Creating a supervised learning model for mineral identification is challenging due to the lack of ground-truth data. This study utilizes a method from existing literature that generates a training dataset by augmenting available spectra in the MICA spectral library. However, rather than using entire spectra for identification, this study extracts spectral features from each spectrum for model training. It employs the apparent continuum removal method, Segmented Curve Fitting, to identify the most informative or distinguishable parts in the spectral domain. Spectral features are then extracted based on band-centers and band-areas for each selected part. The model is evaluated against a Targeted Reduced Data Record (TRDR) dataset obtained using a hierarchical Bayesian model, demonstrating improved identification performance than the existing supervised models. Finally, using this model, dominant minerals are identified in MTRDR data from the Nilli Fossae region of Mars, and a corresponding mineral map is presented.

Matching a target spectrum with known spectra in a spectral library is a common method for material identification in hyperspectral imaging research. Hyperspectral spectra exhibit precise absorption features across different wavelength segments, and the unique shapes and positions of these absorptions create distinct spectral signatures for each material, aiding in their identification. Therefore, only the specific positions can be considered for material identification. This study introduces the Weighted Sum of Segmented Correlation method, which calculates correlation indices between various segments of a library and a test spectrum, and derives a matching index, favoring positive correlations and penalizing negative correlations using assigned weights. The effectiveness of this approach is evaluated for mineral identification in hyperspectral images from both Earth and Martian surfaces.

Watershed partitioning, following a maximal vertex-cut constraint, ensures each basin is strictly isolated from its neighboring basins. This partition is composed of watershed arcs positioned between pairs of adjacent basins. When these arcs create a connected partition, applying watershed partition on an arc-graph ensures that the corresponding arcs of watershed points in the arc-graph still maintain this connected partition. This crucial property is leveraged in the proposed iterative watershed partition method for extracting hierarchical partition lines in an image. The method effectively extracts river basins from SRTM DEM data of the Indian state Uttarakhand, revealing a well-structured hierarchy of catchment basins.

While we agree that “not all DEMs are derived through remotely sensed data and are not equal,” there is a strong need to rely on the contours plotted on surveyed topographic maps that are available at a specific spatial resolution. As we do not have such contours from all possible spatial scales, there is a need to have a framework to generate the contours at all possible spatial scales from the contours available from surveyed topographic maps available at the specific. We proposed a simple yet effective morphological approach to convert a sparse digital elevation model (DEM) to a dense DEM. The conversion is similar to that of the generation of high-resolution DEM from its low-resolution DEM. The approach involves the generation of median contours to achieve the purpose. It is a sequential step of: 1) decomposition of the existing sparse contour map into the maximum possible threshold elevation region (TER); 2) computing all possible nonnegative and nonweighted median elevation region (MER) hierarchically between the successive TERs decomposed from a sparse contour map; and 3) computing the gradient of all TERs, and MERs computed from previous steps would yield the predicted intermediate elevation contour at a higher spatial resolution. We present this approach initially with some self-made synthetic data to show how the contour prediction works and then experiment with the available contour map of Washington, NH, to justify its usefulness and compare the result with some existing methods. This approach considers the geometric information of existing contours and interpolates the elevation contour at a new spatial region of a topographic surface until no elevation contours are necessary to generate. This novel approach is also very low cost and robust as it uses elevation contours.

In this letter, we adapt the dilation operator from mathematical morphology to propose dilation distances. These dilation distances are then used for band selection in hyperspectral images. It is shown that dilation distances between bands can capture the spatial distance between the objects. Hence, using dilation-based distances would select those bands which identify spatially separated objects. This is illustrated using both toy and real data sets. Furthermore, we compare the proposed approach with existing methods and show empirically that dilation-distance-based band selection provided competitive results outperforming several methods.

Watershed Arcs Removal for node-weighted graphs method addressed the over-segmentation problem of classical watershed transformation, in a significantly shorter run-time. In this study, a variation of Watershed Arcs Removal is proposed that generates hierarchical partitioning in an edge-weighted graph. In the proposed method, regions are grown from the nodes having high local similarity to find the initial arcs, and neighbouring regions are merged by gradually removing arcs with low local dissimilarity. The arcs to be removed in a level are selected solely from the arc-graph constructed from the existing arcs in the previous level, weighted by their local dissimilarity. In contrast to the node-weighted variation, a strategy is employed here to preserve the critical arcs. Although the proposed method can be effectively applied to any multi-band image by transforming it into an edge-weighted graph, in this study we evaluated its performance particularly in RGB image segmentation.

Hyperspectral images (HSIs) 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, spectral-spatial residual network (SSRN), and attention-based adaptive spectral-spatial kernel residual networks (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 Indian Pines (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 athttps://github.com/ac20/TripletWatershed_Code.

It is widely known that there are several interdependent phenomena. The zones of influence (ZoIs) of water bodies (WBs) can be considered as typical examples. Over 289000 ZoIs are computed for the corresponding WBs mapped from remotely sensed satellite data of Indian peninsular. The size of WBs ranges between the smallest size of 5.1594 m2to 628.1642 km2, and the range of the ZoIs is in between 416.2497 m2to 8862.3362 km2. The basic geometric measures were computed for all WBs and their ZoIs. These measures were employed to derive power laws that are found scale-invariant, supporting the fact that these interdependent phenomena belong to two different universality classes, and explaining the commonly shared physical mechanisms. It is also inferred that power laws derived for this very large set of WBs and their ZoIs are similar to the ones derived for a smaller data set, that is, they are indeed fractals. The study shows the importance of deriving power-law relationships for natural phenomena mapped from remotely sensed satellite data across very fine to coarse spatial, spectral, and temporal resolutions.

This paper provides watershed-specific information dimensions computed through construction of binomial multiplicative process based multifractal spectra. Information dimension of watersheds provides clues on the distribution of terrestrial elevations spread across all the spatial positions within the watershed. This information dimension could be related to the responses of watersheds to the perturbation caused due to cascade of endogenic and exogenic forces. Higher the information dimension, lesser is the response to the cascade of endogenic and exogenic forces. Based on the information dimension computed through multifractal spectra for thirty one watersheds partitioned from the Cartosat DEM of the Lower Indus subbasin, we inferred that the watersheds are within the range of highly heterogeneous to highly homogeneous categories. It would be interesting to adopt this approach to study watersheds belonging to physiographically distinct regions.

Watershed technique from mathematical morphology (MM) is one of the most widely used operators for image segmentation. Recently watersheds are adapted to edge weighted graphs, allowing for wider applicability. However, a few questions remain to be answered - How do the boundaries of the watershed operator behave? Which loss function does the watershed operator optimize? How does watershed operator relate with existing ideas from machine learning. In this letter, a framework is developed, which allows one to answer these questions. This is achieved by generalizing the maximum margin principle to maximum margin partition and proposing a generic solution, morphMedian, resulting in the maximum margin principle. It is then shown that watersheds form a particular class of morphMedian classifiers. Using the ensemble technique, watersheds are also extended to ensemble watersheds. These techniques are compared with relevant methods from the literature and it is shown that watersheds perform better than support vector machines on some datasets, and ensemble watersheds usually outperform random forest classifiers.

Clustering is one of the most important steps in the data processing pipeline. Of all the clustering techniques, perhaps the most widely used technique is K-Means. However, K-Means does not necessarily result in clusters which are spatially connected and hence the technique remains unusable for several remote sensing, geoscience and geographic information science (GISci) data. In this article, we propose an extension of K-Means algorithm which results in spatially connected clusters. We empirically verify that this indeed is true and use the proposed algorithm to obtain most significant group of waterbodies mapped from multispectral image acquired by IRS LISS-III satellite.

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 are many possible solutions. The solution is thus usually dictated by the choice of the constraints/assumptions, which in turn relies on the domain of application. In this article we follow the approach of obtaining a solution to the interpolation problem using the operators from Mathematical Morphology (MM). These operators have an advantage of preserving structures since the operators are defined on sets. In this work we explore the solutions obtained using MM, and provide several results along with proofs which corroborates the validity of the assumptions, provide links among existing methods and intuition about them. We also summarize few possible extensions and prospective problems of current interest.

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.

We show an application of Moran's Index to process and analyze the waterbody-spread extracted from remotely sensed data. A method that is employed to quantify division-wise waterbody-spread, district-wise waterbody-spread and taluk-wise waterbody-spread spatial complexity is based on Moran's Index computation. The waterbody-spread data for each of the hierarchically partitioned geographical unit-wise (divisions, districts and taluks) of the state of Karnataka was collated from remotely sensed data. The result of Moran's Index calculations on (i) division-wise waterbody-spread, (ii) districts-wise waterbody-spread and (iii) taluks-wise waterbody-spread of Karnataka, India, were analyzed and discussed. The results offer new directions of research within the context environmetrics.

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.

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.

We show an application of Mahalanobis Distance to compute the degree of similarity between the bi-variables corresponding to two regions. The bi-variables considered include areas of each district and the areas of wetland regions within each district o f a Division-A and similar variables for each district of another Division-B. We considered four political divisions of state Karnataka that include 27 districts. Areal extent data for each district and the district-wise wetland regions are collated. Between every possible divisions, the Mahalanobis Distance is computed with respect to these two variables.

Based on a set of morphological distances computed between the grayscale images (spatial fields) of similar size specifications, the ratios of selected morphological distances, and the ratios of areas of infima and suprema of grayscale images, a new metric to quantify the degree of similarity between the grayscale images is proposed. We denote the two spatial fields (grayscale images), respectively, with f(i) and f(j), and the infima and suprema of these spatial fields with (f(i)∧f(j)) and ( f(i)∨f(j)). The three morphology-based distances include: 1) dilation distance d( f(i),f(j)) ; 2) erosion distance e( f(i),f(j)); and 3) median-based distance MN ( f(i),f(j)) . By employing these parameters, which play vital role in construction of parameter-specific interaction matrices, we provide a metric to designate every possible pair of images that can be considered out of a database consisting of a huge number of images. We demonstrate the whole approach on: 1) synthetic spatial fields; 2) a set of 12 similar-sized grayscale images representing cloud-top temperatures of a specific region for 12 different time instants; and 3) four spatial elevation fields to rank possible pairs of images.

The author of the paper "Visualization of Spatiotemporal Behavior of Discrete Maps via Generation of Recursive Median Elements," which appeared in the IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 32, no. 2, pp. 378-384, Feb. 2010, points out various corrections to equation (15), Table 3, and the first sentence following this table on page 383. The author is grateful to Raghvendra Sharma for finding these typos/errors while understanding the algorithm's description.

The ability to derive spatially significant zones (e.g., water bodies and zones of influence) within a cluster of zones has interesting applications in understanding commonly sharing physical mechanisms. Using a morphological dilation distance technique, we introduce geometric-based criteria that serve as indicator of the spatial significance of zones within a cluster of zones. This letter focuses on the problem of identifying zones that are “strategic” in the sense that they are the most central or important based on their proximity to other zones. We have applied this technique to a task aiming at detecting a spatially significant water body from a cluster of water bodies retrieved from Indian Remote Sensing Satellite Linear Imaging Self-scanning Sensor (IRS LISS-III) multispectral satellite data.

Automatic detection of orientation of mapped units via directional granulometries is addressed in this letter. A flat symmetric structuring element (B) of size 3 × 3 with nine elements, which is a disk in eight-connectivity grid, is decomposed into four 1-D directional structuring elements (Bis). Multiscale opening transformations are performed on each mapped unit with respect to these four directional structuring elements to eventually compute direction-specific morphologic entropy values. Based on these values, the orientations of mapped units are classified into four classes that include those units with orientations of: i) South East-North West (B1), ii) North-South (B2), iii) South West-North East (B3), and iv) East-West (B4). We demonstrated this approach on five model objects, and nine major river basins extracted from DEM of Indian peninsular. This approach yields quantitative results, based on which the mapped units could be automatically classified into four different orientations.

Data about many variables are available as numerical values at specific geographical locations. We develop a methodology based on mathematical morphology to convert point-specific data into zonal map. This methodology relies on weighted skeletonization by zone of influence that determines the points of contact of multiple frontlines propagating, from various points spread over the space, at the traveling rates depending upon the variable's strength. We demonstrate this approach for converting rainfall data available at specific rain gauge locations (points) into a spatially distributed zonal map that suggests zones of equal rainfall.

Spatial interpolation is one of the demanding techniques in Geographic Information Science (GISci) to generate interpolated maps in a continuous manner by using two discrete spatial and/or temporal data sets. Noise-free data (thematic layers) depicting a specific theme at varied spatial or temporal resolutions consist of connected components either in aggregated or in disaggregated forms. This short paper provides a simple framework: 1) to categorize the connected components of layered sets of two different time instants through their spatial relationships and the Hausdorff distances between the companion-connected components and 2) to generate sequential maps (interpolations) between the discrete thematic maps. Development of the median set, using Hausdorff erosion and dilation distances to interpolate between temporal frames, is demonstrated on lake geometries mapped at two different times and also on the bubonic plague epidemic spread data available for 11 consecutive years. We documented the significantly fair quality of the median sets generated for epidemic data between alternative years by visually comparing the interpolated maps with actual maps. They can be used to visualize (animate) the spatiotemporal behavior of a specific theme in a continuous sequence.

A speech model inspired by the signal subspace methods was recently proposed as a speech classifier with modest results. Fashioned along a "best representation" approach, the absence of valuable interclass information in the speech model, however, impairs the ability of the classifier to distinguish between phonetically alike classes. This letter proposes an improved classifier that implements interclass information. Specifically, a measure of the discriminative quality of individual class elements is defined and determined for all class elements. The discrimination measures thus obtained are subsequently applied in the classification procedure. Simulation results of the proposed signal subspace classifier in an isolated digit speech recognition problem reveal an improved performance over its predecessor

A speech model inspired by the signal subspace approach was recently proposed as a speech classifier with modest results. The method entails, in general, the assemblage of a set of subspace trajectories that consist of the right singular vectors of measurement matrices of the signal under consideration. Given an unknown signal, a simple distortion measure then applies in the classification procedure to pick the best matched class prototype. This letter examines the issue of robustness in the subspace classification scheme. Borrowing an important result on noisy measurement matrices, this letter formally establishes the notion of robustness in subspace classification and proceeds to propose a class of robust distortion measures for signal subspace models. Simulation results of subspace classifiers implementing the new distortion measures in an isolated digit speech recognition problem reveal no degradation in recognition accuracy, even under low SNR conditions.

We provide a simple and elegant framework based on morphological transformations to generate multiscale digital elevation models (DEMs) and to extract topologically significant multiscale geophysical networks. These terrain features at multiple scales are collectively useful in deriving scaling laws, which exhibit several significant terrain characteristics. We present results derived from a part of Cameron Highlands DEM.

Training methodology of the Back Propagation Network (BPN) is well documented. One aspect of BPN that requires investigation is whether or not the BPN would get trained for a given training data set and architecture. In this paper the behavior of the BPN is analyzed during its training phase considering convergent and divergent training data sets. Evolution of the weights during the training phase was monitored for the purpose of analysis. The evolution of weights was plotted as return map and was characterized by means of fractal dimension. This fractal dimensional analysis of the weight evolution trajectories is used to provide a new insight to understand the behavior of BPN and dynamics in the evolution of weights.

This short note presents an application of an algorithm to extract two singular networks of topological interest, such as channel and ridge connectivity networks, from a contour based Digital Elevation Model (DEM) of a region with hilly terrain. From these two extracted networks, a sub-watershed map of this region has been automatically generated. This study facilitates in understanding the watershed morphological processes in a firm quantitative manner in discrete space.