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

Feature-sensitive and Adaptive Image Triangulation: A Super-pixel-based Scheme for Image Segmentation and Mesh Generation

With increasing utilization of various imaging techniques (such as CT, MRI and PET) in medical fields, it is often in great need to computationally extract the boundaries of objects of interest, a process commonly known as image segmentation. While numerous approaches have been proposed in literature on automatic/semi-automatic image segmentation, most of these approaches are based on image pixels. The number of pixels in an image can be huge, especially for 3D imaging volumes, which renders the pixel-based image segmentation process inevitably slow. On the other hand, 3D mesh generation from imaging data has become important not only for visualization and quantification but more critically for finite element based numerical simulation. Traditionally image-based mesh generation follows such a procedure as: (1) image boundary segmentation, (2) surface mesh generation from segmented boundaries, and (3) volumetric (e.g., tetrahedral) mesh generation from surface meshes. These three majors steps have been commonly treated as separate algorithms/steps and hence image information, once segmented, is not considered any more in mesh generation. In this thesis, we investigate a super-pixel based scheme that integrates both image segmentation and mesh generation into a single method, making mesh generation truly an image-incorporated approach. Our method, called image content-aware mesh generation, consists of several main steps. First, we generate a set of feature-sensitive, and adaptively distributed points from 2D grayscale images or 3D volumes. A novel image edge enhancement method via randomized shortest paths is introduced to be an optional choice to generate the features’ boundary map in mesh node generation step. Second, a Delaunay-triangulation generator (2D) or tetrahedral mesh generator (3D) is then utilized to generate a 2D triangulation or 3D tetrahedral mesh. The generated triangulation (or tetrahedralization) provides an adaptive partitioning of a given image (or volume). Each cluster of pixels within a triangle (or voxels within a tetrahedron) is called a super-pixel, which forms one of the nodes of a graph and adjacent super-pixels give an edge of the graph. A graph-cut method is then applied to the graph to define the boundary between two subsets of the graph, resulting in good boundary segmentations with high quality meshes. Thanks to the significantly reduced number of elements (super-pixels) as compared to that of pixels in an image, the super-pixel based segmentation method has tremendously improved the segmentation speed, making it feasible for real-time feature detection. In addition, the incorporation of image segmentation into mesh generation makes the generated mesh well adapted to image features, a desired property known as feature-preserving mesh generation

Automatic Mesh-Based Segmentation of Multiple Organs in MR Images

La segmentation de structures anatomiques multiples dans des images de résonance magnétique (RM) est souvent requise dans des applications de génie biomédical telles que la simulation numérique, la chirurgie guidée par l’image, la planification de traitements, etc. De plus, il y a un besoin croissant pour une segmentation automatique d’organes multiples et de structures complexes à partir de cette modalité d’imagerie. Il existe plusieurs techniques de segmentation multi-objets qui ont été appliquées avec succès sur des images de tomographie axiale à rayons-X (CT). Cependant, dans le cas des images RM cette tâche est plus difficile en raison de l’inhomogénéité des intensités dans ces images et de la variabilité dans l’apparence des structures anatomiques. Par conséquent, l’état de l’art sur la segmentation multi-objets sur des images RM est beaucoup plus faible que celui sur les images CT. Parmi les travaux qui portent sur la segmentation d’images RM, les approches basées sur la segmentation de régions sont sensibles au bruit et la non uniformité de l’intensité dans les images. Les approches basées sur les contours ont de la difficulté à regrouper les informations sur les contours de sorte à produire un contour fermé cohérent. Les techniques basées sur les atlas peuvent avoir des problèmes en présence de structures complexes avec une grande variabilité anatomique. Les modèles déformables représentent une des méthodes les plus populaire pour la détection automatique de différents organes dans les images RM. Cependant, ces modèles souffrent encore d’une limitation importante qui est leur sensibilité à la position initiale et la forme du modèle. Une initialisation inappropriée peut conduire à un échec dans l’extraction des frontières des objets. D’un autre côté, le but ultime d’une segmentation automatique multi-objets dans les images RM est de produire un modèle qui peut aider à extraire les caractéristiques structurelles d’organes distincts dans les images. Les méthodes d’initialisation automatique actuelles qui utilisent différents descripteurs ne réussissent pas complètement l’extraction d’objets multiples dans les images RM. Nous avons besoin d’exploiter une information plus riche qui se trouve dans les contours des organes. Dans ce contexte les maillages adaptatifs anisotropiques semblent être une solution potentielle au problème soulevé. Les maillages adaptatifs anisotropiques construits à partir des images RM contiennent de l’information à un plus haut niveau d’abstraction représentant les éléments, d’une orientation et d’une forme donnée, qui constituent les différents organes dans l’image. Les méthodes existantes pour la construction de maillages adaptatifs sont basées sur les intensités dans l’image et possèdent une limitation pratique qui est l’alignement inadéquat des éléments du maillage en présence de contours inclinés dans l’image. Par conséquent, nous avons aussi besoin d’améliorer le processus d’adaptation de maillage pour produire une meilleure représentation de l’image basée sur un maillage.----------ABSTRACT: Segmentation of multiple anatomical structures in MR images is often required for biomedical engineering applications such as clinical simulation, image-guided surgery, treatment planning, etc. Moreover, there is a growing need for automatic segmentation of multiple organs and complex structures from this medical imaging modality. Many successful multi-object segmentation attempts were introduced for CT images. However in the case of MR images it is a more challenging task due to intensity inhomogeneity and variability of anatomy appearance. Therefore, state-of-the-art in multi-object MR segmentation is very inferior to that of CT images. In literature dealing with MR image segmentation, the region-based approaches are sensitive to noise and non-uniformity in the input image. The edge-based approaches are challenging to group the edge information into a coherent closed contour. The atlas-based techniques can be problematic for complicated structures with anatomical variability. Deformable models are among the most popular methods for automatic detection of different organs in MR images. However they still have an important limitation which is that they are sensitive to initial position and shape of the model. An unsuitable initialization may provide failure to capture the true boundaries of the objects. On the other hand, a useful aim for an automatic multi-object MR segmentation is to provide a model which promotes understanding of the structural features of the distinct objects within the MR images. The current automatic initialization methods which have used different descriptors are not completely successful in extracting multiple objects from MR images and we need to find richer information that is available from edges. In this regard, anisotropic adaptive meshes seem to be a potential solution to the aforesaid limitation. Anisotropic adaptive meshes constructed from MR images contain higher level, abstract information about the anatomical structures of the organs within the image retained as the elements shape and orientation. Existing methods for constructing adaptive meshes based on image features have a practical limitation where manifest itself in inadequate mesh elements alignment to inclined edges in the image. Therefore, we also have to enhance mesh adaptation process to provide a better mesh-based representation. In this Ph.D. project, considering the highlighted limitations we are going to present a novel method for automatic segmentation of multiple organs in MR images by incorporating mesh adaptation techniques. In our progress, first, we improve an anisotropic adaptation process for the meshes that are constructed from MR images where the mesh elements align adequately to the image content and improve mesh anisotropy along edges in all directions. Then the resulting adaptive meshes are used for initialization of multiple active models which leads to extract initial object boundaries close to the true boundaries of multiple objects simultaneously. Finally, the Vector Field Convolution method is utilized to guide curve evolution towards the object boundaries to obtain the final segmentation results and present a better performance in terms of speed and accuracy

The Adaptive Particle Representation (APR) for Simple and Efficient Adaptive Resolution Processing, Storage and Simulations

This thesis presents the Adaptive Particle Representation (APR), a novel adaptive data representation that can be used for general data processing, storage, and simulations. The APR is motivated, and designed, as a replacement representation for pixel images to address computational and memory bottlenecks in processing pipelines for studying spatiotemporal processes in biology using Light-sheet Fluo- rescence Microscopy (LSFM) data. The APR is an adaptive function representation that represents a function in a spatially adaptive way using a set of Particle Cells V and function values stored at particle collocation points P∗. The Particle Cells partition space, and implicitly define a piecewise constant Implied Resolution Function R∗(y) and particle sampling locations. As an adaptive data representation, the APR can be used to provide both computational and memory benefits by aligning the number of Particle Cells and particles with the spatial scales of the function. The APR allows reconstruction of a function value at any location y using any positive weighted combination of particles within a distance of R∗(y). The Particle Cells V are selected such that the error between the reconstruction and the original function, when weighted by a function σ(y), is below a user-set relative error threshold E. We call this the Reconstruction Condition and σ(y) the Local Intensity Scale. σ(y) is motivated by local gain controls in the human visual system, and for LSFM data can be used to account for contrast variations across an image. The APR is formed by satisfying an additional condition on R∗(y); we call the Resolution Bound. The Resolution Bound relates the R∗(y) to a local maximum of the absolute value function derivatives within a distance R∗(y) or y. Given restric- tions on σ(y), satisfaction of the Resolution Bound also guarantees satisfaction of the Reconstruction Condition. In this thesis, we present algorithms and approaches that find the optimal Implied Resolution Function to general problems in the form of the Resolution Bound using Particle Cells using an algorithm we call the Pulling Scheme. Here, optimal means the largest R∗(y) at each location. The Pulling Scheme has worst-case linear complexity in the number of pixels when used to rep- resent images. The approach is general in that the same algorithm can be used for general (α,m)-Reconstruction Conditions, where α denotes the function derivative and m the minimum order of the reconstruction. Further, it can also be combined with anisotropic neighborhoods to provide adaptation in both space and time. The APR can be used with both noise-free and noisy data. For noisy data, the Reconstruction Condition can no longer be guaranteed, but numerical results show an optimal range of relative error E that provides a maximum increase in PSNR over the noisy input data. Further, if it is assumed the Implied Resolution Func- tion satisfies the Resolution Bound, then the APR converges to a biased estimate (constant factor of E), at the optimal statistical rate. The APR continues a long tradition of adaptive data representations and rep- resents a unique trade off between the level of adaptation of the representation and simplicity. Both regarding the APRs structure and its use for processing. Here, we numerically evaluate the adaptation and processing of the APR for use with LSFM data. This is done using both synthetic and LSFM exemplar data. It is concluded from these results that the APR has the correct properties to provide a replacement of pixel images and address bottlenecks in processing for LSFM data. Removal of the bottleneck would be achieved by adapting to spatial, temporal and intensity scale variations in the data. Further, we propose the simple structure of the general APR could provide benefit in areas such as the numerical solution of differential equations, adaptive regression methods, and surface representation for computer graphics