Aditya Challa

An Introduction to Gamma-Convergence for Spectral Clustering

The problem of clustering is to partition the dataset into groups such that elements belonging to the same group are similar and elements belonging to the different groups are dissimilar. The unsupervised nature of the problem makes it widely applicable and also tough to solve objectively. Clustering in the context of image data is referred to as image segmentation. Distance based methods such as K-means fail to detect the non-globular clusters and hence spectral clustering was proposed to overcome this problem. This method detects the non globular structures by projecting the data set into a subspace, in which the usual clustering methods work well. Gamma convergence is the study of asymptotic behavior of minimizers of a family of minimization problems. Such a limit of minimizers is referred to as the gamma limit. Calculating the gamma limit for various variational problems has been proved useful - giving a different algorithm and insights into why existing methods work. In this article, we calculate the gamma limit of the spectral clustering methods, analyze its properties, and compare them with minimum spanning tree based clustering methods and spectral clustering methods.

Morphological interpolation for temporal changes

The problem of interpolation of images is defined as - given two images at time t = 0 and t = T, one must find the series of images for the intermediate time. This problem is not well posed, in the sense that without further constraints, there might be many solutions possible. We thus focus on the interpolation problem with respect to problems in geoscience and remote sensing. Mathematical Morphology (MM) can be considered as the theory of non-linear operators on images. The aim of this article is to review the techniques of morphological interpolation, compare the various techniques and observe its implications on a problem in geoscience and remote Sensing. Also, we provide a new approach combining ideas from the other methods and compare them to the original morphological interpolation methods. Application of these methods are shown on the RADARSAT images of pre and post flood images of the Mekong river.

A morphology-based approach for cloud detection

The aim of this paper is to present a simple and robust morphology-based approach to detect clouds in remote sensing images based on a single band. The algorithm generates for every pixel, a possibility value of not being a cloud pixel and thus provides an additional advantage over hard classification of pixels for further processing of these images. We have validated the performance of our algorithm on Moderate Resolution Imaging Spectroradiometer (MODIS) images and established its superiority over the results obtained by thresholding techniques in presence of noise such as clouds in presence of ice land cover.

Power Tree Filter: A Theoretical Framework Linking Shortest Path Filters and Minimum Spanning Tree Filters

Edge-preserving image filtering is an important pre-processing step in many filtering applications. In this article, we analyse the basis of edge-preserving filters and also provide theoretical links between the MST filter, which is a recent state-of-art edge-preserving filter, and filters based on geodesics. We define shortest path filters, which are closely related to adaptive kernel based filters, and show that MST filter is an approximation to the \(\varGamma -\)limit of the shortest path filters. We also propose a different approximation for the \(\varGamma -\)limit that is based on union of all MSTs and show that it yields better results than that of MST approximation by reducing the leaks across object boundaries. We demonstrate the effectiveness of the proposed filter in edge-preserving smoothing by comparing it with the tree filter.

Power spectral clustering on hyperspectral data

Classification of remotely sensed data is an important task for many practical applications. However, it is not always possible to get the ground truth for supervised learning methods. Thus unsupervised methods form a valuable tool in such situations. Such methods are referred to as clustering methods. There exists several strategies for clustering the given data — K-means, density based methods, spectral clustering etc. Recently we proposed a novel method for clustering data — Power Spectral Clustering. In this article we aim to introduce the method in the context of Geoscience and Remote Sensing, apply the method to hyperspectral data and validate its applicability to remotely sensed images.