This chapter contains three tutorial overviews of theoretical and methodological ideas that are important to students of visual perception. From the vast scope of the material we could have covered, we have chosen a small set of topics that form the foundations of vision research. To help fill the inevitable gaps, we have provided pointers to the literature, giving preference to works written at a level accessible to a beginning graduate student. First, we provide a sketch of the theoretical foundations of our field. We lay out four major research programs (in the past they might have been called "schools"), and then discuss how they address eight foundational questions that promise to occupy our discipline for many years to come. Second, we discuss psychophysics, which offers indispensable tools for the researcher. Here we lead the reader from the idea of threshold to the tools of signal detection theory. To illustrate our presentation of methodology, we have not focused on the classics that appear in much of the secondary literature. Rather, we have chosen recent research that showcases the current practice in the field, and the applicability of these methods to a wide range of problems. The contemporary view of perception maintains that perceptual theory requires an understanding of our environment as well as the perceiver. That is why, in the third section, we ask what are the regularities of the environment, how may they be discovered, and to what extent do perceivers use them. Here, too, we use recent research to exemplify this approach.

Perceived duration of a sensory event often exceeds its actual duration. This phenomenon is called time dilation. The distortion may occur because sensory systems are optimized for perception within their respective modalities and not for perception of time. We investigated how the dilation of visual events depends on the duration and content of events. Observers compared the durations of two successive visual stimuli while the luminance of one of the stimuli was modulated at different temporal frequencies. Time dilation correlated with the frequency of modulation and the duration of the stimulus: the faster the modulation and the longer the stimulus duration, the larger the dilation. Notably, time dilation was also accompanied by a decreased sensitivity to stimulus duration. We show that these results are consistent with the notion that stimulus duration is estimated using measurement intervals of the lengths that depend on stimulus frequency content. Estimation of temporal frequency content is more precise using longer measurement intervals, whereas estimation of temporal location is more precise using shorter ones. As a result, visual perception will benefit from using longer intervals when the stimulus is modulated so that its frequency content is measured more precisely. A side effect of using longer temporal intervals is a larger uncertainty about the timing of stimulus offset (temporal location), ensuing time dilation and the reduction of sensitivity to duration. Our findings support the view that time dilation follows from basic principles of measurement and from the notion that visual systems are optimized for visual perception rather than for perception of time.

Perception of stereoscopic depth requires that visual systems solve a correspondence problem: find parts of the left-eye view of the visual scene that correspond to parts of the right-eye view. The standard model of binocular matching implies that similarity of left and right images is computed by inter-ocular correlation. But the left and right images of the same object are normally distorted relative to one another by the binocular projection, in particular when slanted surfaces are viewed from close distance. Correlation often fails to detect correct correspondences between such image parts. We investigate a measure of inter-ocular similarity that takes advantage of spatially invariant computations similar to the computations performed by complex cells in biological visual systems. This measure tolerates distortions of corresponding image parts and yields excellent performance over a much larger range of surface slants than the standard model. The results suggest that, rather than serving as disparity detectors, multiple binocular complex cells take part in the computation of inter-ocular similarity, and that visual systems are likely to postpone commitment to particular binocular disparities until later stages in the visual process.

The proximity principle is a fundamental fact of spatial vision. It has been a cornerstone of the Gestalt approach to perception, it is supported by overwhelming empirical evidence, and its utility has been proven in studies of the ecological statistics of optical stimulation. We show, however, that the principle does not generalize to dynamic scenes, i.e., no spatiotemporal proximity principle governs the perception of motion. In other words, elements of a dynamic display separated by short spatiotemporal distances are not more likely to be perceived as parts of the same object than elements separated by longer spatiotemporal distances.

Two traditions have had a great impact on the theoretical and experimental research of perception. One tradition is statistical, stretching from Fechner's enunciation of psychophysics in 1860 to the modern view of perception as statistical decision making. The other tradition is phenomenological, from Brentano's "empirical standpoint" of 1874 to the Gestalt movement and the modern work on perceptual organization. Each tradition has at its core a distinctive assumption about the indivisible constituents of perception: the just-noticeable differences of sensation in the tradition of Fechner vs. the phenomenological Gestalts in the tradition of Brentano. But some key results from the two traditions can be explained and connected using an approach that is neither statistical nor phenomenological. This approach rests on a basic property of any information exchange: a principle of measurement formulated in 1946 by Gabor as a part of his quantal theory of information. Here the indivisible components are units (quanta) of information that remain invariant under changes of precision of measurement. This approach helped to understand how sensory measurements are implemented by single neural cells. But recent analyses suggest that this approach has the power to explain larger-scale characteristics of sensory systems.

Early normative studies of human behavior revealed a gap between the norms of practical rationality (what humans ought to do) and the actual human behavior (what they do). It has been suggested that, to close the gap between the descriptive and the normative, one has to revise norms of practical rationality according to the Quinean, engineering view of normativity. On this view, the norms must be designed such that they effectively account for behavior. I review recent studies of human perception which pursued normative modeling and which found good agreement between the normative prescriptions and the actual behavior. I make the case that the goals and methods of this work have been incompatible with those of the engineering approach. I argue that norms of perception and action are observer-independent properties of biological agents; the norms are discovered using methods of the natural science rather than the norms are designed to fit the observed behavior.

We show that grouping by proximity can be modeled with a simple model that has few of the characteristics that one might expect of a Gestalt phenomenon. We do phenomenological psychophysics. Because the observers' responses are based on phenomenal experiences, which are still in bad repute among psychologists, we conclude with an explication of the roots of such skeptical views, and show that they have limited validity.

Vision and haptics have different limitations and advantages because they obtain information by different methods. If the brain combined information from the two senses optimally, it would rely more on the one providing more precise information for the current task. In this study, human observers judged the distance between two parallel surfaces in two within-modality experiments (vision-alone and haptics-alone) and in an intermodality experiment (vision and haptics together). We find that the combined size estimates are finer than it is possible with either vision or haptics alone. Indeed, the combined estimates approach statistical optimality.

It is is natural to think that in perceiving dynamic scenes, vision takes a series of snapshots. Motion perception can ensue when the snapshots are different. The snapshot metaphor suggests two questions: (i) How does the visual system put together elements within each snapshot to form objects? This is the spatial grouping problem. (ii) When the snapshots are different, how does the visual system know which element in one snapshot corresponds to which element in the next? This is the temporal grouping problem. The snapshot metaphor is a caricature of the dominant model in the field (the sequential model) according to which spatial and temporal grouping are independent. The model we propose here is an interactive model, according to which the two grouping mechanisms are not separable.