Unsupervised Detection of Sub-pixel Objects in Hyper-spectral Images via Diffusion Bases

Sub-pixel objects are defined as objects which due to their size and due to the resolution of the camera occupy a fraction of a pixel or partially span adjacent pixels. Unsupervised detection of sub-pixel objects can be highly useful in areas such as medical imaging, and surveillance, to name a few. Hyper-spectral images offer extensive intensity information by describing a scene at hundreds and even thousands of wavelengths. This information can be utilized to obtain better sub-pixel detection results compared to those that are obtained using RGB images. Usually, only a small number of wavelengths contain the information that is required for the detection. Furthermore, the intensity images of many wavelengths are noisy and contain very little information. Accordingly, hyper-spectral images must be pre-processed first in order to extract the information that is needed for the sub-pixel detection. This extraction process produces an image where each pixel is represented by a small number of features which allows the application of fast and efficient detection algorithms. In this paper we propose the Diffusion Bases (DB) dimensionality reduction algorithm in order to derive the essential features for the sub-pixel detection. The effectiveness of the DB algorithm facilitates the application of a very simple algorithm for the detection of sub-pixel objects in the feature space. The proposed approach does not assume any distribution of the background pixels. We demonstrate the proposed framework for the detection of cardboard objects in airborne hyper-spectral images of a desert terrain.