A note on circle packing

The problem of packing circles into a domain of prescribed topology is considered. The circles need not have equal radii. The Collins-Stephenson algorithm computes such a circle packing. This algorithm is parallelized in two different ways and its performance is reported for a triangular, planar domain test case. The implementation uses the highly parallel graphics processing unit (GPU) on commodity hardware. The speedups so achieved are discussed based on a number of experiments.     

On the method-independent lower bound (MILB) to the variance of attenuation estimation in random reflection

Based on the Cramer-Rao inequality, the MILB is calculated for the problem of estimating the frequency slope of the attenuation coefficient of tissue from random reflections of ultrasonic waves. Under typical signal conditions, this bound for a 1-cm x 1-cm region was found to be about 0.08 db/(MHz-cm), rather close to the clinical requirement of 0.1 dB/(MHz-cm). Comparison to existing methods (including an autoregressive deconvolution method) shows room for further improvement.     

Color quantitation through image processing in dermatology

Classical color models and their applications to computer vision are reviewed. The performances of color quantitation from digitized images are compared with those derived from a chromameter. The color quantitation obtained from either digitized color slides or directly digitized images is proved to be more efficient than the conventional visual assessment of observers. A methodology is proposed for determining the specific color indices which are needed in dermatology. An application of this methodology is developed for designing a blanching quantitation index in order to replace the visual assessment during McKenzie tests.     

3-D segmentation of MR images of the head for 3-D display

Algorithms for 3-D segmentation and reconstruction of anatomical surfaces from magnetic resonance imaging (MRI) data are presented. The 3-D extension of the Marr-Hildreth operator is described, and it is shown that its zero crossings are related to anatomical surfaces. For an improved surface definition, morphological filters-dilation and erosion-are applied. From these contours, 3-D reconstructions of skin, bone, brain, and the ventricular system can be generated. Results obtained with different segmentation parameters and surface rendering methods are presented. The fidelity of the generated images comes close to anatomical reality. It is noted that both the convolution and the morphological filtering are computationally expensive, and thus take a long time on a general-purpose computer. Another problem is assigning labels to the constituents of the head; in the current implementation, this is done interactively.     

Ring piezoelectric transducers radiating ultrasonic energy into the air

Ring piezoelectric transducers generating ultrasonic energy in air were designed and tested experimentally and numerically. The radiation pattern of the transducer is very narrow (4 degrees ) and its frequency response has a broadband character. Resonant frequencies of the transducers were determined experimentally and verified theoretically. Applications of the proposed ring transducers in a robotic ranging system were examined.     

Using previous models to bias structural learning in the hierarchical BOA

Estimation of distribution algorithms (EDAs) are stochastic optimization techniques that explore the space of potential solutions by building and sampling explicit probabilistic models of promising candidate solutions. While the primary goal of applying EDAs is to discover the global optimum or at least its accurate approximation, besides this, any EDA provides us with a sequence of probabilistic models, which in most cases hold a great deal of information about the problem. Although using problem-specific knowledge has been shown to significantly improve performance of EDAs and other evolutionary algorithms, this readily available source of problem-specific information has been practically ignored by the EDA community. This paper takes the first step toward the use of probabilistic models obtained by EDAs to speed up the solution of similar problems in the future. More specifically, we propose two approaches to biasing model building in the hierarchical Bayesian optimization algorithm (hBOA) based on knowledge automatically learned from previous hBOA runs on similar problems. We show that the proposed methods lead to substantial speedups and argue that the methods should work well in other applications that require solving a large number of problems with similar structure.     

A neuron membrane mesh representation for visualization of electrophysiological simulations

We present a process to automatically generate three-dimensional mesh representations of the complex, arborized cell membrane surface of cortical neurons (the principal information processing cells of the brain) from nonuniform morphological measurements. Starting from manually sampled morphological points (3D points and diameters) from neurons in a brain slice preparation, we construct a polygonal mesh representation that realistically represents the continuous membrane surface, closely matching the original experimental data. A mapping between the original morphological points and the newly generated mesh enables simulations of electrophysiolgical activity to be visualized on this new membrane representation. We compare the new mesh representation with the state of the art and present a series of use cases and applications of this technique to visualize simulations of single neurons and networks of multiple neurons.     

A note on octonionic support vector regression

This note presents an analysis of the octonionic form of the division algebraic support vector regressor (SVR) first introduced by Shilton A detailed derivation of the dual form is given, and three conditions under which it is analogous to the quaternionic case are exhibited. It is shown that, in the general case of an octonionic-valued feature map, the usual "kernel trick" breaks down. The cause of this (and its interpretation) is discussed in some detail, along with potential ways of extending kernel methods to take advantage of the distinct features present in the general case. Finally, the octonionic SVR is applied to an example gait analysis problem, and its performance is compared to that of the least squares SVR, the Clifford SVR, and the multidimensional SVR.     

On mesh-free valley surface extraction with application to low frequency sound simulation

Crease surfaces describe extremal structures of 3D scalar fields. We present a new region-growing-based approach to the meshless extraction of adaptive nonmanifold valley and ridge surfaces that overcomes limitations of previous approaches by decoupling point seeding and triangulation of the surface. Our method is capable of extracting valley surface skeletons as connected minimum structures. As our algorithm is inherently mesh-free and curvature adaptive, it is suitable for surface construction in fields with an arbitrary neighborhood structure. As an application for insightful visualization with valley surfaces, we choose a low frequency acoustics simulation. We use our valley surface construction approach to visualize the resulting complex-valued scalar pressure field for arbitrary frequencies to identify regions of sound cancellation. This provides an expressive visualization of the topology of wave node and antinode structures in simulated acoustics.