Form From Projected Shadow (FFPS): An algorithm for 3D shape analysis of sedimentary particles

In this paper we present a simple and effective method based on measuring the projected shadow of sedimentary particles by means of a digital image processing algorithm that enables the three principal axes of the particle to be determined from a single 2D color image. The method consists in projecting the shadow of the particle when it is resting on the maximum projection area (“c” axis pointing almost vertical, since in this configuration minimal distance from the center of mass to the floor is achieved minimizing the gravitational potential energy), by means of an oblique incident illumination system. Using HSL (hue-saturation-lightness) color space segmentation, two axes of the particle are measured directly from the maximum projected area. The length of the shadow provides the third axis of the particle. Multiple textured and colored sedimentary particles can be easily segmented from a green background and their corresponding shadows by means of a single space color transformation. This simple method enables the lengths of the three main axes of several particles to be determined at the same time without expensive equipment (the software is provided free by the authors). The axis lengths can span a broad range of sizes, and are measured with low experimental error (less than 5%).