A Semi-Supervised Reduced-Space Method for Hyperspectral Imaging Segmentation

Abstract

The development of the hyperspectral remote sensor technology allows the acquisition of images with a very detailed spectral information for each pixel. Because of this, hyperspectral images (HSI) potentially possess larger capabilities in solving many scientific and practical problems in agriculture, biomedical, ecological, geological, hydrological studies. However, their analysis requires developing specialized and fast algorithms for data processing, due the high dimensionality of the data. In this work, we propose a new semi-supervised method for multilabel segmentation of HSI that combines a suitable linear discriminant analysis, a similarity index to compare different spectra, and a random walk based model with a direct label assignment. The user-marked regions are used for the projection of the original high-dimensional feature space to a lower dimensional space, such that the class separation is maximized. This allows to retain in an automatic way the most informative features, lightening the successive computational burden. The part of the random walk is related to a combinatorial Dirichlet problem involving a weighted graph, where the nodes are the projected pixel of the original HSI, and the positive weights depend on the distances between these nodes. We then assign to each pixel of the original image a probability quantifying the likelihood that the pixel (node) belongs to some subregion. The computation of the spectral distance involves both the coordinates in a features space of a pixel and of its neighbors. The final segmentation process is therefore reduced to a suitable optimization problem coupling the probabilities from the random walker computation, and the similarity with respect the initially labeled pixels. We discuss the properties of the new method with experimental results carried on benchmark images.

Keywords: hyperspectral image segmentation; linear discriminant analysis; random walks; spectral similarity.

Figure 1

Visual representation of the RLDA algorithm and distance computation of the neighborhoods. First row: example with just 3 pixels and their hyperspectral distribution, reduced in their 2D principal components. Second row: RLDA applied to a larger image. Third row: extraction of the 8-neighborhoods of two pixels in each principal component.

Figure 2

Flow chart of Algorithm 2.

Figure 3

Indian Pines segmentation results. (a): false gray scale image. (b): segmentation result. (c): true labels. (d): accuracy over the classes. The colormaps in (b,c) are different because the segmentation process takes into account 5 labels, while the ground truth contains 16 labels. Each region in the ground truth falls almost entirely in one of the 5 manually selected labels.

Figure 4

(a–c): false grayscale image, segmentation result and ground truth labels for the Pavia University dataset. (d–f): false grayscale image, segmentation result and ground truth labels for the Salinas HSI dataset. The former experiments achieves an Overall Accuracy of 0.93, whilst the latter achieves an OA of 0.9696.

Figure 5

(a–c): Dependence of the RI wrt $$\alpha$$ for several values of $$\lambda$$, from 1 to $${10}^{-6}$$ for Indian Pines, Pavia University and Salinas HSI datasets, respectively. The RI remains high, there is a peak around $$\alpha =0.85$$ in the former cases, while the Salinas HSI datasets achieve its best performance for $$\alpha =0.65$$ when $$\lambda$$ is lower than 1. The number of bands obtained by the dimensionality reduction is stable wrt $$\lambda$$.

Figure 6

(a) Ground truth labels. (b–d) Random seeds for the proposed procedure, chosen among the ground truth mask. From left to right: square seeds of dimension 3, 5, and 7 pixels. The squares are clipped in order to refer to the correct region.

Figure 7

Result of the segmentation of Pavia Center using the ground truth labels as atlas. From left to right: image of the landscape in false colors, labels of the ground truth, final result. The latter panel shows that all the roofs are remarkably recognized, as the shadows they project on the ground. The vegetation is segmented with a very high level of precision. We reported the labels as reported in the database we used for these experiments: there are clearly some errors, since some classes (such as Shadows, Meadows and Bare Soils) refers to objects that are not the ones described by these labels.

Figure 8

Segmentation results on the KSC dataset. From left to right: false color image, ground truth labels employed as seeds, and segmentation result. On the bottom of the images the legend associates the color to the labels.

Figure 9

Overlay between the segmentation and original image (in grayscale) for the KSC dataset.