Incorporating Different Reflection Models into Surface Reconstruction

Generation of elevation maps of the seafloor is an important component of any autonomous system designed to navigate underwater. Because of its long range, sonar is the sensing medium of choice for underwater navigation. However, sonar systems designed to directly generate 3D images are generally complex or have low resolution. For these reasons, techniques that generate 3D elevation maps from 2D sonar intensity images are necessary for terrain modeling and navigation. Furthermore, recovering intrinsic terrain properties, such as albedo and surface roughness, is important for undersea mapping and exploration. This paper presents two techniques for the generation of elevation maps of the seafloor from side scan sonar intensity images and sparse bathymetric data. These techniques employ a reflection model of the seafloor to establish a correspondence between the intensity at a point and the surface normal at that point. The first technique uses a constraint between the surface normal and the position of the sensor to generate a partial differential equation that describes the surface. This PDE is repeatedly solved using finite differences until the intensity from the surface is close to the actual intensity data. The second technique uses an iterative relaxation method to generate the surface by minimizing the difference between the intensity data and the calculated surface intensity. This technique is similar to shape from shading methods used in computer vision. In both techniques the sparse bathymetric data is used to generate an initial guess for the shape of the seafloor and an initial guess for the reflection model parameters. These techniques are designed to support different reflection models, so they can be applied to different underwater environments. This is in contrast with other approaches that are generally less flexible with respect to the reflection model used. In addition to the elevation map of the seafloor, the parameters of the reflection model at every point in the image are generated. These parameters describe material properties of the seafloor, so the maps of the reflection model parameters can be used to segment the seafloor by material. Both techniques were tested on real and noisy synthetic data by comparing the calculated elevation map to the real elevation map. Using a lambertian reflection model the average error in the elevation maps was found to be less than 0.5m at 150m range while the maximum error was less than 4.5m for an image with bathymetric data spaced evenly every 16m. Furthermore, for synthetic images, the parameter (albedo) of the reflection model was calculated to within 5% of its actual value. On real data the actual albedo is not known, but qualitatively correct segmentation of albedo was obtained. In general the two methods performed equally well. Other reflection models were used with similar results.