Samir Chettri

Spectral unmixing of remotely sensed imagery using maximum entropy

This paper addresses the importance of a maximum entropy formulation for the extraction of content from a single picture element in a remotely sensed image. Most conventional classifiers assume a winner take all procedure in assigning classes to a pixel whereas in general it is the case that there exists more than one class within the picture element. There have been attempts to perform spectral unmixing using variants of least-squares techniques, but these suffer from conceptual and numerical problems which include the possibility that negative fractions of ground cover classes may be returned by the procedure. In contrast, a maximum entropy (MAXENT) based approach for sub-pixel content extraction possesses the useful information theoretic property of not assuming more information than is given, while automatically guaranteeing positive fractions. In this paper we apply MAXENT to obtain the fractions of ground cover classes present in a pixel and show its clear numerical superiority over conventional methods. The optimality of this method stems from the combinatorial properties of the information theoretic entropy.

Harmonic wavelets, constant Q transforms, and the cone kernel TFD

In this research we compare general harmonic wavelet transforms (GHWT), constant Q transforms (CQT) and the Cone kernel time-frequency distribution (CKTFD) for the analysis of musical signals. The first two consist of a series of band pass filters that have a constant Q (quality), each of which correspond to a semitone interval (or better) in the musical scale. The CKTFD is not a constant Q type transform but belongs to the more general class of bilinear time-frequency distributions with the special property of reducing the (usually) undesirable interference terms common in these types of distributions. Their computation schemes are compared and the advantages of each discussed. All three have a structure that may be easily parallelized. We used the three methods to analyze a musical note (middle C) played on an electric piano. There are subtle differences in the results of the methods. All three quite clearly show the first four harmonics of the musical note (C4). However, the CQT reveals that harmonics higher than four extend in time for almost the entire duration of the note. Neither the GHWT nor the CKTFD show harmonics higher than four for the entire length of the signal, though they do reveal them (i.e., frequencies higher than 1024 Hz.) at the initiation of the note. The power spectrum of the signal does reveal harmonics from one through four as having most of the power but harmonics five through ten are also revealed. Unfortunately, the time variation of the signal cannot be extracted from the power spectrum hence the use of time-frequency or time-scale diagrams. Aside from musical applications, such methods would be useful for t-f analysis of vibrating machinery.

De-noising remotely sensed digital imagery

This paper applies two recent methods to denoise remotely sensed images - wavelet based Markov Random Field (MRF) methods, Independent Component Analysis (ICA) and compares them with the standard Wiener filter. In order to facilitate the continued use of these methods in remote sensing the theory behind each method is discussed in detail. Subsequently they are applied to de-noising remotely sensed images. The efficiency of each algorithm is obtained by computing the signal to noise ratio (SNR) before and after de-noising. Results indicate that the MRF based methods, though slightly more complicated to program and only marginally slower than ICA de-noising, generally perform better than both ICA and Wiener filtering. The article ends by discussing future areas of research in de-noising remotely sensed images.

Comparing the computational complexity of the PNN, the PDM, and the MMNN (M2N2)

In classification, the goal is to assign an input vector to a discrete number of output classes. Classifier design has a long history and they have been put to a large number of uses. In this paper we continue the task of categorizing classifiers by their computational complexity as begun. In particular, we derive analytical formulas for the number of arithmetic operations in the probabilistic neural network (PNN) and its polynomial expansion, also known as the polynomial discriminant method (PDM) and the mixture model neural network (M2N2). In addition we perform tests of the classification accuracy of the PDM with respect to the PNN and the M2N2 find that all three are close in accuracy. Based on this research we now have the ability to choose one or the other based on the computational complexity, the memory requirements and the size of the training set. This is a great advantage in an operational environment. We also discus the extension of such methods to hyperspectral data and find that only the M2N2 is suitable for application to such data.

Newton, Einstein, Jeffreys and Bayesian model selection

In Jefferys and Berger apply Bayesian model selection to the problem of choosing between rival theories, in particular between Einstein’s theory of general relativity (GR) and Newtonian gravity (NG). [1] presents a debate between Harold Jeffreys and Charles Poor regarding the observed 43″/century anomalous perhelion precession of Mercury. GR made a precise prediction of 42.98″/century while proponents of NG suggested several physical mechanisms that were eventually refuted, with the exception of a modified inverse square law. Using Bayes Factors (BF) and data available in 1921, shows that GR is preferable to NG by a factor of about 25 to 1. A scale for BF used by Jeffreys, suggests that this is positive to strong evidence for GR over modified NG but it is not very strong or even overwhelming.In this work we calculate the BF from the period 1921 till 1993. By 1960 we see that the BF, due to better data gathering techniques and advances in technology, had reached a factor of greater than 100 to 1, making GR...

Parallel image classification on the HIVE

Remotely sensed imagery represents a growing source of information to many practical applications. Technologies to rapidly process imagery data into useful information products has not kept pace with the rapidly growing volume and complexity of imagery data increasingly available from Government and commercial sources. Significant processing speed improvements have been achieved by implementation of classification methods on the highly-parallel integrated virtual environment (HIVE) - a Beowulf class system using parallel virtual machine software. This paper discusses our parallel processing architecture and how three different classification algorithms performed in this computing environment. Also discussed are conclusions and recommendations for future work to apply these techniques to more complex data and further improve the processing speeds.

Stereo pair design for cameras with a fovea

In this paper we describe the methodology for the design and selection of a stereo pair when the cameras have a greater concentration of sensing elements in the center of the image plane (fovea). Binocular vision is important for the purpose of depth estimation, which in turn is important in a variety of applications such as gaging and autonomous vehicle guidance. Thus, proper design of a stereo pair is essential if we are to be successful in these areas. In this paper we assume that one camera has square pixels of size dv and the other has pixels of size rdv, where 0 < r