| We want to develop algorithms which allow a computer vision system to qualitatively estimate the roughness of reflective surfaces from a single image, under normal lighting conditions, and with incoherent light. In order to make such a system applicable to most imaging situations, we attempt to constrain the environment as little as possible, and thus, we will study the reflected images of step edges, since these are ubiquitous and algorithms for their detection are mature.; We first derive a six-parameter model of reflected step edges, and show that with this model it is possible to differentiate surfaces by roughness. In order for this differentiation to be correct, however, certain information about the imaging geometry must be known; we list what information is necessary, and describe the effect of changes in these parameters on the appearance of reflected edges.; We then use this knowledge of the appearance of the reflected edges to develop two methods of roughness estimation. The first method fits a curve described by the six-parameter model to the reflected edge profile data by a combination of gradient descent and singular value decomposition algorithms. The output of this algorithm is the best-fit values of the six parameters, one of which is the root-mean-square slope of the surface, which we use to quantify the roughness. We then discuss the imaging conditions for which this algorithm works well. The next method of roughness estimation treats the equation for the reflected radiance as a first kind Volterra integral equation. After solving the integral equation, it calculates a quantity which allows it to order surfaces by roughness. Although it does not calculate the roughness directly, as the first method does, it works for many imaging situations for which the first algorithm does not.; We test these algorithms on the images of step edges reflected in the surfaces of five steel disks of different roughness. We measure the root-mean-square slopes of these surfaces with a profilometer and compare the output of our algorithms with these values. We find that both algorithms order the surfaces correctly by roughness. |
