TEST DE INHIBICIÓN DE CASPASAS 3 Y

Computational modelling of the early visual system is highly informative about the way in which disparities are processed and perceived. This is of particular relevance to the first strand of the thesis, where we consider what depth-defined objects are, and how they are perceived.

We begin with a short discussion of cognitive neuroscience, and the levels of computational modelling. These were first laid out by Marr in 1976 (Marr, 1976) and have been widely used in the study and interpretation of computational modelling of neural systems e.g. (Churchland & Sejnowski, 1988; Griffiths, Lieder, & Goodman, 2015; Marr & Poggio, 1976b; Poggio, 2012). These levels lay down the different way in which any system that performs a computation can be understood: 1) The basic components, that is how do the neurons or transistors work; 2) The circuitry, how and why are the basic components interconnected; 3) The algorithm, this is the step-by-step processing that is implemented by the hardware; 4) The overall computational goal. While each of these levels are interconnected and

knowledge about one can strongly inform another, it is possible to progress understanding at one level without understanding another – for example you can understand how

transistors work, but not how they are arranged to calculate a trigonometric function; or know the equation to calculate a point spread function but not know how it is implemented algorithmically.

The most basic models of the early visual system use cross correlational techniques between the two eyes – these models take small areas or windows from each eye’s view and perform a cross correlation between the windows. By taking windows with different horizontal separations, then the disparity is calculated as the horizontal offset that creates a maximal response in the cross correlator e.g. (Harris, 2014), similar to the banks of disparity receptive neurons in the early visual system. This simple methodology creates a map of disparities in the visual field, which can then be analysed to consider how the model has performed.

These modelling techniques can recreate many of the fundamental properties of disparity extraction – for example the minimum and maximum limits for perceiving disparity (Banks, Gepshtein, & Landy, 2004; Filippini & Banks, 2009) and can be extended to understand the origins of other features of human stereovision e.g. (Allenmark & Read, 2010, 2011; Anzai & DeAngelis, 2010). The models have been improved until they are highly sophisticated;

36

adding stages such as spatial frequency filtering (Goutcher & Hibbard, 2014; Kane, Guan, & Banks, 2014) and variable size receptive fields e.g. (Allenmark & Read, 2011). One

particularly successful model is the constantly evolving disparity energy model (Read & Cumming, 2003; Tsai & Victor, 2003) which is capable of imitating some very complex behaviour in the binocular visual system, in both human and non-human subjects (e.g. Nienborg et al., 2004).

There are some circumstances in which the current understanding of disparity extraction can cause apparently large scale effects. A prime example of this was discovered by Kaufman et al (Kaufman, Bacon, & Barroso, 1973) when working with random dot

stereograms (RDS) – these are a field of randomly located dots displayed separately to each eye, which provide a disparity signal with little to no other cues to form (see Figure 1.2, discussed in detail in Section 3.1). Kaufman et al. used these RDSs to display two

overlapping transparent planes of different depth (called stereotransparency). They found that the two planes were perceived as a single plane at the average disparity of the two transparent planes. This effect typically occurs when the disparity between the two planes is smaller than 2-6 arcmin (Parker & Yang, 1989; Stevenson, Cormack, & Schor, 1991; Tsirlin, Allison, & Wilcox, 2008).

The apparent long range interaction between these large overlapping planes can be explained by short range interactions in algorithmic models of the visual system (Harris, 2014; Tsirlin et al., 2008). When the overlapping two planes of random dots are generated, then adjacent elements often have little horizontal separation but are of very different disparities. This means these elements fall within one receptive field, meaning that the neuron with a maximal response (for small separations between the two planes) is then the neuron tuned to detect the disparity that is an average between these two planes as it responds strongly to both elements (Harris, 2014). As would be expected from this result, when the planes are separated into two adjacent opaque planes the effect is no longer observed (Akerstrom & Todd, 1988).

These models imply that the visual system extracts disparity from every point in the scene, and the perceived depth of any given point is then given by the disparity extracted for that exact location. However, this is not the end of the story. The algorithmic models presented here are replicating behaviour in the early visual system, primarily in V1. We know that the behaviour of V1 cannot explain some of the key characteristics of binocular depth

perception (Goutcher & Hibbard, 2010; Parker, 2004; Tsai & Victor, 2003). For example, neurons in V1 respond identically to anti-correlated and correlated random dot

stereograms, but no depth is perceived in anti-correlated RDS (Cumming & Parker, 1997; Cumming et al., 1998). To fully understand binocular vision, we must therefore consider areas beyond the early visual system.

Of particular interest to us is some of the literature discussed at the end of Section 2.2.4, which shows that the perception of 3D shapes and depth intervals occurs late in the visual

37

hierarchy. This indicates that in order to fully capture the scope of processing that is involved in detecting and identifying camouflaged objects, we must consider what

processing is done after the early visual system, specifically what processing is done to the extracted disparities (Anzai & DeAngelis, 2010). A good way to explore the overall effects of the stages of processing disparity in the visual system is to develop quantitative models to assist in understanding and characterizing the response of the participant to the displayed stimuli. In this thesis we model our results using a general quantitative model with two aims: to have a better understanding of the mechanisms an animal could exploit in for stereoscopic camouflage; and to inform the development of more complex models of the visual system.

In the next Chapter, we review the discoveries that cannot be explained by these models of early disparity extraction. For the first strand of this thesis, we are particularly interested in those relating to the perception of objects, as we wish to investigate what a disparity defined object is, and how it is perceived.