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The fundamental question of how the brain derives 3D information from the inherently ambiguous visual input has been approached during the last two decades with probabilistic theories of 3D perception. Probabilistic models, such as the Maximum Likelihood Estimation (MLE) model, derive from multiple independent depth cues the most probable 3D interpretations. These estimates are then combined by weighing them according to their uncertainty to obtain the most accurate and least noisy estimate. In three experiments we tested an alternative theory of cue integration termed the Intrinsic Constraint (IC) theory. This theory postulates that the visual system does not derive the most probable interpretation of the visual input, but the most stable interpretation amid variations in viewing conditions. This goal is achieved with the Vector Sum model, that represents individual cue estimates as components of a multidimensional vector whose norm determines the combined output. In contrast with the MLE model, individual cue estimates are not accurate, but linearly related to distal 3D properties through a deterministic mapping. In Experiment 1, we measured the cue-specific biases that arise when viewing single-cue stimuli of various simulated depths and show that the Vector Sum model accurately predicts an increase in perceived depth when the same cues are presented together in a combined-cue stimulus. In Experiment 2, we show how Just Noticeable Differences (JNDs) are accounted for by the IC theory and demonstrate that the Vector Sum model predicts the classic finding of smaller JNDs for combined-cue versus single-cue stimuli. Most importantly, this prediction is made through a radical re-interpretation of the JND, a hallmark measure of stimulus discriminability previously thought to estimate perceptual uncertainty. In Experiment 3, we show that biases found in cue-integration experiments cannot be attributed to flatness cues, as assumed by the MLE model. Instead, we show that flatness cues produce no measurable difference in perceived depth for monocular (3A) or binocular viewing (3B), as predicted by the Vector Sum model.

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Bayesian inference theories have been extensively used to model how the brain derives three-dimensional (3D) information from ambiguous visual input. In particular, the maximum likelihood estimation (MLE) model combines estimates from multiple depth cues according to their relative reliability to produce the most probable 3D interpretation. Here, we tested an alternative theory of cue integration, termed the intrinsic constraint (IC) theory, which postulates that the visual system derives the most stable, not most probable, interpretation of the visual input amid variations in viewing conditions. The vector sum model provides a normative approach for achieving this goal where individual cue estimates are components of a multidimensional vector whose norm determines the combined estimate. Individual cue estimates are not accurate but related to distal 3D properties through a deterministic mapping. In three experiments, we show that the IC theory can more adeptly account for 3D cue integration than MLE models. In Experiment 1, we show systematic biases in the perception of depth from texture and depth from binocular disparity. Critically, we demonstrate that the vector sum model predicts an increase in perceived depth when these cues are combined. In Experiment 2, we illustrate the IC theory radical reinterpretation of the just noticeable difference (JND) and test the related vector sum model prediction of the classic finding of smaller JNDs for combined-cue versus single-cue stimuli. In Experiment 3, we confirm the vector sum prediction that biases found in cue integration experiments cannot be attributed to flatness cues, as the MLE model predicts.