Cleve Moler

Bio: Cleve Moler is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 977 citations.

Closed-form solution of absolute orientation using unit quaternions

Abstract: Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task . It finds applications i n stereoph and in robotics . I present here a closed-form solution to the least-squares problem for three or more paints . Currently various empirical, graphical, and numerical iterative methods are in use . Derivation of the solution i s simplified by use of unit quaternions to represent rotation . I emphasize a symmetry property that a solution to thi s problem ought to possess . The best translational offset is the difference between the centroid of the coordinates i n one system and the rotated and scaled centroid of the coordinates in the other system . The best scale is equal to th e ratio of the root-mean-square deviations of the coordinates in the two systems from their respective centroids . These exact results are to be preferred to approximate methods based on measurements of a few selected points . The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue o f a symmetric 4 X 4 matrix . The elements of this matrix are combinations of sums of products of correspondin g coordinates of the points .

A pyramid approach to subpixel registration based on intensity

Abstract: We present an automatic subpixel registration algorithm that minimizes the mean square intensity difference between a reference and a test data set, which can be either images (two-dimensional) or volumes (three-dimensional). It uses an explicit spline representation of the images in conjunction with spline processing, and is based on a coarse-to-fine iterative strategy (pyramid approach). The minimization is performed according to a new variation (ML*) of the Marquardt-Levenberg algorithm for nonlinear least-square optimization. The geometric deformation model is a global three-dimensional (3-D) affine transformation that can be optionally restricted to rigid-body motion (rotation and translation), combined with isometric scaling. It also includes an optional adjustment of image contrast differences. We obtain excellent results for the registration of intramodality positron emission tomography (PET) and functional magnetic resonance imaging (fMRI) data. We conclude that the multiresolution refinement strategy is more robust than a comparable single-stage method, being less likely to be trapped into a false local optimum. In addition, our improved version of the Marquardt-Levenberg algorithm is faster.

Theory of the backpropagation neural network

Abstract: Publisher Summary This chapter presents a survey of the elementary theory of the basic backpropagation neural network architecture, covering the areas of architectural design, performance measurement, function approximation capability, and learning. The survey includes a formulation of the backpropagation neural network architecture to make it a valid neural network and a proof that the backpropagation mean squared error function exists and is differentiable. Also included in the survey is a theorem showing that any L2 function can be implemented to any desired degree of accuracy with a three-layer backpropagation neural network. An appendix presents a speculative neurophysiological model illustrating the way in which the backpropagation neural network architecture might plausibly be implemented in the mammalian brain for corticocortical learning between nearby regions of cerebral cortex. One of the crucial decisions in the design of the backpropagation architecture is the selection of a sigmoidal activation function.

Kinetics of water loss from cells at subzero temperatures and the likelihood of intracellular freezing.

Abstract: The survival of various cells subjected to low temperature exposure is higher when they are cooled slowly. This increase is consistent with the view that slow cooling decreases the probability of intracellular freezing by permitting water to leave the cell rapidly enough to keep the protoplasm at its freezing point. The present study derives a quantitative relation between the amount of water in a cell and temperature. The relation is a differential equation involving cooling rate, surface-volume ratio, membrane permeability to water, and the temperature coefficient of the permeability constant. Numerical solutions to this equation give calculated water contents which permit predictions as to the likelihood of intracellular ice formation. Both the calculated water contents and the predictions on internal freezing are consistent with the experimental observations of several investigators.