MESOPIC CONTRAST MEASURED WITH A COMPUTATIONAL MODEL OF THE RETINA 1

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Decuypere Justine , Capron Jean-Luc , Dutoit Thierry , Renglet Michel 1 2 University of Mons, Belgium, University of Louvain-la-Neuve, Belgium [email protected]

Abstract In the mesopic range, cones and rods of the retina are simultaneously responsible for visual perception. They do not have the same physiological behaviour, both in their response to light and in their temporal comportment. But after the retinal processing, they share the same circuitries to the brain. The aim of this work is to develop a computational model that simulates the physiological mechanisms occurring in retinal cells in mesopic lighting conditions. This computational retina should be able to react to images of visual scenes in the same way as the eye does in front of the real scene. It is built of spatiotemporal filters that mimic the functioning of the retinal layers. In order to validate our approach, this paper compares our results to the results of the new recommended system for mesopic photometry based on visual performance. Keywords: Mesopic, Retina Model, Contrast

1 Context 1.1 Lighting issues Mesopic lighting conditions are defined by lighting scientists as the luminance levels between 0.005 cd/m² and 5 cd/m² (CIE, 2010). At those levels, the spectral sensitivity of the eye varies due to the simultaneous activation of both kinds of photoreceptors (cones and rods). In the photopic range (> 5 cd/m²), visual perception involves three types of cones. The eye spectral sensitivity is defined by the V(λ) function, with its maximum at 555 nm. In the scotopic range (< 0,005 cd/m²), visual perception is handled by rods. The Purkinje’s phenomenon shows a shift of the sensitivity toward the blue end of the visible spectrum. The sensitivity of the eye is maximal at 507 nm, as described by the V ′ (λ) function.

Figure 1 – Variations of spectral sensitivity In the mesopic range, spectral sensitivity varies according to the light level and the spectral content of light rays reaching the eye. Therefore, there is no fixed function to describe the sensitivity of the eye in mesopic lighting conditions. The CIE has recommended a practical model of mesopic photometry (CIE, 2010) that specifies the mesopic luminance of a stimulus as a function of its photopic luminance, the photopic adaptation luminance and the S/P ratio of the light source. This enables the calculation of mesopic curves with various weighting factors m (Figure 1). The assessment of the adaptation luminance remains problematical.

1.2 Physiological issues The retina is a layered neural structure that captures and processes the visual information before sending it to the brain (Hubel, 1995). The first neural layer consists of photoreceptors. Their response to a stimulus depends on its intensity and its spectrum (for the same energy, an L cone responds more strongly to a red stimulus than to a blue stimulus). They transduce lighting signals into graduated electrical signals and send those signals to horizontal and bipolar cells. From bipolar cells, the signals are processed and transmitted to ganglion cells whose axons form the optic nerve. There are various types of ganglion cells that work in parallel and create maps of different features in the visual field.

Figure 2 – Pathways through the retina In photopic conditions, there are three major pathways working in parallel (Wässle, 2004; Masland, 2001). The parvocellular pathway (P-pathway) deals with red/green opponency and has sensitivity to high spatial and low temporal frequencies. It takes inputs from L and M cones. The magnocellular pathway (M-pathway) is sensitive to high temporal and low spatial frequencies. This circuitry receives mixed inputs from L and M cones, so that it can discriminate luminance variations but no colour variations. The koniocellular pathway (Kpathway) mediates blue/yellow opponency. It compares inputs from S cones and a mix of signals from L and M cones. The P- and the M- pathways have concentric receptive fields with a centre/surround organisation. The size of those receptive fields grows up with eccentricity, leading to a loss of spatial acuity in the periphery of the visual field (Dacey, 1992; Dacey, 1993; Croner, 1995). In scotopic conditions, the signal is captured by rods and transmitted to rod bipolars. AII amacrine cells receive signals from rod bipolars and send those to the magnocellular pathway. From there, the way to the brain is the same as for cones (there is a limited number of fibres in the optic nerve). In mesopic conditions, the luminous image is captured by both rods and cones. The electrical connections within the photoreceptors layer are activated so that rods messages can be directly sent to the cones pathways through gap junctions (Sharpe, 1999; Stockman, 2006). This enables the visual system to receive rods information much faster than through the scotopic pathway. All of the three photopic pathways are influenced by the rods response in various proportions (clear rod input in the M-pathway, less influence on P- and K-pathways) (Pokorny, 2010; Field, 2009; Lee, 1997).

2 Set up of the model This work develops a non-chromatic computational model of the retina that mimics the retinal processing in mesopic lighting conditions. The magnocellular pathway and the parvocellular pathway (only for high spatial contrasts, not for colour opponency) are simulated. The model is implemented in C++ using OpenCV library (Bradski, 2000). The aim is to analyse the spatiotemporal perception of a mesopic scene. In order to validate this approach, we compare results of a contrast test to results of the CIE recommended model.

Figure 3 summarises the steps of the model. More details about the model building (formulas and parameters) can be found in (Decuypere, 2011).

Figure 3 – Scheme of the computational model functioning

2.1 Response and adaptation state (photoreceptors layer) At first, an image of a visual scene is displayed to the retina model. It cannot be a classical image, the luminance range of which is too restricted. We use either a simplified image with parameters or an HDR image or a multispectral image. The image is processed pixel by pixel. The first step is the conversion from pixel values to luminance values. The photopic and the scotopic luminances of the point represented by each pixel are calculated. To evaluate the response of rods and cones, the method is similar to Pattanaik’s operator (Pattanaik, 2000; Irawan, 2005, Ledda, 2004). The response depends not only on the luminance of the point but also on the adaptation state of the considered photoreceptor (Hood, 1986). The adaptation state of a cell (cone or rod) is a function of the adaptation state of its neighbours and the stimuli that the cell has previously captured. Pattanaik divides adaptation is two processes: the “neural” part of adaptation and the “chemical” part of adaptation. The “neural” adaptation is quite quick and is attributed to connections within the cells network. We model its spatial functioning with a Gaussian filter convolved with the luminance image, so that a cell adaptation value is dependent both on the stimulus reaching and on the stimuli reaching nearby cells (closer is the cell, stronger is its influence). Temporally, an exponential decay function reproduce the latency of adaptation, so that adaptation at time T depends on adaptation at time t