Topologically Accurate Dual Isosurfacing Using Ray Intersection

“Dual contouring” approaches provide an alternative to standard Marching Cubes (MC) method to extract and approximate an isosurface from trivariate data given on a volumetric mesh. These dual approaches solve some of the problems encountered by the MC methods. We present a simple method based on the MC method and the ray intersection technique to compute isosurface points in the cell interior. One of the advantages of our method is that it does not require us to use Hermite interpolation scheme, unlike other dual contouring methods. We perform a complete analysis of all possible configurations to generate a look-up table for all configurations. We use the look-up table to optimize the ray-intersection method to obtain minimum number of points necessarily sufficient for defining topologically correct isosurfaces in all possible configurations. Isosurface points are connected using a simple strategy.

Volume Haptics and Dendritic Spine Editing

Esta tesis se ha desarrollado en el contexto del proyecto Cajal Blue Brain, una iniciativa europea dedicada al estudio del cerebro. Uno de los objetivos de esta iniciativa es desarrollar nuevos métodos y nuevas tecnologías que simplifiquen el análisis de datos en el campo neurocientífico. El presente trabajo se ha centrado en diseñar herramientas que combinen información proveniente de distintos canales sensoriales con el fin de acelerar la interacción y análisis de imágenes neurocientíficas. En concreto se estudiará la posibilidad de combinar información visual con información háptica. Las espinas dendríticas son pequeñas protuberancias que recubren la superficie dendrítica de muchas neuronas del cerebro. A día de hoy, se cree que tienen un papel clave en la transmisión de señales neuronales. Motivo por el cual, el interés por parte de la comunidad científica por estas estructuras ha ido en aumento a medida que las técnicas de adquisición de imágenes mejoraban hasta alcanzar una calidad suficiente para analizar dichas estructuras. A menudo, los neurocientíficos utilizan técnicas de microscopía con luz para obtener los datos que les permitan analizar estructuras neuronales tales como neuronas, dendritas y espinas dendríticas. A pesar de que estas técnicas ofrezcan ciertas ventajas frente a su equivalente electrónico, las técnicas basadas en luz permiten una menor resolución. En particular, estructuras pequeñas como las espinas dendríticas pueden capturarse de forma incorrecta en las imágenes obtenidas, impidiendo su análisis. En este trabajo, se presenta una nueva técnica, que permite editar imágenes volumétricas, mediante un dispositivo háptico, con el fin de reconstruir de los cuellos de las espinas dendríticas. Con este objetivo, en un primer momento se desarrolló un algoritmo que proporciona retroalimentación háptica en datos volumétricos, completando la información que provine del canal visual. Dicho algoritmo de renderizado háptico permite a los usuarios tocar y percibir una isosuperficie en el volumen de datos. El algoritmo asegura un renderizado robusto y eficiente. Se utiliza un método basado en las técnicas de “marching tetrahedra” para la extracción local de una isosuperficie continua, lineal y definida por intervalos. La robustez deriva tanto de una etapa de detección de colisiones continua de la isosuperficie extraída, como del uso de técnicas eficientes de renderizado basadas en un proxy puntual. El método de “marching tetrahedra” propuesto garantiza que la topología de la isosuperficie extraída coincida con la topología de una isosuperficie equivalente determinada utilizando una interpolación trilineal. Además, con el objetivo de mejorar la coherencia entre la información háptica y la información visual, el algoritmo de renderizado háptico calcula un segundo proxy en la isosuperficie pintada en la pantalla. En este trabajo se demuestra experimentalmente las mejoras en, primero, la etapa de extracción de isosuperficie, segundo, la robustez a la hora de mantener el proxy en la isosuperficie deseada y finalmente la eficiencia del algoritmo. En segundo lugar, a partir del algoritmo de renderizado háptico propuesto, se desarrolló un procedimiento, en cuatro etapas, para la reconstrucción de espinas dendríticas. Este procedimiento, se puede integrar en los cauces de segmentación automática y semiautomática existentes como una etapa de pre-proceso previa. El procedimiento está diseñando para que tanto la navegación como el proceso de edición en sí mismo estén controlados utilizando un dispositivo háptico. Se han diseñado dos experimentos para evaluar esta técnica. El primero evalúa la aportación de la retroalimentación háptica y el segundo se centra en evaluar la idoneidad del uso de un háptico como dispositivo de entrada. En ambos casos, los resultados demuestran que nuestro procedimiento mejora la precisión de la reconstrucción. En este trabajo se describen también dos casos de uso de nuestro procedimiento en el ámbito de la neurociencia: el primero aplicado a neuronas situadas en la corteza cerebral humana y el segundo aplicado a espinas dendríticas situadas a lo largo de neuronas piramidales de la corteza del cerebro de una rata. Por último, presentamos el programa, Neuro Haptic Editor, desarrollado a lo largo de esta tesis junto con los diferentes algoritmos ya mencionados. ABSTRACT This thesis took place within the Cajal Blue Brain project, a European initiative dedicated to the study of the brain. One of the main goals of this project is the development of new methods and technologies simplifying data analysis in neuroscience. This thesis focused on the development of tools combining information originating from distinct sensory channels with the aim of accelerating both the interaction with neuroscience images and their analysis. In concrete terms, the objective is to study the possibility of combining visual information with haptic information. Dendritic spines are thin protrusions that cover the dendritic surface of numerous neurons in the brain and whose function seems to play a key role in neural circuits. The interest of the neuroscience community toward those structures kept increasing as and when acquisition methods improved, eventually to the point that the produced datasets enabled their analysis. Quite often, neuroscientists use light microscopy techniques to produce the dataset that will allow them to analyse neuronal structures such as neurons, dendrites and dendritic spines. While offering some advantages compared to their electronic counterpart, light microscopy techniques achieve lower resolutions. Particularly, small structures such as dendritic spines might suffer from a very low level of fluorescence in the final dataset, preventing further analysis. This thesis introduces a new technique enabling the edition of volumetric datasets in order to recreate dendritic spine necks using a haptic device. In order to fulfil this objective, we first presented an algorithm to provide haptic feedback directly from volumetric datasets, as an aid to regular visualization. The haptic rendering algorithm lets users perceive isosurfaces in volumetric datasets, and it relies on several design features that ensure a robust and efficient rendering. A marching tetrahedra approach enables the dynamic extraction of a piecewise linear continuous isosurface. Robustness is derived using a Continuous Collision Detection step coupled with acknowledged proxy-based rendering methods over the extracted isosurface. The introduced marching tetrahedra approach guarantees that the extracted isosurface will match the topology of an equivalent isosurface computed using trilinear interpolation. The proposed haptic rendering algorithm improves the coherence between haptic and visual cues computing a second proxy on the isosurface displayed on screen. Three experiments demonstrate the improvements on the isosurface extraction stage as well as the robustness and the efficiency of the complete algorithm. We then introduce our four-steps procedure for the complete reconstruction of dendritic spines. Based on our haptic rendering algorithm, this procedure is intended to work as an image processing stage before the automatic segmentation step giving the final representation of the dendritic spines. The procedure is designed to allow both the navigation and the volume image editing to be carried out using a haptic device. We evaluated our procedure through two experiments. The first experiment concerns the benefits of the force feedback and the second checks the suitability of the use of a haptic device as input. In both cases, the results shows that the procedure improves the editing accuracy. We also report two concrete cases where our procedure was employed in the neuroscience field, the first one concerning dendritic spines in the human cortex, the second one referring to an ongoing experiment studying dendritic spines along dendrites of mouse cortical pyramidal neurons. Finally, we present the software program, Neuro Haptic Editor, that was built along the development of the different algorithms implemented during this thesis, and used by neuroscientists to use our procedure.

Soil CO(2) emission estimated by different interpolation techniques

Soil CO(2) emissions are highly variable, both spatially and across time, with significant changes even during a one-day period. The objective of this study was to compare predictions of the diurnal soil CO(2) emissions in an agricultural field when estimated by ordinary kriging and sequential Gaussian simulation. The dataset consisted of 64 measurements taken in the morning and in the afternoon on bare soil in southern Brazil. The mean soil CO(2) emissions were significantly different between the morning (4.54 mu mol m(-2) s(-1)) and afternoon (6.24 mu mol m(-2) s(-1)) measurements. However, the spatial variability structures were similar, as the models were spherical and had close range values of 40.1 and 40.0 m for the morning and afternoon semivariograms. In both periods, the sequential Gaussian simulation maps were more efficient for the estimations of emission than ordinary kriging. We believe that sequential Gaussian simulation can improve estimations of soil CO(2) emissions in the field, as this property is usually highly non-Gaussian distributed.

A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements

To translate and transfer solution data between two totally different meshes (i.e. mesh 1 and mesh 2), a consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements is presented in this paper. The proposed algorithm has the following significant advantages: (1) The use of a point-searching strategy allows a point in one mesh to be accurately related to an element (containing this point) in another mesh. Thus, to translate/transfer the solution of any particular point from mesh 2 td mesh 1, only one element in mesh 2 needs to be inversely mapped. This certainly minimizes the number of elements, to which the inverse mapping is applied. In this regard, the present algorithm is very effective and efficient. (2) Analytical solutions to the local co ordinates of any point in a four-node quadrilateral element, which are derived in a rigorous mathematical manner in the context of this paper, make it possible to carry out an inverse mapping process very effectively and efficiently. (3) The use of consistent interpolation enables the interpolated solution to be compatible with an original solution and, therefore guarantees the interpolated solution of extremely high accuracy. After the mathematical formulations of the algorithm are presented, the algorithm is tested and validated through a challenging problem. The related results from the test problem have demonstrated the generality, accuracy, effectiveness, efficiency and robustness of the proposed consistent point-searching algorithm. Copyright (C) 1999 John Wiley & Sons, Ltd.

Compression Efficiency Analysis of Wyner-Ziv Video Coding with Motion Compensated Side Information Interpolation

The Wyner-Ziv video coding (WZVC) rate distortion performance is highly dependent on the quality of the side information, an estimation of the original frame, created at the decoder. This paper, characterizes the WZVC efficiency when motion compensated frame interpolation (MCFI) techniques are used to generate the side information, a difficult problem in WZVC especially because the decoder only has available some reference decoded frames. The proposed WZVC compression efficiency rate model relates the power spectral of the estimation error to the accuracy of the MCFI motion field. Then, some interesting conclusions may be derived related to the impact of the motion field smoothness and the correlation to the true motion trajectories on the compression performance.

Image upsampling algorithms applied on Nuclear Medicine: comparision of hqnx and nxSaI algorithms families with two interpolation algorithms - nearest neighbour and bicubic interpolation

Introduction: Image resizing is a normal feature incorporated into the Nuclear Medicine digital imaging. Upsampling is done by manufacturers to adequately fit more the acquired images on the display screen and it is applied when there is a need to increase - or decrease - the total number of pixels. This paper pretends to compare the “hqnx” and the “nxSaI” magnification algorithms with two interpolation algorithms – “nearest neighbor” and “bicubic interpolation” – in the image upsampling operations. Material and Methods: Three distinct Nuclear Medicine images were enlarged 2 and 4 times with the different digital image resizing algorithms (nearest neighbor, bicubic interpolation nxSaI and hqnx). To evaluate the pixel’s changes between the different output images, 3D whole image plot profiles and surface plots were used as an addition to the visual approach in the 4x upsampled images. Results: In the 2x enlarged images the visual differences were not so noteworthy. Although, it was clearly noticed that bicubic interpolation presented the best results. In the 4x enlarged images the differences were significant, with the bicubic interpolated images presenting the best results. Hqnx resized images presented better quality than 4xSaI and nearest neighbor interpolated images, however, its intense “halo effect” affects greatly the definition and boundaries of the image contents. Conclusion: The hqnx and the nxSaI algorithms were designed for images with clear edges and so its use in Nuclear Medicine images is obviously inadequate. Bicubic interpolation seems, from the algorithms studied, the most suitable and its each day wider applications seem to show it, being assumed as a multi-image type efficient algorithm.

Using a prioritized medium access control protocol for incrementally obtaining an interpolation of sensor readings

This paper addresses sensor network applications which need to obtain an accurate image of physical phenomena and do so with a high sampling rate in both time and space. We present a fast and scalable approach for obtaining an approximate representation of all sensor readings at high sampling rate for quickly reacting to critical events in a physical environment. This approach is an improvement on previous work in that after the new approach has undergone a startup phase then the new approach can use a very small sampling period.

Evaluation of Spatial interpolation techniques for mapping climate variables with low sample density: a case study using a new gridded dataset of Bangladesh

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Ground truth determination for segmentation of tomographic volumes using interpolation

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Interpolation methods for stochastic processes spaces

In this paper the scales of classes of stochastic processes are introduced. New interpolation theorems and boundedness of some transforms of stochastic processes are proved. Interpolation method for generously-monotonous rocesses is entered. Conditions and statements of interpolation theorems concern he xed stochastic process, which diers from the classical results.

Interpolation and sampling in small Bergman spaces

"Vegeu el resum a l'inici del document del fitxer adjunt."

Interpolation-free Coregistration and Phase-Correction of Airborne SAR Interferograms

This letter discusses the detection and correction ofresidual motion errors that appear in airborne synthetic apertureradar (SAR) interferograms due to the lack of precision in the navigationsystem. As it is shown, the effect of this lack of precision istwofold: azimuth registration errors and phase azimuth undulations.Up to now, the correction of the former was carried out byestimating the registration error and interpolating, while the latterwas based on the estimation of the phase azimuth undulations tocompensate the phase of the computed interferogram. In this letter,a new correction method is proposed, which avoids the interpolationstep and corrects at the same time the azimuth phase undulations.Additionally, the spectral diversity technique, used to estimateregistration errors, is critically analyzed. Airborne L-bandrepeat-pass interferometric data of the German Aerospace Center(DLR) experimental airborne SAR is used to validate the method

Three-dimensional interpolation of soil data: fertility and pedomorphological features in southern Brazil

The graphical representation of spatial soil properties in a digital environment is complex because it requires a conversion of data collected in a discrete form onto a continuous surface. The objective of this study was to apply three-dimension techniques of interpolation and visualization on soil texture and fertility properties and establish relationships with pedogenetic factors and processes in a slope area. The GRASS Geographic Information System was used to generate three-dimensional models and ParaView software to visualize soil volumes. Samples of the A, AB, BA, and B horizons were collected in a regular 122-point grid in an area of 13 ha, in Pinhais, PR, in southern Brazil. Geoprocessing and graphic computing techniques were effective in identifying and delimiting soil volumes of distinct ranges of fertility properties confined within the soil matrix. Both three-dimensional interpolation and the visualization tool facilitated interpretation in a continuous space (volumes) of the cause-effect relationships between soil texture and fertility properties and pedological factors and processes, such as higher clay contents following the drainage lines of the area. The flattest part with more weathered soils (Oxisols) had the highest pH values and lower Al3+ concentrations. These techniques of data interpolation and visualization have great potential for use in diverse areas of soil science, such as identification of soil volumes occurring side-by-side but that exhibit different physical, chemical, and mineralogical conditions for plant root growth, and monitoring of plumes of organic and inorganic pollutants in soils and sediments, among other applications. The methodological details for interpolation and a three-dimensional view of soil data are presented here.