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27
Geometric Theory of Images
, 1998
"... space whose dimension is measured A measure F A field V A vector space U Open sets H s Hausdor# measure Appendix B # A Gaussian probability density function # # A Gaussian distribution tangent to a manifold ## A Gaussian distribution normal to a manifold # Sample covariance matrix E, ..."
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space whose dimension is measured A measure F A field V A vector space U Open sets H s Hausdor# measure Appendix B # A Gaussian probability density function # # A Gaussian distribution tangent to a manifold ## A Gaussian distribution normal to a manifold # Sample covariance matrix E, E Error cost functions x x Center of a#ne subspace x Sample mean X A shifted data matrix Appendix C No special symbols Appendix D # Set of all images I An image I(x) Pixel brightness of image I at x P() A morph between two images Z(, , ) A general morph between images # A control line # Unit vector along the control line # # Vector perpendicular to the control line # # 1 ,# 0 The destination and source endpoints of # # The perpendicular proportion of a point to a control line # The signed perpendicular distance of a point to a control line d The Euclidean distance of a point to a control line #(#, , x) The point with the same relation to the control line # as ...
Projective Mappings for Image Warping
 in Fundamentals of Texture Mapping and Image Warping (Paul Heckbert, Master’s Thesis), U.C.Berkeley
, 1989
"... The homogeneous representation for points provides a consistent notation for affine and projective mappings. Homogeneous notation was used in projective geometry [Maxwell46], [Coxeter78] long before its introduction to computer graphics [Roberts66]. The homogeneous notation is often misunderstood so ..."
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The homogeneous representation for points provides a consistent notation for affine and projective mappings. Homogeneous notation was used in projective geometry [Maxwell46], [Coxeter78] long before its introduction to computer graphics [Roberts66]. The homogeneous notation is often misunderstood so we will take a moment to clarify its use and properties. In familiar Euclidean geometry we represent points of the real plane 2 by vectors of the form ¡£¢¥¤§¦© ¨. Projective geometry deals with the projective plane, a superset of the real plane, whose homogeneous coordinates are ¡£¢���¤§¦��£¤§�� ¨. In projective geometry the 2D real point ¡£¢¥¤§¦©¨ nonzero number. Vectors of the form � for � is represented by the homogeneous vector, where is an arbitrary 0 form the equivalence class of homogeneous representations for the real point ¡£¢¥¤§¦© ¨. To recover the actual coordinates from a homogeneous vector, we simply divide by the homogeneous component; e.g., the homogeneous vector ����¡£¢���¤§¦���¤§��¨���¡£¢��£¤§¦���¤§�� ¨ represents the actual point ¡£¢¥¤§¦©¨���¡£¢�������¤§¦������� ¨. This division, a projection onto the �� � 1 plane, cancels the effect of scalar multiplication by �. When representing real points with homogeneous notation we could use any nonzero � , but it is usually most convenient to choose �� � 1 so that the real coordinates can be recovered without division. Projective space also includes the points at infinity: vectors of the form ¡£¢��£¤§¦��£ ¤ 0 ¨ , excluding ¡ 0 ¤ 0 ¤ 0 ¨. The points at infinity lie on the line at infinity. We will see later how augmentation of the real plane by these points simplifies projective geometry. In homogeneous notation, 2D points are represented by 3vectors and 3D points are represented by 4vectors. For affine and projective mappings, we denote points in source space by ����� ¡£����¤§���£¤��� ¨ and points in the destination space by ������¡£¢���¤§¦���¤§�� ¨. 2
1 Wideband, bandpass and versatile Hybrid Filter Bank A/D conversion for software radio
, 2009
"... Abstract—This paper deals with analogtodigital (A/D) conversion for future software/cognitive radio systems. For these applications, A/D converters should convert wideband signals and offer high resolutions. In order to achieve this and to overcome technological limitations, the A/D conversion sys ..."
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Abstract—This paper deals with analogtodigital (A/D) conversion for future software/cognitive radio systems. For these applications, A/D converters should convert wideband signals and offer high resolutions. In order to achieve this and to overcome technological limitations, the A/D conversion systems should be versatile, i.e. it should be possible to adapt the conversion characteristics (resolution and bandwidth) by software. This work studies and adapts Hybrid Filter Banks (HFBs) in this context. First, HFBs, which can provide large conversion bandwidth, are extended to bandpass sampling, thus minimizing the sampling frequency. Then, we provide efficient ways of improving the HFB resolution in a smaller frequency band, only by reprogramming the digital part. Moreover, this study takes into account the main drawback of HFBs which is their very high sensitivity to analog imperfections. Simulation results are presented to demonstrate the performance of HFBs. Index Terms—Analogtodigital conversion, hybrid filter
Maximum Likelihood Estimation Of Exponentials Contained In SignalDependent Noises
, 1991
"... The problem of maximum likelihood estimation (MLE) of exponentials in signaldependent noise is addressed as well as a methodology to attack the problem. Estimation of exponentials has a long history, but much of the research is aimed at the stationary noise case. Signaldependent noise can arise ..."
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The problem of maximum likelihood estimation (MLE) of exponentials in signaldependent noise is addressed as well as a methodology to attack the problem. Estimation of exponentials has a long history, but much of the research is aimed at the stationary noise case. Signaldependent noise can arise in a variety of circumstances, however, e.g. magnetic and optical recording. A general signal model, loglikelihood function, and CramerRao lower bounds (CRB) are developed for the signaldependent noise case. A methodology splits the MLE problem into linear transformations, coarse search, localized search, and quality metric phases. An additional CRB derivation is used to assess the linear transforms for the estimation problem. Classical and multilayer perceptron artificial ...
I. In1roduction
"... This paper describes a novel approach to monitoring the condition of small permanentmagnet synchronous motors (PMSM) uperating under thermal stress. The approach begins with the estiraalion of lemperaturedependenl motor parameters from measurements of line voltages and currents. The parameters ..."
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This paper describes a novel approach to monitoring the condition of small permanentmagnet synchronous motors (PMSM) uperating under thermal stress. The approach begins with the estiraalion of lemperaturedependenl motor parameters from measurements of line voltages and currents. The parameters are then used to derive estimates of motor temperatures. Next, the electrically estimated temperatures are combined with a surface measurement of motor temperature and a dynamic thcrmal model of the motor to yield an observer that is a Kalman filter
1 Projective Mappings for Image Warping
, 1995
"... The homogeneous representation for points provides a consistent notation for affine and projective mappings. Homogeneous notation was used in projective geometry [Maxwell46], [Coxeter78] long before its introduction to computer graphics [Roberts66]. The homogeneous notation is often misunderstood so ..."
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The homogeneous representation for points provides a consistent notation for affine and projective mappings. Homogeneous notation was used in projective geometry [Maxwell46], [Coxeter78] long before its introduction to computer graphics [Roberts66]. The homogeneous notation is often misunderstood so we will take a moment to clarify its use and properties. In familiar Euclidean geometry we represent points of the real plane 2 by vectors of the form. Projective geometry deals with the projective plane, a superset of the real plane, whose homogeneous coordinates are. In projective geometry the 2D real point is represented by the homogeneous vector, where is an arbitrary nonzero number. Vectors of the form for 0 form the equivalence class of homogeneous representations for the real point. To recover the actual coordinates from a homogeneous vector, we simply divide by the homogeneous component; e.g., the homogeneous vector represents the actual point! #" $ %" $. This division, a projection onto & the 1 plane, cancels the effect of scalar multiplication by. When
The American Mathematical Monthly is currently published by Mathematical Association of America.
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
A Markov Game Controller for Finite State Space Nonlinear Systems
"... Abstract — The optimal control problem for nonlinear systems, in presence of external disturbances, has been formulated as a twoplayer zerosum Markov game between the disturbance and the control. In Reinforcement Learning (RL) paradigm, controller design for nonlinear systems has been framed eithe ..."
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Abstract — The optimal control problem for nonlinear systems, in presence of external disturbances, has been formulated as a twoplayer zerosum Markov game between the disturbance and the control. In Reinforcement Learning (RL) paradigm, controller design for nonlinear systems has been framed either using the Markov Decision Process (MDP) setting or the H ∞ theory. While MDP framework assumes a stationary environment, optimal policy generation in the H∞setting is computationally cumbersome and at times infeasible. In this paper we propose to formulate optimal control problem as finding a minmax solution of a Markov game value function and generate an optimal policy via a simple linear program The Markov game approach gives a strategy capable of handling “varying ” disturbance conditions. We empirically evaluate the approach on two finite statespace control problems: i) Inverted pendulum swingup, and ii) Steering control of a nonholonomic mobile robot, and compare its performance against standard Q learning. Copyright c ○ 2006 Yang’s