Triplet-Watershed for Hyperspectral Image Classification

TL;DR

The watershed classifier exploits the connectivity patterns, a characteristic of HSI datasets, for better inference, and it is shown that exploiting such characteristics allows the Triplet-Watershed to achieve state-of-art results in supervised and semi-supervised contexts.

Abstract

Hyperspectral images (HSI) consist of rich spatial and spectral information, which can potentially be used for several applications. However, noise, band correlations and high dimensionality restrict the applicability of such data. This is recently addressed using creative deep learning network architectures such as ResNet, SSRN, and A2S2K. However, the last layer, i.e the classification layer, remains unchanged and is taken to be the softmax classifier. In this article, we propose to use a watershed classifier. Watershed classifier extends the watershed operator from Mathematical Morphology for classification. In its vanilla form, the watershed classifier does not have any trainable parameters. In this article, we propose a novel approach to train deep learning networks to obtain representations suitable for the watershed classifier. The watershed classifier exploits the connectivity patterns, a characteristic of HSI datasets, for better inference. We show that exploiting such characteristics allows the Triplet-Watershed to achieve state-of-art results in supervised and semi-supervised contexts. These results are validated on Indianpines (IP), University of Pavia (UP), Kennedy Space Center (KSC) and University of Houston (UH) datasets, relying on simple convnet architecture using a quarter of parameters compared to previous state-of-the-art networks. The source code for reproducing the experiments and supplementary material (high resolution images) is available at https://github.com/ac20/TripletWatershed Code.

Figures (12)

• Figure 1: Illustration of maximum margin for support vector machines (SVM)DBLP:journals/spl/ChallaDSN19. The key observation is - The margin is defined as the minimum distance between the training point labelled $0$ and what would be labelled $1$ after classification. And vice versa. The aim of the (linear) SVM classifier is to obtain a decision boundary that maximizes the margin. This can be extended to obtain a maximum-margin partition on an edge-weighted graph. Using \ref{['eq:max margin']}, a solution of this is provided by the watershed classifier.
• Figure 2: Figure illustrating the watershed boundariesDBLP:journals/spl/ChallaDSN19. Observe that in all these cases the boundary is in-between the classes. Also, it is in the middle of the zero density (no points exist) regions. This maximizes the margin between the boundaries and the classes. This is consistent with the maximum margin principle of SVM.
• Figure 3: Illustrating the watershed classifier. Let (a) denote the edge-weighted. The two distinct colours indicate two different classes. No colour indicates that the vertex is not yet labelled. (b) denotes the graph obtained by adding edges with weight $1$. Each vertex is given a label accordingly. (c) denotes the graph obtained by adding the edges with weight $2$ and Propagating the labels. Observe that all the points are now labelled and hence the algorithm terminates.
• Figure 4: Schematic of learning representations for the watershed classifier. Using a generic neural network we obtain the representation for the dataset. These representations are fed into the watershed classifier to obtain the labels using the seeds. Using the labels and the representation, we use triplet loss to compute the loss and also for obtaining the parameters for the neural network. Observe that the watershed classifier needs to be computed at every epoch.
• Figure 5: Neural Network architecture used for obtaining the representations. The architecture is composed of 3 convolution layers followed by a fully connected layer to get the representation. Batch normalization is performed before each layer for efficient training. The number of parameters is 87K.