On The Continuous Steering of the Scale of Tight Wavelet Frames

In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation of steering steerable wavelets. The fundamental aspects of the construction are the same: an admissible collection of Fourier multipliers is used to extend a tight wavelet frame, and the "scale" of the wavelets is adapted by scaling the multipliers. As an application, the proposed wavelets can be used to improve the frequency localization. Importantly, the localized frequency bands specified by this construction can be scaled efficiently using matrix multiplication

Biologically inspired feature extraction for rotation and scale tolerant pattern analysis

Biologically motivated information processing has been an important area of scientific research for decades. The central topic addressed in this dissertation is utilization of lateral inhibition and more generally, linear networks with recurrent connectivity along with complex-log conformal mapping in machine based implementations of information encoding, feature extraction and pattern recognition. The reasoning behind and method for spatially uniform implementation of inhibitory/excitatory network model in the framework of non-uniform log-polar transform is presented. For the space invariant connectivity model characterized by Topelitz-Block-Toeplitz matrix, the overall network response is obtained without matrix inverse operations providing the connection matrix generating function is bound by unity. It was shown that for the network with the inter-neuron connection function expandable in a Fourier series in polar angle, the overall network response is steerable. The decorrelating/whitening characteristics of networks with lateral inhibition are used in order to develop space invariant pre-whitening kernels specialized for specific category of input signals. These filters have extremely small memory footprint and are successfully utilized in order to improve performance of adaptive neural whitening algorithms. Finally, the method for feature extraction based on localized Independent Component Analysis (ICA) transform in log-polar domain and aided by previously developed pre-whitening filters is implemented. Since output codes produced by ICA are very sparse, a small number of non-zero coefficients was sufficient to encode input data and obtain reliable pattern recognition performance

Multi-Sensor Image Registration, Fusion and Dimension Reduction

With the development of future spacecraft formations comes a number of complex challenges such as maintaining precise relative position and specified attitudes, as well as being able to communicate with each other. More generally, with the advent of spacecraft formations, issues related to performing on-board and automatic data computing and analysis as well as decision planning and scheduling will figure among the most important requirements. Among those, automatic image registration, image fusion and dimension reduction represent intelligent technologies that would reduce mission costs,would enable autonomous decisions to be taken on-board, and would make formation flying adaptive, self-reliant, and cooperative. For both on-board and on-the-ground applications, the particular need for dimension reduction is two-fold, first to reduce the communication bandwidth, second as a pre-processing to make computations feasible,simpler and faster

Statistical analysis and transfer of coarse-grain pictorial style

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 96-103).We show that image statistics can be used to analyze and transfer simple notions of pictorial style of paintings and photographs. We characterize the frequency content of pictorial styles, such as multi-scale, spatial variations, and anisotropy properties, using a multi-scale and oriented decomposition, the steerable pyramid. We show that the average of the absolute steerable coefficients as a function of scale characterizes simple notions of "look" or style. We extend this approach to account for image non-stationarity, that is, we capture and transfer the spatial variations of multi-scale content. In addition, we measure the standard deviation of the steerable coefficients across orientation, which characterizes image anisotropy and permits analysis and transfer of oriented structures. We focus on the statistical features that can be transferred. Since we couple analysis and transfer, our statistical model and transfer tools are consistent with the visual effect of pictorial styles. For this reason, our technique leads to more intuitive manipulation and interpolation of pictorial styles. In addition, our statistical model can be used to classify and retrieve images by style.by Soonmin Bae.S.M