The Measurement and Modelling of Reflectance

The Bi-directional reflectance distribution function

Summary:

Surface reflectance can be exactly described by its bidirectional distribution function (BRDF). This function describes how light from a given direction is reflected from a surface at a given orientation. In its full generality different spectra of light may be reflected in an orientation dependent way; thus, the BRDF may be (at least theoretically) very complex indeed.

Current research:

Koenderink and van Doorn[JKS96] have measured the BRDFs for a variety of surfaces. Their measurements indicate they are fairly well behaved and can be represented using a relatively small ( 50 or less) number of basis BRDFs.

Future research:

Even 50 parameters makes the problem of surface estimation from images intolerably hard. However, accurate models of surface BRDFs will drive research into simpler reflectance models which can be used in computer vision.

Possible application areas for this research include the automotive respray industry. Many typical paints have very complex reflectance characteristics. Understanding and measuring these reflectances would provide a useful tool for matching colours in the automotive industry.

Lambertian reflectance

Summary:

The Lambertian model is the simplest model of reflectance and predicts that light incident on a surface is scattered equally in all directions; the total amount of light reflected depends on the angle of incidence of the illumination. The Lambertian model is often used to model reflectances of matte appearance.

Current research:

Recent work by Wolff[Wol96] has demonstrated that the Lambertian model only really applies when the angle of incidence and the angle of reflection is small (relative to the surface normal). Importantly, Wolff has developed a simple modification of Lambert's law which accurately accounts for all illumination and viewing directions.

Future research:

Wolff's modified Lambert's law should be used in computer vision algorithms (e.g. shape from shading). Particular attention needs to be paid to the advantages/disadvantages of Wolff's model. For example, while Wolff's model is a strictly more accurate description of matte reflection, adopting it need not necessarily lead to more accurate estimation.

The dichromatic reflectance model

Summary:

Under the dichromatic reflection model[KSK88,Sha85] the light that is reflected from a surface is the sum of body and interface reflectance components. The body reflectance follows Lambert's law. Interface reflectance models the highlight component of surfaces.

Current research:

The dichromatic model has proved useful for a variety of computer vision tasks including colour constancy[LBS90,Lee90,Hea89,TW89,Tom94], shape recovery[DK94] and segmentation[Bri90,PK94].

Future research

Most current dichromatic estimation algorithms are designed to work in local image areas. In contrast recent work by Maxwell and Shafer[MS94,MS96] attempts to estimate surface parameters for the dichromatic (and more complex) models by integrating global information. While initial results appear promising, much research needs to be carried out in this area.

Spectral reflectance measurement

Summary:

The spectral reflectance function of a surface records the percentage of incoming light that is reflected on a per wavelength basis. The reflectance function determines the colour of a surface. A function which reflects strongly in only the red (long-wave) part of the spectrum will look red to a human observer. Accurate measures of surface spectral reflectance are useful for object recognition, segmentation and material classification.

Current research:

A series of studies have demonstrated that the spectral reflectance curves of reflectances are not arbitrary[Mal86,PHJ89,VGI94]. Indeed it is now accepted that reflectance curves can be accurately represented with a small (6, 7 or 8) basis functions. However, recovery of reflectances (e.g. the basis coefficients) can be confounded by the choice of viewing illuminants. Investigations have been carried out into optimizing camera design so that reflectances can be measured over a variety of illuminants[BWC89]; though little progress has been made.

Future research:

Current spectral reflectance databases usually record reflectance characteristics of highly specialized material sets (e.g. paint chips used for colour matching). Measures of typical everyday scenes would be of great value in computer vision reseach. (David Brainard at the University of California at Santa Barbara will be attempting to collate such a database; though, no results are yet available.) Camera design for reflectance measurement is currently an active area of research.

Surface colour: colorimetric measurement of reflectance

Summary:

In many applications it makes sense to obtain measures of surface reflectance which correlate with those made by the human visual system. A colorimetric measurement of reflectance, surface colour, is defined to be the response of the eye (the induced quanta catches of the long-, medium-, and short-wave cones) for a given surface under a fixed canonical viewing illuminant. This problem is not simply solved by equipping a camera with sensors equivalent to the human cones since measurements often take places under lights other than the canonical. When the viewing illuminant is not the canonical then camera measurements must be transformed in order to make them colorimetric.

Current research:

There has been much research into how camera RGBs measured under an arbitrary light might be mapped to measures of surface colour. Importantly, Marimont and Wandell[MW92] have shown that this task is a much easier than recovering the full spectral reflectance curves since cone responses for surfaces measured across illuminants are approximately a linear transform apart. In related research Vrhel and Trussell[VT94] have derived the optimal camera curves for surface colour recovery (assuming that illuminant change is linear)

Future research:

Colorimetric measurement is a very time consuming process. Typically devices such as spectrophotometers and colorimeters are used. These devices are expensive and have the disadvantage that only one surface colour can be measured at any one time. A colour camera which is colorimetric would allow many samples to be measured quickly. However, to be accepted as a tool for colour measurement in the colour industries the camera would have to be very accurate.

It is possible that a colorimetric camera might also form a bridge linking research on human colour vision and computer vision.

Polarization methods

Summary:

Light reflected from Lambertian surfaces is never polarized (even when illuminated by polarized light). In contrast polarity is maintained in the specular reflection component.

Current research:

The intensity of specularities in an image depend on the polarity of filter through which the scene is viewed. By using three polarized filters, Lee et al[LL96] and Moller[Mul96] have shown that the specular reflection component of reflectance can be isolated and removed from images. In related research Bolle et al[BCH+96] illuminate a scene with a single light source of fixed polarity. The scene is then imaged through a filter of reverse polarity. Because, specular highlights have the same polarity as the incident illumination this simple technique provides an elegant method for removing specularities from images.

Future research:

The use of polarized filters or polarized illumination is in its infancy. Both techniques have the potential to deliver considerable benefits for accurate reflectance estimation.