Optical techniques for 3D surface reconstruction in computer-assisted laparoscopic surgery

One of the main challenges for computer-assisted surgery (CAS) is to determine the intra-opera- tive morphology and motion of soft-tissues. This information is prerequisite to the registration of multi-modal patient-specific data for enhancing the surgeon’s navigation capabilites by observ- ing beyond exposed tissue surfaces and for providing intelligent control of robotic-assisted in- struments. In minimally invasive surgery (MIS), optical techniques are an increasingly attractive approach for in vivo 3D reconstruction of the soft-tissue surface geometry. This paper reviews the state-of-the-art methods for optical intra-operative 3D reconstruction in laparoscopic surgery and discusses the technical challenges and future perspectives towards clinical translation. With the recent paradigm shift of surgical practice towards MIS and new developments in 3D opti- cal imaging, this is a timely discussion about technologies that could facilitate complex CAS procedures in dynamic and deformable anatomical regions

Monocular slam for deformable scenarios.

El problema de localizar la posición de un sensor en un mapa incierto que se estima simultáneamente se conoce como Localización y Mapeo Simultáneo --SLAM--. Es un problema desafiante comparable al paradigma del huevo y la gallina. Para ubicar el sensor necesitamos conocer el mapa, pero para construir el mapa, necesitamos la posición del sensor. Cuando se utiliza un sensor visual, por ejemplo, una cámara, se denomina Visual SLAM o VSLAM. Los sensores visuales para SLAM se dividen entre los que proporcionan información de profundidad (por ejemplo, cámaras RGB-D o equipos estéreo) y los que no (por ejemplo, cámaras monoculares o cámaras de eventos). En esta tesis hemos centrado nuestra investigación en SLAM con cámaras monoculares.Debido a la falta de percepción de profundidad, el SLAM monocular es intrínsecamente más duro en comparación con el SLAM con sensores de profundidad. Los trabajos estado del arte en VSLAM monocular han asumido normalmente que la escena permanece rígida durante toda la secuencia, lo que es una suposición factible para entornos industriales y urbanos. El supuesto de rigidez aporta las restricciones suficientes al problema y permite reconstruir un mapa fiable tras procesar varias imágenes. En los últimos años, el interés por el SLAM ha llegado a las áreas médicas donde los algoritmos SLAM podrían ayudar a orientar al cirujano o localizar la posición de un robot. Sin embargo, a diferencia de los escenarios industriales o urbanos, en secuencias dentro del cuerpo, todo puede deformarse eventualmente y la suposición de rigidez acaba siendo inválida en la práctica, y por extensión, también los algoritmos de SLAM monoculares. Por lo tanto, nuestro objetivo es ampliar los límites de los algoritmos de SLAM y concebir el primer sistema SLAM monocular capaz de hacer frente a la deformación de la escena.Los sistemas de SLAM actuales calculan la posición de la cámara y la estructura del mapa en dos subprocesos concurrentes: la localización y el mapeo. La localización se encarga de procesar cada imagen para ubicar el sensor de forma continua, en cambio el mapeo se encarga de construir el mapa de la escena. Nosotros hemos adoptado esta estructura y concebimos tanto la localización deformable como el mapeo deformable ahora capaces de recuperar la escena incluso con deformación.Nuestra primera contribución es la localización deformable. La localización deformable utiliza la estructura del mapa para recuperar la pose de la cámara con una única imagen. Simultáneamente, a medida que el mapa se deforma durante la secuencia, también recupera la deformación del mapa para cada fotograma. Hemos propuesto dos familias de localización deformable. En el primer algoritmo de localización deformable, asumimos que todos los puntos están embebidos en una superficie denominada plantilla. Podemos recuperar la deformación de la superficie gracias a un modelo de deformación global que permite estimar la deformación más probable del objeto. Con nuestro segundo algoritmo de localización deformable, demostramos que es posible recuperar la deformación del mapa sin un modelo de deformación global, representando el mapa como surfels individuales. Nuestros resultados experimentales mostraron que, recuperando la deformación del mapa, ambos métodos superan tanto en robustez como en precisión a los métodos rígidos.Nuestra segunda contribución es la concepción del mapeo deformable. Es el back-end del algoritmo SLAM y procesa un lote de imágenes para recuperar la estructura del mapa para todas las imágenes y hacer crecer el mapa ensamblando las observaciones parciales del mismo. Tanto la localización deformable como el mapeo que se ejecutan en paralelo y juntos ensamblan el primer SLAM monocular deformable: \emph{DefSLAM}. Una evaluación ampliada de nuestro método demostró, tanto en secuencias controladas por laboratorio como en secuencias médicas, que nuestro método procesa con éxito secuencias en las que falla el sistema monocular SLAM actual.Nuestra tercera contribución son dos métodos para explotar la información fotométrica en SLAM monocular deformable. Por un lado, SD-DefSLAM que aprovecha el emparejamiento semi-directo para obtener un emparejamiento mucho más fiable de los puntos del mapa en las nuevas imágenes, como consecuencia, se demostró que es más robusto y estable en secuencias médicas. Por otro lado, proponemos un método de Localización Deformable Directa y Dispersa en el que usamos un error fotométrico directo para rastrear la deformación de un mapa modelado como un conjunto de surfels 3D desconectados. Podemos recuperar la deformación de múltiples superficies desconectadas, deformaciones no isométricas o superficies con una topología cambiante.<br /

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure

Automatic 3D bi-ventricular segmentation of cardiac images by a shape-refined multi-task deep learning approach

Deep learning approaches have achieved state-of-the-art performance in cardiac magnetic resonance (CMR) image segmentation. However, most approaches have focused on learning image intensity features for segmentation, whereas the incorporation of anatomical shape priors has received less attention. In this paper, we combine a multi-task deep learning approach with atlas propagation to develop a shape-constrained bi-ventricular segmentation pipeline for short-axis CMR volumetric images. The pipeline first employs a fully convolutional network (FCN) that learns segmentation and landmark localisation tasks simultaneously. The architecture of the proposed FCN uses a 2.5D representation, thus combining the computational advantage of 2D FCNs networks and the capability of addressing 3D spatial consistency without compromising segmentation accuracy. Moreover, the refinement step is designed to explicitly enforce a shape constraint and improve segmentation quality. This step is effective for overcoming image artefacts (e.g. due to different breath-hold positions and large slice thickness), which preclude the creation of anatomically meaningful 3D cardiac shapes. The proposed pipeline is fully automated, due to network's ability to infer landmarks, which are then used downstream in the pipeline to initialise atlas propagation. We validate the pipeline on 1831 healthy subjects and 649 subjects with pulmonary hypertension. Extensive numerical experiments on the two datasets demonstrate that our proposed method is robust and capable of producing accurate, high-resolution and anatomically smooth bi-ventricular 3D models, despite the artefacts in input CMR volumes

Analysis and Manipulation of Repetitive Structures of Varying Shape

Self-similarity and repetitions are ubiquitous in man-made and natural objects. Such structural regularities often relate to form, function, aesthetics, and design considerations. Discovering structural redundancies along with their dominant variations from 3D geometry not only allows us to better understand the underlying objects, but is also beneficial for several geometry processing tasks including compact representation, shape completion, and intuitive shape manipulation. To identify these repetitions, we present a novel detection algorithm based on analyzing a graph of surface features. We combine general feature detection schemes with a RANSAC-based randomized subgraph searching algorithm in order to reliably detect recurring patterns of locally unique structures. A subsequent segmentation step based on a simultaneous region growing is applied to verify that the actual data supports the patterns detected in the feature graphs. We introduce our graph based detection algorithm on the example of rigid repetitive structure detection. Then we extend the approach to allow more general deformations between the detected parts. We introduce subspace symmetries whereby we characterize similarity by requiring the set of repeating structures to form a low dimensional shape space. We discover these structures based on detecting linearly correlated correspondences among graphs of invariant features. The found symmetries along with the modeled variations are useful for a variety of applications including non-local and non-rigid denoising. Employing subspace symmetries for shape editing, we introduce a morphable part model for smart shape manipulation. The input geometry is converted to an assembly of deformable parts with appropriate boundary conditions. Our method uses self-similarities from a single model or corresponding parts of shape collections as training input and allows the user also to reassemble the identified parts in new configurations, thus exploiting both the discrete and continuous learned variations while ensuring appropriate boundary conditions across part boundaries. We obtain an interactive yet intuitive shape deformation framework producing realistic deformations on classes of objects that are difficult to edit using repetition-unaware deformation techniques

Shape Registration in the Time of Transformers

In this paper, we propose a transformer-based procedure for the efficient registration of non-rigid 3D point clouds. The proposed approach is data-driven and adopts for the first time the transformers architecture in the registration task. Our method is general and applies to different settings. Given a fixed template with some desired properties (e.g. skinning weights or other animation cues), we can register raw acquired data to it, thereby transferring all the template properties to the input geometry. Alternatively, given a pair of shapes, our method can register the first onto the second (or vice-versa), obtaining a high-quality dense correspondence between the two. In both contexts, the quality of our results enables us to target real applications such as texture transfer and shape interpolation. Furthermore, we also show that including an estimation of the underlying density of the surface eases the learning process. By exploiting the potential of this architecture, we can train our model requiring only a sparse set of ground truth correspondences (10∼20% of the total points). The proposed model and the analysis that we perform pave the way for future exploration of transformer-based architectures for registration and matching applications. Qualitative and quantitative evaluations demonstrate that our pipeline outperforms state-of-the-art methods for deformable and unordered 3D data registration on different datasets and scenarios

Shape analysis and description based on the isometric invariances of topological skeletonization

ilustracionesIn this dissertation, we explore the problem of how to describe the shape of an object in 2D and 3D with a set of features that are invariant to isometric transformations. We focus to based our approach on the well-known Medial Axis Transform and its topological properties. We aim to study two problems. The first is how to find a shape representation of a segmented object that exhibits rotation, translation, and reflection invariance. The second problem is how to build a machine learning pipeline that uses the isometric invariance of the shape representation to do both classification and retrieval. Our proposed solution demonstrates competitive results compared to state-of-the-art approaches. We based our shape representation on the medial axis transform (MAT), sometimes called the topological skeleton. Accepted and well-studied properties of the medial axis include: homotopy preservation, rotation invariance, mediality, one pixel thickness, and the ability to fully reconstruct the object. These properties make the MAT a suitable input to create shape features; however, several problems arise because not all skeletonization methods satisfy all the above-mentioned properties at the same time. In general, skeletons based on thinning approaches preserve topology but are noise sensitive and do not allow a proper reconstruction. They are also not invariant to rotations. Voronoi skeletons also preserve topology and are rotation invariant, but do not have information about the thickness of the object, making reconstruction impossible. The Voronoi skeleton is an approximation of the real skeleton. The denser the sampling of the boundary, the better the approximation; however, a denser sampling makes the Voronoi diagram more computationally expensive. In contrast, distance transform methods allow the reconstruction of the original object by providing the distance from every pixel in the skeleton to the boundary. Moreover, they exhibit an acceptable degree of the properties listed above, but noise sensitivity remains an issue. Therefore, we selected distance transform medial axis methods as our skeletonization strategy, and focused on creating a new noise-free approach to solve the contour noise problem. To effectively classify an object, or perform any other task with features based on its shape, the descriptor needs to be a normalized, compact form: $\Phi$ should map every shape $\Omega$ to the same vector space $\mathrm{R}^{n}$. This is not possible with skeletonization methods because the skeletons of different objects have different numbers of branches and different numbers of points, even when they belong to the same category. Consequently, we developed a strategy to extract features from the skeleton through the map $\Phi$, which we used as an input to a machine learning approach. After developing our method for robust skeletonization, the next step is to use such skeleton into the machine learning pipeline to classify object into previously defined categories. We developed a set of skeletal features that were used as input data to the machine learning architectures. We ran experiments on MPEG7 and ModelNet40 dataset to test our approach in both 2D and 3D. Our experiments show results comparable with the state-of-the-art in shape classification and retrieval. Our experiments also show that our pipeline and our skeletal features exhibit some degree of invariance to isometric transformations. In this study, we sought to design an isometric invariant shape descriptor through robust skeletonization enforced by a feature extraction pipeline that exploits such invariance through a machine learning methodology. We conducted a set of classification and retrieval experiments over well-known benchmarks to validate our proposed method. (Tomado de la fuente)En esta disertación se explora el problema de cómo describir la forma de un objeto en 2D y 3D con un conjunto de características que sean invariantes a transformaciones isométricas. La metodología propuesta en este documento se enfoca en la Transformada del Eje Medio (Medial Axis Transform) y sus propiedades topológicas. Nuestro objetivo es estudiar dos problemas. El primero es encontrar una representación matemática de la forma de un objeto que exhiba invarianza a las operaciones de rotación, translación y reflexión. El segundo problema es como construir un modelo de machine learning que use esas invarianzas para las tareas de clasificación y consulta de objetos a través de su forma. El método propuesto en esta tesis muestra resultados competitivos en comparación con otros métodos del estado del arte. En este trabajo basamos nuestra representación de forma en la transformada del eje medio, a veces llamada esqueleto topológico. Algunas propiedades conocidas y bien estudiadas de la transformada del eje medio son: conservación de la homotopía, invarianza a la rotación, su grosor consiste en un solo pixel (1D), y la habilidad para reconstruir el objeto original a través de ella. Estas propiedades hacen de la transformada del eje medio un punto de partida adecuado para crear características de forma. Sin embargo, en este punto surgen varios problemas dado que no todos los métodos de esqueletización satisfacen, al mismo tiempo, todas las propiedades mencionadas anteriormente. En general, los esqueletos basados en enfoques de erosión morfológica conservan la topología del objeto, pero son sensibles al ruido y no permiten una reconstrucción adecuada. Además, no son invariantes a las rotaciones. Otro método de esqueletización son los esqueletos de Voronoi. Los esqueletos de Voronoi también conservan la topología y son invariantes a la rotación, pero no tienen información sobre el grosor del objeto, lo que hace imposible su reconstrucción. Cuanto más denso sea el muestreo del contorno del objeto, mejor será la aproximación. Sin embargo, un muestreo más denso hace que el diagrama de Voronoi sea más costoso computacionalmente. Por el contrario, los métodos basados en la transformada de la distancia permiten la reconstrucción del objeto original, ya que proporcionan la distancia desde cada píxel del esqueleto hasta su punto más cercano en el contorno. Además, exhiben un grado aceptable de las propiedades enumeradas anteriormente, aunque la sensibilidad al ruido sigue siendo un problema. Por lo tanto, en este documento seleccionamos los métodos basados en la transformada de la distancia como nuestra estrategia de esqueletización, y nos enfocamos en crear un nuevo enfoque que resuelva el problema del ruido en el contorno. Para clasificar eficazmente un objeto o realizar cualquier otra tarea con características basadas en su forma, el descriptor debe ser compacto y estar normalizado: $\Phi$ debe relacionar cada forma $\Omega$ al mismo espacio vectorial $\mathrm{R}^{n}$. Esto no es posible con los métodos de esqueletización en el estado del arte, porque los esqueletos de diferentes objetos tienen diferentes números de ramas y diferentes números de puntos incluso cuando pertenecen a la misma categoría. Consecuentemente, en nuestra propuesta desarrollamos una estrategia para extraer características del esqueleto a través de la función $\Phi$, que usamos como entrada para un enfoque de aprendizaje automático. % TODO completar con resultados. Después de desarrollar nuestro método de esqueletización robusta, el siguiente paso es usar dicho esqueleto en un modelo de aprendizaje de máquina para clasificar el objeto en categorías previamente definidas. Para ello se desarrolló un conjunto de características basadas en el eje medio que se utilizaron como datos de entrada para la arquitectura de aprendizaje automático. Realizamos experimentos en los conjuntos de datos: MPEG7 y ModelNet40 para probar nuestro enfoque tanto en 2D como en 3D. Nuestros experimentos muestran resultados comparables con el estado del arte en clasificación y consulta de formas (retrieval). Nuestros experimentos también muestran que el modelo desarrollado junto con nuestras características basadas en el eje medio son invariantes a las transformaciones isométricas. (Tomado de la fuente)Beca para Doctorados Nacionales de Colciencias, convocatoria 725 de 2015DoctoradoDoctor en IngenieríaVisión por computadora y aprendizaje automátic

Three-Dimensional Object Search, Understanding, and Pose Estimation with Low-Cost Sensors

With the recent development of low-cost depth sensors, an entirely new type of 3D data is being generated rapidly by regular consumers. Traditionally, 3D data is produced by a small number of professional designers (i.e., the Computer Aided Design (CAD) model); however, 3D data from massive consumer-level sensors has the potential of introducing many new applications, such as user-captured 3D warehouse and search engines, robots with 3D sensing capability, and customized 3D printing. Nevertheless, the low-cost sensors used by general consumers also pose new technological challenges. First, they have relatively high levels of sensor noise. Second, the use of such consumer devices is often in uncontrolled settings, resulting in challenging conditions, such as poor lighting, cluttered scenes, and object occlusion. To address such emerging opportunities and associated challenges, this dissertation is dedicated to the development of novel algorithms and systems for 3D data understanding and processing, using input from a consumer-level 3D sensor. In particular, the key problems of 3D shape retrieval, scene understanding, and pose recognition are explored in order to present a comprehensive coverage of the key aspects of content-based 3D shape analysis. To resolve the aforementioned challenges, we propose a flexible Markov Random Field (MRF) framework that uses local information to allow partial matching, and thus address the model incompleteness problem; the framework also uses higher-order correlation to provide additional robustness against sensor noise. With the MRF framework, these 3D analysis problems can be transformed into a unified potential energy minimization problem, while preserving the flexibility to adapt to different settings and resolve the unique challenges of each problem. The contributions of the dissertation include: a. Cross-Domain 3D Retrieval: First we tackle the problem of searching 3D noise- free models using noisy data captured by low-cost 3D sensors – a unique cross-domain setting. To manage the challenges of sensor noise and model incompleteness from consumer-level sensors, we propose a novel MRF formulation for the retrieval problem. The potential function of the random field is designed to capture both the local shape and global spatial consistency in order to preserve the local matching capability, while offering robustness against the sensor noise. The specific form of the potential functions is determined efficiently by a series of weak classifiers, thus forming a variant of the Regression Tree Field (RTF). We achieve better retrieval precision and recall in the cross-domain settings with a consumer-level depth sensor compared with state-of-the-art approaches. b. 3D Scene Understanding: We develop a scene understanding system based on input from consumer-level depth sensors. To resolve the key challenge of the lack of annotated 3D training data, we construct an MRF that connects the input 3D point cloud and the associated 2D reference images, based on which the 3D point cloud is stitched. A series of weak classifiers are trained to obtain an approximate semantic segmentation result from the reference images. The potential function of the field is designed to integrate the results from the classifiers, while taking advantage of the 3D spatial consistency in order to output a comprehensive scene understanding result. We achieve comparable accuracy and much faster speed compared with state-of-the-art 3D scene understanding systems, with the difference that we do not require annotated 3D training data. c. Pose Recognition of Deformable Objects: We develop a method for supporting a robotics system to recognize pose and manipulate deformable objects. More specifically, garment pose is recognized with the help of an offline simulated database and the proposed retrieval approach. We use a novel binary feature representation extracted from the reconstructed 3D surfaces in order to allow efficient matching, thus achieving real-time performance. A spatial weight is further learned in order to integrate the local matching result. The system shows superior recognition accuracy and faster speed than the state-of-the-art approaches. d. Application with 2D Data: In addition to the traditional 3D applications, we explore the possibility of extending MRF formulation to 2D data, especially those used in classical low-level 2D vision problems, such as image deblurring and denoising. One well-known technique that uses image prior, the probabilistic patched-based prior, is known to have bottlenecks in finding the most similar model from a model set, which can be posed as a retrieval problem. Therefore, we apply the MRF formulation originally developed for 3D shape retrieval, and extend it to this 2D problem by introducing a grid-like random field structure. We can achieve 40x acceleration compared with the state-of-the-art algorithm, while preserving quality. We organize the dissertation as follows. First, the core problems of 3D shape retrieval, scene understanding, and pose recognition, and with the proposed solutions that use MRF and RTF are explored in Part I. In Part II, the extension to 2D data is discussed. Extensive evaluation is performed in each specific task in order to compare the proposed approaches with state-of-the-art algorithms and systems, and also to justify the components of the proposed methods. Finally, in Part III, we include the conclusion remarks and discussion of open issues and future work