects each part of the pattern independently and then combines those local outputs through probability summation (these models predict less summation). This is then rejected in favour of a model that detects the whole RF pattern globally (predicting more summation). The “Quick pooling” probability summation model they use is based on the High Threshold Theory (HTT) of detection however, which lacks empirical support. In our study we first measured receiver operating characteristic curves to demonstrate that models of RF pattern detection should be based on Signal Detection Theory (SDT). Our data followed the SDT prediction (curved lines) rather than the HTT prediction (straight lines). We then measured psychometric functions for a four-cycle RF pattern as its lobes were modulated individually and in combination. We also collected data for summation between individual cycles in a quad of RF patterns to see whether within-RF summation differed from between-RF summation. Although thresholds for the between-RF condition were higher, the level of summation was very similar to that in the within-RF condition. We analysed our data using a maximum-likelihood fit of SDT-based additive and probability summation models. These include five parameters: individual gains for each cycle of the RF and a transducer exponent. We find that our probability summation model is able to provide as good a fit to both datasets as the additive summation (global) model. We discuss how the use of a HTT model may have led to premature rejection of probability summation in the past.