Grayscale morphological operators are often used for image structure analysis. Normally these operators use the maximum (dilation) or minimum (erosion) of nearest neighbor values. This study introduces the use of an adaptive structural element for use as a grayscale morphological operator in image analysis. The structural element introduces changes with grayscale pixel value. Simple and more complex synthetic sets are presented along with their dilation and erosion analyses. This adaptive operator permits calculation of the image surface area with changing resolution. The surface area is estimated from the adaptive operator through dilation or erosion with differencing of constructed images. Results illustrate the ability to use a signature or multi-fractal function to show effects of particle distributions. The rate of change of the surface area is used to estimate the multi-fractal dimension (signature) as a function of changing resolution. Results appear promising for use in evaluating size and distribution of particles. Future applications of this method include quantifying and analyzing image features in geologic materials.