Awareness and understanding of atmospheric visibility has strong implications for our daily lives. In addition to being critical for navigation, it acts as an indicator for air quality and pollution. The devices traditionally used to measure visibility, transmissometers and nephelometers, are expensive and often require field maintenance and calibration. Visibility camera systems are increasingly being deployed to measure atmospheric visibility; however, their use has so far been limited to qualitative analysis. The primary focus of this study is to develop image analysis techniques to derive quantitative measurements of visibility from such camera systems. We take advantage of the Beer-Lambert law, which defines the exponential relation by which light is attenuated when traveling through a medium. This is used to define a standard visibility model, which then allows us to frame the problem as a simple log-linear relation. We investigate several numerical models to estimate visibility, including single and multivariate linear least square regression, Laplacian-regularized linear least squares regression, and approximation with the M5' linear regression tree algorithm. We demonstrate the effectiveness of these algorithms on images and ground truth visibility measurements from the PhoenixVis.net visibility camera system. The features chosen by the multivariate feature selection process provide insight into the benefit of edge contrast and color saturation as indicators for poor visibility. In addition, we investigate Lambertian lighting and a dark channel prior as cues for salient regions for visibility estimation.