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The work examines what changes can occur to the orbit of trivially equilibrating configurations for a pseudo-rigid body possessing a natural state when perturbing loads are applied. The question is analyzed by formulating it as a problem of bifurcation on a group orbit to which the theory of singularities applies. The analysis indicates how alterations of the orbit depend upon features of the perturbing load, and of the material composing the body.

The sets of polynomial stress-strain relations for elastic points which are transversely hemitropic and transversely isotropic are presented as projections of free algebraic modules having 20 and 10 generators, respectively. Complete sets of relations for the projections are presented which allow the sets of interest to be identified as free submodules having 12 and 6 generators, respectively. The results are established using the Cartan decomposition of the representation of the adjoint action of the two-dimensional rotation and orthogonal groups on the space of three-by-three symmetric matrices. The results are compared to known representations for nonlinear transversely isotropic stress-strain relations and for linear, transversely hemitropic and transversely isotropic ones.

We present a hierarchical classification technique that discriminates broad categories of surface materials in terms of ground true features, such as water, vegetation, and soils from spectral information. Subsequently, we further discriminate these materials and extract finer ground features, like chemistries, peculiar to each. The interaction at various scales of the 3D spatial and the spectral domains is decomposed by using wavelet tools to address scale dependencies in the spatial domain, a robust spectral unmixing technique, called Hierarchical Foreground Background Analysis (HFBA) along the spectral axis. HFBA sequentially derives a series of weighting vectors discriminating features at different levels of detection: (1) constituent materials, (2) types within constituents, and (3) chemistries peculiar to each type. Our goal is two-fold. First, we present the combination of HFBA and wavelets as a supervised classification technique validating the categories imposed by the supervised classification, and manifesting clusters which can refine the classification at different scales. Second, we identify spectral redundancies between hyperspectral and multispectral information, studying mixture at different spatial/spectral resolutions and assess whether targeted features may be extracted as efficiently from multispectral data as they could be from hyperspectral data. Results on AVIRIS and simulated MODIS data illustrate the robustness and effectivity of the technique.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

We present a method for automatically registering images based on nonlinear compression. The method involves three steps: (i) analysis of the complexity of the images, (ii) high level compression for extracting control points in the images, (iii) registration of the images by matching control points. The first step analyzes the complexity of the given images. It numerically computes from any image a complexity index which determines the efficiency at which the image can be compressed. This index is used in the second step of the algorithm to select coefficients in the wavelet representation of the image to produce a highly compressed image. The wavelet coefficients of the highly compressed image are then transformed to pixel values. Only a few pixel values are nontrivial. The third stage of the algorithm uses a point alignment technique to identify matching control points and to erect the registering transformations. The algorithm is tested on two quite different scenes: a portrait, representing an uncomplicated scene, and a Landsat TM image of the Pacific Northwest. In both cases, images are tested which differ by a rotation and which differ by a rigid transformation. The algorithm allows a choice of different metrics in which to do the compression and selection of control points.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The need for fast, accurate, and reliable image registration techniques is increasing primarily due to the large amount of remote sensing data which will be generated by future Earth and space missions and the diversity of such data in temporal, spatial and spectral components. Registration of the remote sensing imagery is one of the most important steps in view of further processing and interpretation of such data since the information fusion from multiple sensors start with the registration of the data. Traditional approaches to image registration require substantial human involvement in the selection and matching of the ground control points in the reference and input data sets. Considering the dramatic increase that is predicted in the volume of remote sensing data that will be collected during future missions, it is imperative that fully automatic registration algorithms be utilized. We present a three-step approach to automatic registration of remote sensing imagery. The first step involves the wavelet decomposition of the reference and input images to be registered. In the second step, we extract domain independent features to be used as the control points from the low-low components of the wavelet decompositions of the reference and input images employing the Lerner algebraic edge detector (LAED) and the Sobel edge detector. Finally, we utilize the maxima of the low-low wavelet coefficients preprocessed by the edge detectors and an exclusive-or based similarity metric to compute the transformation function. We illustrate the effectiveness of the proposed registration method on a Landsat thematic mapper image of the Pacific Northwest, and show that the performance of the LAED is superior to that of the Sobel edge detector.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In an earlier paper [Pierce, J. F. 1968. Application of combinatorial programming to a class of all-zero-one integer programming problems. Management Sci. 15 (3, November) 191–209.] combinatorial programming procedures were presented for solving a class of integer programming problems in which all elements are zero or one. By representing the problem elements in a binary computer as bits in a word and employing logical “and” and “or” operations in the problem-solving process, a number of problems involving several hundred integer variables were solved in a matter of seconds. In the present paper a number of improvements in these earlier algorithms are presented, including a new search strategy, methods for reducing the original problem, and mechanisms for feasibility filtering in multi-word problems. With these improvements problem-solving efficiency has been increased in many instances by an order of magnitude. In addition, the present paper contains computational experience obtained in solving problems for the k-best solutions.

Problem-solving procedures based on the methods of combinatorial programming are presented for solving a class of integer programming problems in which all elements are zero or one. All of the procedures seek first a feasible solution and then successively better and better feasible solutions until ultimately one is discovered which is shown to be optimal. By representing the problem elements in a binary computer as bits in a word and employing logical “and” and “or” operations in the problem-solving process, a number of problems involving several hundred integer variables have been solved in a matter of seconds.