A good image metric is often needed in digital image synthesis. It can be used to check the convergence behavior in progressive methods, or to compare images rendered using various rendering methods. If images are rendered using various levels of detail (LOD) it is very important to evaluate if a certain LOD image is sufficient. Furthermore lossy compression methods should also be evaluated somehow. Reproductions on various media should be compared as well. Finally, an image query problem, when the most similar image to a target image is seeked in the large image data-base, happens to be another image metric application.
Of course, it is possible to compare two images by averaging pixel by pixel differences. Unfortunately, human vision does not compare images this way, therefore the results differ significantly from human comparison. As digital images are in most cases rendered in order to be observed by humans, a metric should correspond in some way to human vision. More precisely, if a human observer would state that the distance between images A and B is greater than that between images B and C, we expect a metric to give the same results. Comparing images with the popular mean square error metric (MSE) produces results that can differ greatly from human evaluation [Giro93]. Our intention is not to give the final solution for a perceptual metric, but rather to offer a simple, efficient way of how images can be compared in the original space with one single number.
More complex comparisons transform the image in the Fourier [RWPSR95] or wavelet [GaMY97] space and perform the comparison there. Rushmeier et al. [RWPSR95] introduce various techniques for comparing luminance images. They use some ideas from image compression and develop new metrics. All these metrics are computed after the images are transformed to Fourier space, and the whole method is designed for luminance images. As luminance images contain no information on color, these metrics obviously fail for color images, they are intended to be used for gray scale images only.
Jacobs et al. [JaFS95] have introduced a very fast multi-resolution querying method, which is intended for a different purpose. Their work is based on the wavelet transform.
Gaddipati et al. [GaMY97] have introduced a wavelet based metric. In
order to compute some coefficients used by this metric, images should
be transformed to the Fourier space first, which makes this metric very
computationally expensive. The whole metric operates on the separate
CIE LUV components, actually only the 
component of the CIE LUV
space was used by the authors, and they did not suggest how other
components could be used and combined with the measure.
We are going to offer a solution for color images in original space using some human vision characteristics. Of course, it is possible to compute the luminance of each pixel and then to use a metric for luminance images, but as stated before, some color differences would be lost. Our idea is to find the weighted average of color differences of an appropriate set of ``area pairs''. The areas will be rectangles, which are quasi-randomly defined in the image. The results of various sizes and numbers of rectangles are combined.
The contrast sensitivity function (see Human vision section) as suggested by Manos and Sacrison [MaSa74] will be used as the weighting function. The same function is used by Rushmeier et al. [RWPSR95] and Gaddipati et al. [GaMY97].