Physical significance of image measurements

The extraction of quantitative information from gray-scale images can be achieved using classical measurements defined for sets. For binary images, sets delineate portions of the image plane, being therefore two-dimensional (2-D) objects. Gray-scale images are constructed by adding another dimension, light intensity. The corresponding set is therefore 3-D. However, this 3-D space is not homogeneous: the physical quantities are not the same, for the image plane and the intensity axis. Consequently, not all the measurements have physical units. In this paper, we present a criterion to assess whether a measurement has a physical signification or not. We then illustrate the concept by applying this criterion to some useful image measurements: the surface, the fractal dimension, and granulometries. We study the behavior of these measurements under illumination changes. We show that a physically invalid measurement outputs erratic results under such circumstances. This has major consequences on the robustness of image analysis algorithms, because, most of the time, the illumination factor, or the image acquisition gain is unknown