The problem of anomaly is important in many image processing applications, such as military target detection, automation of quality assurance and analysis of medical images. Traditional methods usually require statistical modeling of the background or using training data to learn a model. The problem with such approaches is that the choice of model in high-dimensional data is not obvious and in cases where the background is multi-class, estimation of the parameters becomes complex.
In our research, we propose a data-driven approach to anomaly detection in images, combining spectral dimensionality reduction and a nearest-neighbor-based anomaly score. We use diffusion maps to embed the data in a low dimensional representation, which separates the anomaly from the background. The diffusion distance between points is then used to estimate the local density of each pixel in the new embedding.
The diffusion map is constructed based on a subset of samples from the image and then extended to all other pixels. Due to the interpolative nature of extension methods, this may limit the ability of the diffusion map to reveal the presence of the anomaly in the data. To overcome this limitation, we propose a multiscale approach based on Gaussian pyramid image representation, which drives the sampling process to ensure separability of the anomaly from the background clutter. The algorithm was successfully tested on side-scan sonar images of sea-mines.