Induction operators for a computational colour–texture representation

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Abstract

The aim of this paper is to outline a perceptual approach to a computational colour–texture representation based on some colour induction phenomena. The extension of classical grey level methods for texture processing to the RGB channels of the corresponding colour texture is not the best solution to simulate human perception. Chromatic induction mechanisms of the human visual system, that has been widely studied in psychophysics, play an important role when looking at scenes where the spatial frequency is high as it occurs on texture images. Besides others, chromatic induction includes two complementary effects: chromatic assimilation and chromatic contrast. While the former has been measured by Wandell and Zhang [A spatial extension of CIELAB for digital colour image reproduction, in: SID, 1996] and extended to computer vision by Petrou et al. [Perceptual smoothing and segmentation of colour textures, in: 5th European Conference on Computer Vision, Freiburg, Germany, 1998, pp. 623] as a perceptual blurring, some aspects on the last one still remain to be measured, but it has to be a computational operator that simulates the contrast induction phenomenon performing a perceptual sharpening that preserves the structural properties of the texture. Applying both, the perceptual sharpening and the perceptual blurring, we propose to build a tower of images as an induction front-end that can be the basis of a perceptual representation of colour–textures.

Introduction

Any scene of the world is projected on our retina as a map of different regions that are the projections of 3D surfaces. The properties of these projections are derived from the position and orientation of the surfaces in the scene, the observer location, and the light that provoke the neuronal excitation of the visual system. In computer vision, people usually deal with a set of surface properties, shape, orientation, colour, and texture. In this work we will only deal with the last two and their dependency on the final perception.

Although both are inherent properties of surfaces, these two visual cues have usually been studied separately [3], [4]. This is probably due to their usual representations, while colour is a point feature given by the value of a pixel in several bands or channels, texture has to be modelled as a spatial relationship of the point with its neighbours. In Fig. 1 we see the RGB channels of a colour image, we can observe that the spatial information perceived from the colour image does not appear as it is in any of the channels. Therefore specific representations have to be built in order to deal with both cues at the same time.

The study of colour–texture representations has received increasing attention. The objective of many researchers has been to find co-joint representations of spatial and chromatic information which capture the spatial dependencies (in particular, correlation) within and among spectral bands. One of the most frequent approaches is to define a feature vector joining grey level texture features and colour features [5], [6]. Another one is to extend classical texture models, such as Markov Random fields and the autocorrelation function, in order to deal with multichannel images [7], [8], or wavelet analysis extended to colour images by combining the results in colour channels [9]. Other works, like [10], convert RGB values into a single code from which texture measurements are computed as if it were a grey scale image. Spatio-chromatic representations are computed in [11], [12] over the smoothed Laplacian of the image, and the structural tensor that is usually used to represent local texture properties is extended to colour images in [13].

However, we want to highlight the approach presented in [2], [14] that is based on known perceptual mechanisms of the human visual system. Colour–texture interaction is represented as a perceptual blurring which depends on the spatial frequency of the coloured patterns and the observer position. This approach is based on important conclusions from psychophysical works on colour–texture interaction [1], [15], [16], [17], [18]. We will review the details of this perceptual blurring in Section 5.

Following on from this prior work, in this paper we propose a global perceptual approach of colour–texture representation that combines the introduced perceptual blurring with a first approach to a perceptual sharpening. The combination of these two operators can simulate the visual process of colour–texture perception with the colour induction mechanisms produced by different spatial frequencies.

To this end, in 2 Colour, 3 Texture we give, separately, the basis of computational representations of colour–texture. In Section 4 we briefly introduce the colour induction mechanisms and their relationship to spatial frequency. Section 5 explains the essentials of perceptual blurring that simulates chromatic assimilation, and in Section 6 we introduce a perceptual sharpening that simulates the colour contrast phenomenon. In Section 7 we consider colour–texture perception as a visual process that integrates both induction mechanisms, this will be the basis for a global representation of colour–texture that is introduced in Section 8. Finally, in Section 9 we discuss some properties of the inductors operators and the advantages of using them in computing textural properties and in Section 10 we summarise the open problems that still remain in order to complete the proposed computational model.

Section snippets

Colour

Colour is the visual cue derived from the human visual processing of the electromagnetic radiation that reaches the retina. This process can be seen as a change in representation, which, in general, implies a dimensionality reduction. Although colour was not given much importance in the first decades of computer vision, since most previous work has been undertaken on grey-level images, the situation has changed and colour has become a very important visual cue for most of the vision tasks, such

Texture

Texture is the visual cue derived from non-homogeneous surfaces in scenes. Depending on the surface reflectance, positioning of the observer, and lighting conditions, we can obtain different texture images from the same surface. Although there are some recent works dealing with the recovery of the physical reflectance properties of a texture [26], [27] and some other works that have recovered 3D shape information from texture [28], [29], the most traditional approach in computer vision has been

Colour induction

Colour induction are the colour phenomena that changes the colour appearance of a stimulus due to the influence of the scene contents in the field of view. There are different types of induction phenomena such as colour adaptation, colour assimilation or colour contrast amongst others.

Colour adaptation is involved in any scene interpretation and occurs when scene colours are perceived without being affected by the illuminant influence, this ability presented by the HVS has been modelled in

Colour assimilation as a perceptual blurring

A computational model of colour assimilation has already been given by an isotropic blurring of an image on the opponent-colour space, this has been proposed by Petrou et al. [2] as a perceptual blurring. Colour assimilation effects were first measured by Wandell et al. [1], where they take perceptual measurements of quality on printed patterns. To achieve this goal, they propose the Spatial-CIELAB space that is given by a two-steps process: an opponent colour channel transformation and a

Colour contrast as a perceptual sharpening

As we have already explained in Section 4, colour contrast is a complementary mechanism to colour assimilation. Colour contrast arises on regions of low spatial frequency and shifts the chromaticity of the stimulus in a direction away from the chromaticity of the surround. In this section we define a computational operator that simulates the colour contrast phenomenon.

This operator enhances differences in the transitions among colours of regions presenting low frequencies. While the

Colour–texture perception as a visual process

In 2 Colour, 3 Texture we have explained, respectively, how colour and texture can be computationally represented as separate cues. However, we need to work on images from real world, which is neither a grey world, nor a Mondrian world.

In Section 4 we have briefly introduced the colour induction phenomenon that explains how colour changes depend on spatial frequencies, and how opponency can represent these interactions. These perceptual considerations can be simulated with two types of

A computational colour–texture model

Considering the assumptions done in the previous section, we now define the complete perceptual tower which we intend as a general perceptual representation of coloured textures. Therefore, for a given image we can build a perceptual tower representing colour information as it was observed from different observer distances. It can be considered as a colour–texture front-end representing colour–texture interaction and the basic step for further processing, a parallel approach to a scale-space

Discussion

In this paper we outlined a framework to deal with the interaction between texture and colour in a perceptual sense. Our contribution extends previous working [2] by incorporating into the perceptual tower an inductor operator, perceptual sharpening, which models the effect of chromatic contrast (a complementary effect to assimilation which is modelled by perceptual blurring).

Combining these two operators we can build a global framework that acts as a primal sketch for colour representation.

Future work

The first step to provide a full perceptual approach will require a psychophysical measurement of chromatic contrast, this will imply a tedious task of psychophysical experimentation. Once it is done, we will have to match the measurements with the sharpening parameters.

In the work presented we have taken all the attention on getting induction operators presenting good properties to represent colour appearance, however we have not taken attention to the computational cost of these operators. In

Acknowledgements

This work has been funded by project TIC2000-0382 of the MCYT of the Spanish Goverment.

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