Colour Image Formation

The Colour Group conducts research in such diverse areas as colour reproduction, computer vision, colour measurement, image enhancement, image retreival, and device characterisation/calibration. The unifying theme of all these research areas is colour. Thus to understand any of our research it is helpful to have a basic understanding of what colour is and how it is perceived both by ourselves, and by electronic devices such as colour cameras and colour scanners.

Colour Image Formation at the Eye

Our sensation of colour is a result of the processing of light energy first by the eye and later by the brain. The exact nature of this processing is complex, and indeed not yet fully understood. Fortunately, to gain an understanding of many of the problems we study, a very simple model of image formation suffices. Figure 1 is an illustration of a simple model of image formation. Light energy is emitted from a source (for example, the sun, or a tungsten filament light bulb) and is then incident upon a surface. Some, or all of the energy in the incident light is reflected from this surface and enters the eye. At the eye light is focused by a lens onto a membrane at the back of the eye, called the retina. On the surface of the retina are many light sensitive cells (called cones) which emit a response when light is incident upon them. There are three types of cone cells differentiated by how they respond to light energy. It is the responses of these three different cell types to light energy which are the basis of our colour perception.

Figure 1: A simple model of image formation: light from a source (e.g. the sun) is incident upon and reflected from a surface. The reflected light enters the eye leading eventually to our perception of colour.

Light is essentially a form of electromagentic energy and a light source is characterised by how much energy (or power) it emits at different wavelengths. For example, Figure 2 shows the spectral power distribution for a typical daylight illuminant. The Figure shows how much energy the source emits between 400nm and 700nm. Of course, the source will have energy at wavelengths outside this range but since the human visual system is sensitive to light only within this interval, we restrict our attention to this region. In mathematical terms we can represent a light source by , a continuous function of wavelength .

Figure 2: The spectral power distribution of typical daylight illumination.

A surface can also be characterised by a function of wavelength. Now though the function tells us what proportion of light energy incident upon it, the surface reflects on a per-wavelength basis. We call this function the surface reflectance function. Figure 3 illustrates the surface reflectance function for a certain surface. Once again we restrict attention to the wavelength range 400nm to 700nm.

Figure 3: The surface reflectance function of a bright red surface.

Light incident upon the surface is reflected from it in a manner governed by its surface reflectance function from which it follows that the reflected light (the light which enters the eye) can be written mathematically as:

The function is called the colour signal and it is this signal which is focused by the lens at the retina, and to which the light sensitive cone cells respond. The response of a cone cell depends on how much energy is present in the light incident upon it and importantly a cone cell can respond more or less to a given quantum of light energy depending on the wavelength at which that quantum is emitted. That is, the response of the cone cells to light energy is a function of the wavelength at which the energy is emitted. The three types of cone cells differ in how they respond to light energy at different wavelengths. Figure 4 shows the relative response of the three different cone cells as a function of wavelength. The cone cells are often called long-, medium-, or short-, wavelength sensitive cells since to a first approximation, they are preferrentially sensitive to light in one of these three wavelength regions of the visible spectrum.

Figure 4: The relative spectral response curves for the three types of cone cells.

The total response of the cone cells are the sum of their response to light energy at all wavelengths to which they are sensitive. Mathematically we can write these sums as integrals and if we denote the response of the three types of cone cell as , , and we have:

where , , and represent the relative sensitivities of the three different cone cells and is the wavelength range for which the cells have non-zero response. It is this triplet of cone cell responses which is the basis for all subsequent visual processing by the eye and the brain which result eventually in our sensation of colour.

Colour Image Formation for a Camera

Figure 5: The relative spectral response curves for a typical trichromatic digital still camera.

The model of image formation we have set out above can easily be generalised to the case of a camera or a scanning device. The input to these devices is once again the colour signal . In this case the colour signal is focused onto a CCD array: a 2-dimensional array of light sensitive elements which when light is incident convert the light energy into an electrical charge. In front of these devices are placed one or more filter elements, the role of which is to preferentially transmit light energy at certain wavelengths. The combination of these coloured filters and the CCD array are the correlate of the cone cells in the human eye. Just as there are three types of cone cells in the eye, a typical camera will contain three types of coloured filter which are typically referred to as red, green, and blue filters and whose response are denoted as R, G, and B, or just RGB. Figure 5 shows the relative sensitivities of a filter/CCD combination for a typical digital still camera. Mathematically these responses can be written:

Equations (2) and (3) represent a mathematical description of the image formation process at the eye and in colour imaging devices. In the case of our own visual system however, there is a great deal of subsequent processing of the initial cone responses, processing which leads eventually to our perception of colour and more generally to our visual perception as a whole. Notwithstanding this, this simple model of image formation forms the starting point for much of the research which is undertaken in the group, some of which is described in more detail in these pages.