An Adaptive Algorithm to Identify Ambiguous Prostate Capsule Boundary Lines for Three-Dimensional Reconstruction and Quantitation

Currently there are few parameters that are used to compare the efficiency of different methods of cancerous prostate surgical removal. An accurate assessment of the percentage and depth of extra-capsular soft tissue removed with the prostate by the various surgical techniques can help surgeons determine the appropriateness of surgical approaches. Additionally, an objective assessment can allow a particular surgeon to compare individual performance against a standard. In order to facilitate 3D reconstruction and objective analysis and thus provide more accurate quantitation results when analyzing specimens, it is essential to automatically identify the capsule line that separates the prostate gland tissue from its extra-capsular tissue. However the prostate capsule is sometimes unrecognizable due to the naturally occurring intrusion of muscle and connective tissue into the prostate gland. At these regions where the capsule disappears, its contour can be arbitrarily reconstructed by drawing a continuing contour line based on the natural shape of the prostate gland. Presented here is a mathematical model that can be used in deciding the missing part of the capsule. This model approximates the missing parts of the capsule where it disappears to a standard shape by using a Generalized Hough Transform (GHT) approach to detect the prostate capsule. We also present an algorithm based on a least squares curve fitting technique that uses a prostate shape equation to merge previously detected capsule parts with the curve equation to produce an approximated curve that represents the prostate capsule. We have tested our algorithms using three shapes on 13 prostate slices that are cut at different locations from the apex and the results are promisin

High performance computing for 3D image segmentation

Digital image processing is a very popular and still very promising eld of science, which has been successfully applied to numerous areas and problems, reaching elds like forensic analysis, security systems, multimedia processing, aerospace, automotive, and many more. A very important part of the image processing area is image segmentation. This refers to the task of partitioning a given image into multiple regions and is typically used to locate and mark objects and boundaries in input scenes. After segmentation the image represents a set of data far more suitable for further algorithmic processing and decision making. Image segmentation algorithms are a very broad eld and they have received signi cant amount of research interest A good example of an area, in which image processing plays a constantly growing role, is the eld of medical solutions. The expectations and demands that are presented in this branch of science are very high and dif cult to meet for the applied technology. The problems are challenging and the potential bene ts are signi cant and clearly visible. For over thirty years image processing has been applied to different problems and questions in medicine and the practitioners have exploited the rich possibilities that it offered. As a result, the eld of medicine has seen signi cant improvements in the interpretation of examined medical data. Clearly, the medical knowledge has also evolved signi cantly over these years, as well as the medical equipment that serves doctors and researchers. Also the common computer hardware, which is present at homes, of ces and laboratories, is constantly evolving and changing. All of these factors have sculptured the shape of modern image processing techniques and established in which ways it is currently used and developed. Modern medical image processing is centered around 3D images with high spatial and temporal resolution, which can bring a tremendous amount of data for medical practitioners. Processing of such large sets of data is not an easy task, requiring high computational power. Furthermore, in present times the computational power is not as easily available as in recent years, as the growth of possibilities of a single processing unit is very limited - a trend towards multi-unit processing and parallelization of the workload is clearly visible. Therefore, in order to continue the development of more complex and more advanced image processing techniques, a new direction is necessary. A very interesting family of image segmentation algorithms, which has been gaining a lot of focus in the last three decades, is called Deformable Models. They are based on the concept of placing a geometrical object in the scene of interest and deforming it until it assumes the shape of objects of interest. This process is usually guided by several forces, which originate in mathematical functions, features of the input images and other constraints of the deformation process, like object curvature or continuity. A range of very desired features of Deformable Models include their high capability for customization and specialization for different tasks and also extensibility with various approaches for prior knowledge incorporation. This set of characteristics makes Deformable Models a very ef cient approach, which is capable of delivering results in competitive times and with very good quality of segmentation, robust to noisy and incomplete data. However, despite the large amount of work carried out in this area, Deformable Models still suffer from a number of drawbacks. Those that have been gaining the most focus are e.g. sensitivity to the initial position and shape of the model, sensitivity to noise in the input images and to awed input data, or the need for user supervision over the process. The work described in this thesis aims at addressing the problems of modern image segmentation, which has raised from the combination of above-mentioned factors: the signi cant growth of image volumes sizes, the growth of complexity of image processing algorithms, coupled with the change in processor development and turn towards multi-processing units instead of growing bus speeds and the number of operations per second of a single processing unit. We present our innovative model for 3D image segmentation, called the The Whole Mesh Deformation model, which holds a set of very desired features that successfully address the above-mentioned requirements. Our model has been designed speci cally for execution on parallel architectures and with the purpose of working well with very large 3D images that are created by modern medical acquisition devices. Our solution is based on Deformable Models and is characterized by a very effective and precise segmentation capability. The proposed Whole Mesh Deformation (WMD) model uses a 3D mesh instead of a contour or a surface to represent the segmented shapes of interest, which allows exploiting more information in the image and obtaining results in shorter times. The model offers a very good ability for topology changes and allows effective parallelization of work ow, which makes it a very good choice for large data-sets. In this thesis we present a precise model description, followed by experiments on arti cial images and real medical data

Meshless Mechanics and Point-Based Visualization Methods for Surgical Simulations

Computer-based modeling and simulation practices have become an integral part of the medical education field. For surgical simulation applications, realistic constitutive modeling of soft tissue is considered to be one of the most challenging aspects of the problem, because biomechanical soft-tissue models need to reflect the correct elastic response, have to be efficient in order to run at interactive simulation rates, and be able to support operations such as cuts and sutures. Mesh-based solutions, where the connections between the individual degrees of freedom (DoF) are defined explicitly, have been the traditional choice to approach these problems. However, when the problem under investigation contains a discontinuity that disrupts the connectivity between the DoFs, the underlying mesh structure has to be reconfigured in order to handle the newly introduced discontinuity correctly. This reconfiguration for mesh-based techniques is typically called dynamic remeshing, and most of the time it causes the performance bottleneck in the simulation. In this dissertation, the efficiency of point-based meshless methods is investigated for both constitutive modeling of elastic soft tissues and visualization of simulation objects, where arbitrary discontinuities/cuts are applied to the objects in the context of surgical simulation. The point-based deformable object modeling problem is examined in three functional aspects: modeling continuous elastic deformations with, handling discontinuities in, and visualizing a point-based object. Algorithmic and implementation details of the presented techniques are discussed in the dissertation. The presented point-based techniques are implemented as separate components and integrated into the open-source software framework SOFA. The presented meshless continuum mechanics model of elastic tissue were verified by comparing it to the Hertzian non-adhesive frictionless contact theory. Virtual experiments were setup with a point-based deformable block and a rigid indenter, and force-displacement curves obtained from the virtual experiments were compared to the theoretical solutions. The meshless mechanics model of soft tissue and the integrated novel discontinuity treatment technique discussed in this dissertation allows handling cuts of arbitrary shape. The implemented enrichment technique not only modifies the internal mechanics of the soft tissue model, but also updates the point-based visual representation in an efficient way preventing the use of costly dynamic remeshing operations

On the Real-Time Performance, Robustness and Accuracy of Medical Image Non-Rigid Registration

Three critical issues about medical image non-rigid registration are performance, robustness and accuracy. A registration method, which is capable of responding timely with an accurate alignment, robust against the variation of the image intensity and the missing data, is desirable for its clinical use. This work addresses all three of these issues. Unacceptable execution time of Non-rigid registration (NRR) often presents a major obstacle to its routine clinical use. We present a hybrid data partitioning method to parallelize a NRR method on a cooperative architecture, which enables us to get closer to the goal: accelerating using architecture rather than designing a parallel algorithm from scratch. to further accelerate the performance for the GPU part, a GPU optimization tool is provided to automatically optimize GPU execution configuration.;Missing data and variation of the intensity are two severe challenges for the robustness of the registration method. A novel point-based NRR method is presented to resolve mapping function (deformation field) with the point correspondence missing. The novelty of this method lies in incorporating a finite element biomechanical model into an Expectation and Maximization (EM) framework to resolve the correspondence and mapping function simultaneously. This method is extended to deal with the deformation induced by tumor resection, which imposes another challenge, i.e. incomplete intra-operative MRI. The registration is formulated as a three variable (Correspondence, Deformation Field, and Resection Region) functional minimization problem and resolved by a Nested Expectation and Maximization framework. The experimental results show the effectiveness of this method in correcting the deformation in the vicinity of the tumor. to deal with the variation of the intensity, two different methods are developed depending on the specific application. For the mono-modality registration on delayed enhanced cardiac MRI and cine MRI, a hybrid registration method is designed by unifying both intensity- and feature point-based metrics into one cost function. The experiment on the moving propagation of suspicious myocardial infarction shows effectiveness of this hybrid method. For the multi-modality registration on MRI and CT, a Mutual Information (MI)-based NRR is developed by modeling the underlying deformation as a Free-Form Deformation (FFD). MI is sensitive to the variation of the intensity due to equidistant bins. We overcome this disadvantage by designing a Top-to-Down K-means clustering method to naturally group similar intensities into one bin. The experiment shows this method can increase the accuracy of the MI-based registration.;In image registration, a finite element biomechanical model is usually employed to simulate the underlying movement of the soft tissue. We develop a multi-tissue mesh generation method to build a heterogeneous biomechanical model to realistically simulate the underlying movement of the brain. We focus on the following four critical mesh properties: tissue-dependent resolution, fidelity to tissue boundaries, smoothness of mesh surfaces, and element quality. Each mesh property can be controlled on a tissue level. The experiments on comparing the homogeneous model with the heterogeneous model demonstrate the effectiveness of the heterogeneous model in improving the registration accuracy

Real Time Sequential Non Rigid Structure from motion using a single camera

En la actualidad las aplicaciones que basan su funcionamiento en una correcta localización y reconstrucción dentro de un entorno real en 3D han experimentado un gran interés en los últimos años, tanto por la comunidad investigadora como por la industrial. Estas aplicaciones varían desde la realidad aumentada, la robótica, la simulación, los videojuegos, etc. Dependiendo de la aplicación y del nivel de detalle de la reconstrucción, se emplean diversos dispositivos, algunos específicos, más complejos y caros como las cámaras estéreo, cámara y profundidad (RGBD) con Luz estructurada y Time of Flight (ToF), así como láser y otros más avanzados. Para aplicaciones sencillas es suficiente con dispositivos de uso común, como los smartphones, en los que aplicando técnicas de visión artificial, se pueden obtener modelos 3D del entorno para, en el caso de la realidad aumentada, mostrar información aumentada en la ubicación seleccionada.En robótica, la localización y generación simultáneas de un mapa del entorno en 3D es una tarea fundamental para conseguir la navegación autónoma. Este problema se conoce en el estado del arte como Simultaneous Localization And Mapping (SLAM) o Structure from Motion (SfM). Para la aplicación de estas técnicas, el objeto no ha de cambiar su forma a lo largo del tiempo. La reconstrucción es unívoca salvo factor de escala en captura monocular sin referencia. Si la condición de rigidez no se cumple, es porque la forma del objeto cambia a lo largo del tiempo. El problema sería equivalente a realizar una reconstrucción por fotograma, lo cual no se puede hacer de manera directa, puesto que diferentes formas, combinadas con diferentes poses de cámara pueden dar proyecciones similares. Es por esto que el campo de la reconstrucción de objetos deformables es todavía un área en desarrollo. Los métodos de SfM se han adaptado aplicando modelos físicos, restricciones temporales, espaciales, geométricas o de otros tipos para reducir la ambigüedad en las soluciones, naciendo así las técnicas conocidas como Non-Rigid SfM (NRSfM).En esta tesis se propone partir de una técnica de reconstrucción rígida bien conocida en el estado del arte como es PTAM (Parallel Tracking and Mapping) y adaptarla para incluir técnicas de NRSfM, basadas en modelo de bases lineales para estimar las deformaciones del objeto modelado dinámicamente y aplicar restricciones temporales y espaciales para mejorar las reconstrucciones, además de ir adaptándose a cambios de deformación que se presenten en la secuencia. Para ello, hay que realizar cambios de manera que cada uno de sus hilos de ejecución procesen datos no rígidos.El hilo encargado del seguimiento ya realizaba seguimiento basado en un mapa de puntos 3D, proporcionado a priori. La modificación más importante aquí es la integración de un modelo de deformación lineal para que se realice el cálculo de la deformación del objeto en tiempo real, asumiendo fijas las formas básicas de deformación. El cálculo de la pose de la cámara está basado en el sistema de estimación rígido, por lo que la estimación de pose y coeficientes de deformación se hace de manera alternada usando el algoritmo E-M (Expectation-Maximization). También, se imponen restricciones temporales y de forma para restringir las ambigüedades inherentes en las soluciones y mejorar la calidad de la estimación 3D.Respecto al hilo que gestiona el mapa, se actualiza en función del tiempo para que sea capaz de mejorar las bases de deformación cuando éstas no son capaces de explicar las formas que se ven en las imágenes actuales. Para ello, se sustituye la optimización de modelo rígido incluida en este hilo por un método de procesamiento exhaustivo NRSfM, para mejorar las bases acorde a las imágenes con gran error de reconstrucción desde el hilo de seguimiento. Con esto, el modelo se consigue adaptar a nuevas deformaciones, permitiendo al sistema evolucionar y ser estable a largo plazo.A diferencia de una gran parte de los métodos de la literatura, el sistema propuesto aborda el problema de la proyección perspectiva de forma nativa, minimizando los problemas de ambigüedad y de distancia al objeto existente en la proyección ortográfica. El sistema propuesto maneja centenares de puntos y está preparado para cumplir con restricciones de tiempo real para su aplicación en sistemas con recursos hardware limitados

Proceedings of the fifth international workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015)

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information.The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations.Following the first edition of this workshop in 20061, the second edition in New-York in 20082, the third edition in Toronto in 20113, the forth edition in Nagoya Japan on September 22 20134, the fifth edition was held in Munich on October 9 20155.Contributions were solicited in Riemannian, sub-Riemannian and group theoretical methods, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, time-evolving geometric processes, stratified spaces, optimal transport, approximation methods in statistical learning and related subjects. Among the submitted papers, 14 were selected andorganized in 4 oral sessions