Anisotropic Mesh Adaptation for Image Representation

Triangular meshes have gained much interest in image representation and have been widely used in image processing. This paper introduces a framework of anisotropic mesh adaptation (AMA) methods to image representation and proposes a GPRAMA method that is based on AMA and greedy-point removal (GPR) scheme. Different than many other methods that triangulate sample points to form the mesh, the AMA methods start directly with a triangular mesh and then adapt the mesh based on a user-defined metric tensor to represent the image. The AMA methods have clear mathematical framework and provides flexibility for both image representation and image reconstruction. A mesh patching technique is developed for the implementation of the GPRAMA method, which leads to an improved version of the popular GPRFS-ED method. The GPRAMA method can achieve better quality than the GPRFS-ED method but with lower computational cost.Comment: 25 pages, 15 figure

A Voltage-Sensitive Dye-Based Assay for the Identification of Differentiated Neurons Derived from Embryonic Neural Stem Cell Cultures

BACKGROUND: Pluripotent and multipotent stem cells hold great therapeutical promise for the replacement of degenerated tissue in neurological diseases. To fulfill that promise we have to understand the mechanisms underlying the differentiation of multipotent cells into specific types of neurons. Embryonic stem cell (ESC) and embryonic neural stem cell (NSC) cultures provide a valuable tool to study the processes of neural differentiation, which can be assessed using immunohistochemistry, gene expression, Ca(2+)-imaging or electrophysiology. However, indirect methods such as protein and gene analysis cannot provide direct evidence of neuronal functionality. In contrast, direct methods such as electrophysiological techniques are well suited to produce direct evidence of neural functionality but are limited to the study of a few cells on a culture plate. METHODOLOGY/PRINCIPAL FINDINGS: In this study we describe a novel method for the detection of action potential-capable neurons differentiated from embryonic NSC cultures using fast voltage-sensitive dyes (VSD). We found that the use of extracellularly applied VSD resulted in a more detailed labeling of cellular processes compared to calcium indicators. In addition, VSD changes in fluorescence translated precisely to action potential kinetics as assessed by the injection of simulated slow and fast sodium currents using the dynamic clamp technique. We further demonstrate the use of a finite element model of the NSC culture cover slip for optimizing electrical stimulation parameters. CONCLUSIONS/SIGNIFICANCE: Our method allows for a repeatable fast and accurate stimulation of neurons derived from stem cell cultures to assess their differentiation state, which is capable of monitoring large amounts of cells without harming the overall culture

Échantillonnage basé sur les Tuiles de Penrose et applications en infographie

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal

Radial Basis Functions: Biomedical Applications and Parallelization

Radial basis function (RBF) is a real-valued function whose values depend only on the distances between an interpolation point and a set of user-specified points called centers. RBF interpolation is one of the primary methods to reconstruct functions from multi-dimensional scattered data. Its abilities to generalize arbitrary space dimensions and to provide spectral accuracy have made it particularly popular in different application areas, including but not limited to: finding numerical solutions of partial differential equations (PDEs), image processing, computer vision and graphics, deep learning and neural networks, etc. The present thesis discusses three applications of RBF interpolation in biomedical engineering areas: (1) Calcium dynamics modeling, in which we numerically solve a set of PDEs by using meshless numerical methods and RBF-based interpolation techniques; (2) Image restoration and transformation, where an image is restored from its triangular mesh representation or transformed under translation, rotation, and scaling, etc. from its original form; (3) Porous structure design, in which the RBF interpolation used to reconstruct a 3D volume containing porous structures from a set of regularly or randomly placed points inside a user-provided surface shape. All these three applications have been investigated and their effectiveness has been supported with numerous experimental results. In particular, we innovatively utilize anisotropic distance metrics to define the distance in RBF interpolation and apply them to the aforementioned second and third applications, which show significant improvement in preserving image features or capturing connected porous structures over the isotropic distance-based RBF method. Beside the algorithm designs and their applications in biomedical areas, we also explore several common parallelization techniques (including OpenMP and CUDA-based GPU programming) to accelerate the performance of the present algorithms. In particular, we analyze how parallel programming can help RBF interpolation to speed up the meshless PDE solver as well as image processing. While RBF has been widely used in various science and engineering fields, the current thesis is expected to trigger some more interest from computational scientists or students into this fast-growing area and specifically apply these techniques to biomedical problems such as the ones investigated in the present work

Fractal image compression based on Delaunay triangulation and vector quantization

International audienc

Fractal image compression based on Delaunay triangulation and vector quantization

International audienc

Fractal compression and analysis on remotely sensed imagery

Remote sensing images contain huge amount of geographical information and reflect the complexity of geographical features and spatial structures. As the means of observing and describing geographical phenomena, the rapid development of remote sensing has provided an enormous amount of geographical information. The massive information is very useful in a variety of applications but the sheer bulk of this information has increased beyond what can be analyzed and used efficiently and effectively. This uneven increase in the technologies of gathering and analyzing information has created difficulties in its storage, transfer, and processing. Fractal geometry provides a means of describing and analyzing the complexity of different geographical features in remotely sensed images. It also provides a more powerful tool to compress the remote sensing data than traditional methods. This study suggests, for the first time, the implementation of this usage of fractals to remotely sensed images. In this study, based on fractal concepts, compression and decompression algorithms were developed and applied to Landsat TM images of eight study areas with different land cover types; the fidelity and efficiency of the algorithms and their relationship with the spatial complexity of the images were evaluated. Three research hypotheses were tested and the fractal compression was compared with two commonly used compression methods, JPEG and WinZip. The effects of spatial complexity and pixel resolution on the compression rate were also examined. The results from this study show that the fractal compression method has higher compression rate than JPEG and WinZip. As expected, higher compression rates were obtained from images of lower complexity and from images of lower spatial resolution (larger pixel size). This study shows that in addition to the fractal’s use in measuring, describing, and simulating the roughness of landscapes in geography, fractal techniques were useful in remotely sensed image compression. Moreover, the compression technique can be seen as a new method of measuring the diverse landscapes and geographical features. As such, this study has introduced a new and advantageous passageway for fractal applications and their important applications in remote sensing