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The acquisition of hundreds of images of a scene, each at a different wavelength, is known as hyperspectral imaging. This high amount of data allows the extraction of much more information from hyperspectral images compared with conventional color images. The forward-looking imaging approach emerged from remote sensing, but is still not very widespread in industrial and other practical applications. Spectral unmixing, in particular, aims at the determination of the components present in a scene as well as the abundance to which each component contributes. This information is valuable, for instance, when discrimination tasks are to be performed. Involving not only spectral, but also spatial information was found to have the potential to improve the unmixing results. Several publications use spatial first-order regularization (closely related to the total variation approach) to incorporate this spatial information. Like in classical image processing, this approach favors piecewise constant pixel transitions. This is why it was proposed in the literature to use second-order regularization instead of first order to approach piecewise-linear transitions. Therefore, we introduce Hessian-based regularization to hyperspectral unmixing and propose an algorithm to calculate the regularized result. We use simulated data and images measured in our laboratory to show that both the first- and second-order approaches share many properties and produce similar results. The second-order approach, however, is more robust and thus more accurate in finding the minimum. Both methods smoothen the images in the case of supervised unmixing (i.e., the component spectra are known beforehand) and enhance unsupervised unmixing (when the spectra are not known).

The contribution presents a novel approach to the detection and tracking of lanes based on lidar data. Therefore, we use the distance and reflectivity data coming from a one-dimensional sensor. After having detected the lane through a temporal fusion algorithm, we register the lidar data in a world-fixed coordinate system. To this end, we also incorporate the data coming from an inertial measurement unit and a differential global positioning system. After that stage, an original image of the road can be inferred. Based on this data view, we are able to track the lane either with a Kalman filter or by using a polynomial approximation for the underlying lane model.

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