Analysing the color uniformity of the ATTD05 perceptual space

The aim of this work is to study the uniformity of the perceptual space of the multistage neural colour vision model ATTD05 by comparison with CIECAM02, which is the latest colour appearance model adopted by the CIE. A set of parameters describing the deformation suffered by the loci of constant chroma and hue of the Munsell Atlas, were used to measure the degree of uniformity of the space. From these results we can conclude that ATTD05 is, in general, more uniform as CIECAM02. Introduction Colour vision models try to predict perceptual descriptors of colours under different viewing conditions. There are two main types of colour vision models: colour appearance models [1-7] and neural models [8-17]. Both predict perceptual descriptors, but differ in that neural models also try to follow the stages of the visual system. However, quite often evaluating colour differences between two samples is more important than obtaining numerical values of perceptual descriptors. Over the years, specific models have been developed to fit colour difference data [19-22], but the perfect solution would be to obtain a single model, which could reproduce both perceptual descriptors and colour differences. And if the colour space is uniform, the computation of colour differences becomes easier. In particular, if uniformity results are satisfactory, we mean to use with ATTD05 the procedure followed by Luo et al. [21,22] to obtain a colour difference formula for CIECAM02 [20], the latest colour appearance model adopted by the CIE. Firstly, in this paper we briefly describe the neural model, ATTD05. After that, we study the uniformity of the perceptual space of the model. For that, we compare the uniformity of the perceptual space of ATTD05 with the uniformity of CIECAM02 -the latest colour appearance model adopted by the CIEby representing some Munsell samples in these spaces and checking whether they are uniformly spaced, as they should. The uniformity test is the deformation suffered by the loci of constant chroma and hue of the Munsell Atlas. A set of 8 parameters were used to measure the degree of uniformity of the space. Description of the ATTD05 model ATTD05 [23,24] is a neural model that tries to predict perceptual descriptors of colours under different viewing conditions, following the stages of visual system. This multistage colour vision model has been developed by Capilla, Gómez & Luque (from the University of Valencia) for the last years. A schema of the model appears in Figure 1. Figure 1. Schema of the ATTD05 model. Pre-cortical and cortical stages The ATTD model computes the perceptual descriptors of an object from its XYZ tristimulus values and those of its background. The gain-controlled cone-responses are combined, yielding an achromatic channel, mediated by Magno cells with Type III receptive fields, and three opponent channels: two with red-green opponency but different polarities, mediated by Parvo cells with Type I receptive fields, and one with blueyellow opponency, mediated by Parvo cells with Type II receptive fields. These three opponent channels, after two opponent transformations at cortical level, generate the achromatic, red-green and blue-yellow perceptual mechanisms. The first opponent stage simulates the synapsis between the LGN cells and cells in layer 4Cβ. We admit that the same cell classes exist in the LGN and 4Cβ and that this stage does not modify the LGN signals. The simulated responses of the 4Cβ cells are subsequently combined to yield an achromatic and two chromatic (one red-green and one blue-yellow) intermediate channels. The responses of these channels to the object are modified by the responses to the background by means of a subtractive process. This stage would be mediated by Type III and double-opponent cells in layers 2 and 3. Finally, the responses of these intermediate mechanisms are combined to generate the responses of the perceptual mechanisms, from which we compute descriptors for brightness, hue, colourfulness and saturation. CGIV 2008 and MCS’08 Final Program and Proceedings 71 Uniformity of the perceptual space of the ATTD05 model Firstly, we compare the uniformity of the perceptual space ATTD05 with the uniformity of CIECAM02. To do that, we use perceptually equally spaced samples from the Munsell Atlas and test if they appear to be also uniformly spaced in the perceptual space of the model. We have chosen samples from the Munsell Atlas with constant values, 3, 5 and 7. As can be seen in Figure 2, both CIECAM02 and ATTD05 seem quite uniform under this test. Figure 2. Samples of constant Munsell Value (3, 5 and 7, respectively) plotted on the perceptual plane of the ATTD05 and CIECAM02 models Particularly, the rings in ATTD05 look more circular. However we can see that the centre of the rings is a bit out of place. But those observations are only qualitative. A set of 8 parameters were used to quantify how much the loci differ from equally spaced chroma rings and angularly equally space hue lines. These parameters were: • the position of the centre of gravity, TD(C0) • the mean radius of the Chroma CM ring for Value V, RV,CM • the circularity index of the CM Chroma ring for Value V, εV,CM • the Chroma spacing index, εV,R • the hue spacing index εH,V,CM • the position of the centre of gravity of the Chroma CM ring for Value V, TD(C0,CM) • the eccentricity index of the Chroma CM ring for Value V, ev(C0,CM) • the dispersion index of the centres of gravity, εV,e Definitions of the uniformity parameters Munsell Chromas and Values of the samples will be specified, when necessary, by subscripts CM and V, respectively. For comparison purposes, the values of Tp and Dp and their equivalents in CIECAM02 model (aM, bM) were normalized, for each Value, in such a way that the mean distance between the samples of the Munsell Chroma 6 locus to their own “centre of gravity” is six. That is, for any colour Ci of the Munsell Atlas, with perceptual descriptors ( ) ( ) ( ) [ ] i P i P i P C D , C T C TD = in the chromaticity plane, the normalized descriptors ( ) ( ) ( ) [ ] i i i C D , C T C TD = are defined as follows: ) C ( TD R 6 ) C ( TD i P 6 C , V i