Invariant Parameter Estimation Across Varying Seabeds in Synthetic Aperture Sonar Imagery
Side-look synthetic aperture sonar (SAS) can produce very high quality images of the sea-bed. The imagery generated by SAS sensors display the sea-floor and associated textures, such as sand ripples or sea-grass . The high-quality imagery has prompted the development of algorithms for the detection and classification of targets [2, 3], sea-bed segmentation and classification [4–6], and others [7–9]. In the majority of these methods, SAS imagery are analyzed by considering features that describe image intensity and texture. However, given a particular sensing geometry and bathymetry, the textures and pixel values imaged by a SAS system can vary drastically over the same spatial region of the sea-floor. Features based on image characteristics are often not quantifying invariant parameters of the sea-floor but, instead, are describing the relationship of that particular sensing geometry with respect to that area of the sea-floor. A different pass of the SAS sensor with varying range and aspects over the same region may result in very different image-based features. In this paper, we investigate the use of Gaussian Markov Random Fields (GMRFs) to characterize the underlying bathymetry depicted in a SAS image. In order to estimate the GMRF parameters that describe the bathymetry of a region, relative bathymetry values for imaged sea-floor are needed. However, many of the pixels on the sea-floor are shadowed and, thus, much of the information related to their heights relative to neighboring pixels is unknown. To address this issue, an Expectation Maximization algorithm which can handle missing values is used to estimate the GMRF parameters. The missing values are the relative bathymetry information of the shadowed/occluded pixels. The observed values are those associated with pixels that are not shadowed or occluded. Our current approach for identifying occluded pixels is to apply a local mean and variance filter to the input image. Shadowed and occluded regions have both a small local mean and low variance. Thus, after computing the mean and variance in a local window surrounding each pixel, the mean and variance values are thresholded with predetermined, fixed values. If both the mean and variance are below this threshold, the pixel is labeled as a shadowed or occluded pixel. The intensity information in the SAS image provides slope information of the sea-floor. A large value indicates a steeper sea-floor slope (e.g., maximal values are perpendicular to the grazing angle from the sensor). A small value indicates a shallow sea-floor slope. As the input images are generally not calibrated, intensity information does not provide any absolute height/bathymetry information. Therefore, only relative bathymetry information can be estimated from the input image. Given an assumed value for the first pixel in each row of the image and the first pixel following any occluded region, a relative bathymetry profile for all of the observed pixels can be estimated based on the relative intensity of each pixel. Essentially, all intensity values for observed pixels are normalized and used as a slope estimate (change from the bathymetry value of the preceding pixel) to estimate the bathymetry profile of observed pixels. Once the relative bathymetry profile for the observed pixels is estimated, then the GMRF parameters for that bathymetry profile are estimated using an Expectation-Maximization (EM)[10, 11] with Iterated Conditional Modes (ICM)[11, 12] method.