A Combinatorial Solution to Non-Rigid 3D Shape-to-Image Matching

We propose a combinatorial solution for the problem of non-rigidly matching a 3D shape to 3D image data. To this end, we model the shape as a triangular mesh and allow each triangle of this mesh to be rigidly transformed to achieve a suitable matching to the image. By penalising the distance and the relative rotation between neighbouring triangles our matching compromises between image and shape information. In this paper, we resolve two major challenges: Firstly, we address the resulting large and NP-hard combinatorial problem with a suitable graph-theoretic approach. Secondly, we propose an efficient discretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledge this is the first combinatorial formulation for non-rigid 3D shape-to-image matching. In contrast to existing local (gradient descent) optimisation methods, we obtain solutions that do not require a good initialisation and that are within a bound of the optimal solution. We evaluate the proposed method on the two problems of non-rigid 3D shape-to-shape and non-rigid 3D shape-to-image registration and demonstrate that it provides promising results.Comment: 10 pages, 7 figure

Pose-invariant, model-based object recognition, using linear combination of views and Bayesian statistics

This thesis presents an in-depth study on the problem of object recognition, and in particular the detection of 3-D objects in 2-D intensity images which may be viewed from a variety of angles. A solution to this problem remains elusive to this day, since it involves dealing with variations in geometry, photometry and viewing angle, noise, occlusions and incomplete data. This work restricts its scope to a particular kind of extrinsic variation; variation of the image due to changes in the viewpoint from which the object is seen. A technique is proposed and developed to address this problem, which falls into the category of view-based approaches, that is, a method in which an object is represented as a collection of a small number of 2-D views, as opposed to a generation of a full 3-D model. This technique is based on the theoretical observation that the geometry of the set of possible images of an object undergoing 3-D rigid transformations and scaling may, under most imaging conditions, be represented by a linear combination of a small number of 2-D views of that object. It is therefore possible to synthesise a novel image of an object given at least two existing and dissimilar views of the object, and a set of linear coefficients that determine how these views are to be combined in order to synthesise the new image. The method works in conjunction with a powerful optimization algorithm, to search and recover the optimal linear combination coefficients that will synthesize a novel image, which is as similar as possible to the target, scene view. If the similarity between the synthesized and the target images is above some threshold, then an object is determined to be present in the scene and its location and pose are defined, in part, by the coefficients. The key benefits of using this technique is that because it works directly with pixel values, it avoids the need for problematic, low-level feature extraction and solution of the correspondence problem. As a result, a linear combination of views (LCV) model is easy to construct and use, since it only requires a small number of stored, 2-D views of the object in question, and the selection of a few landmark points on the object, the process which is easily carried out during the offline, model building stage. In addition, this method is general enough to be applied across a variety of recognition problems and different types of objects. The development and application of this method is initially explored looking at two-dimensional problems, and then extending the same principles to 3-D. Additionally, the method is evaluated across synthetic and real-image datasets, containing variations in the objects’ identity and pose. Future work on possible extensions to incorporate a foreground/background model and lighting variations of the pixels are examined

Staple: Complementary Learners for Real-Time Tracking

Correlation Filter-based trackers have recently achieved excellent performance, showing great robustness to challenging situations exhibiting motion blur and illumination changes. However, since the model that they learn depends strongly on the spatial layout of the tracked object, they are notoriously sensitive to deformation. Models based on colour statistics have complementary traits: they cope well with variation in shape, but suffer when illumination is not consistent throughout a sequence. Moreover, colour distributions alone can be insufficiently discriminative. In this paper, we show that a simple tracker combining complementary cues in a ridge regression framework can operate faster than 80 FPS and outperform not only all entries in the popular VOT14 competition, but also recent and far more sophisticated trackers according to multiple benchmarks.Comment: To appear in CVPR 201

Diffeomorphic demons using normalized mutual information, evaluation on multimodal brain MR images

The demons algorithm is a fast non-parametric non-rigid registration method. In recent years great efforts have been made to improve the approach; the state of the art version yields symmetric inverse-consistent largedeformation diffeomorphisms. However, only limited work has explored inter-modal similarity metrics, with no practical evaluation on multi-modality data. We present a diffeomorphic demons implementation using the analytical gradient of Normalised Mutual Information (NMI) in a conjugate gradient optimiser. We report the first qualitative and quantitative assessment of the demons for inter-modal registration. Experiments to spatially normalise real MR images, and to recover simulated deformation fields, demonstrate (i) similar accuracy from NMI-demons and classical demons when the latter may be used, and (ii) similar accuracy for NMI-demons on T1w-T1w and T1w-T2w registration, demonstrating its potential in multi-modal scenarios

Bayesian data assimilation in shape registration

In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions\ud for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterisation in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterisation vector field v, informed by regularity results about the forward model. Having done this, we illustrate how Maximum Likelihood Estimators (MLEs) can be used to find regions of high posterior density, but also how we can apply recently developed MCMC methods on function spaces to characterise the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem

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 /

Dense 3D Face Correspondence

We present an algorithm that automatically establishes dense correspondences between a large number of 3D faces. Starting from automatically detected sparse correspondences on the outer boundary of 3D faces, the algorithm triangulates existing correspondences and expands them iteratively by matching points of distinctive surface curvature along the triangle edges. After exhausting keypoint matches, further correspondences are established by generating evenly distributed points within triangles by evolving level set geodesic curves from the centroids of large triangles. A deformable model (K3DM) is constructed from the dense corresponded faces and an algorithm is proposed for morphing the K3DM to fit unseen faces. This algorithm iterates between rigid alignment of an unseen face followed by regularized morphing of the deformable model. We have extensively evaluated the proposed algorithms on synthetic data and real 3D faces from the FRGCv2, Bosphorus, BU3DFE and UND Ear databases using quantitative and qualitative benchmarks. Our algorithm achieved dense correspondences with a mean localisation error of 1.28mm on synthetic faces and detected $14$ anthropometric landmarks on unseen real faces from the FRGCv2 database with 3mm precision. Furthermore, our deformable model fitting algorithm achieved 98.5% face recognition accuracy on the FRGCv2 and 98.6% on Bosphorus database. Our dense model is also able to generalize to unseen datasets.Comment: 24 Pages, 12 Figures, 6 Tables and 3 Algorithm

Foetal echocardiographic segmentation

Congenital heart disease affects just under one percentage of all live births [1]. Those defects that manifest themselves as changes to the cardiac chamber volumes are the motivation for the research presented in this thesis. Blood volume measurements in vivo require delineation of the cardiac chambers and manual tracing of foetal cardiac chambers is very time consuming and operator dependent. This thesis presents a multi region based level set snake deformable model applied in both 2D and 3D which can automatically adapt to some extent towards ultrasound noise such as attenuation, speckle and partial occlusion artefacts. The algorithm presented is named Mumford Shah Sarti Collision Detection (MSSCD). The level set methods presented in this thesis have an optional shape prior term for constraining the segmentation by a template registered to the image in the presence of shadowing and heavy noise. When applied to real data in the absence of the template the MSSCD algorithm is initialised from seed primitives placed at the centre of each cardiac chamber. The voxel statistics inside the chamber is determined before evolution. The MSSCD stops at open boundaries between two chambers as the two approaching level set fronts meet. This has significance when determining volumes for all cardiac compartments since cardiac indices assume that each chamber is treated in isolation. Comparison of the segmentation results from the implemented snakes including a previous level set method in the foetal cardiac literature show that in both 2D and 3D on both real and synthetic data, the MSSCD formulation is better suited to these types of data. All the algorithms tested in this thesis are within 2mm error to manually traced segmentation of the foetal cardiac datasets. This corresponds to less than 10% of the length of a foetal heart. In addition to comparison with manual tracings all the amorphous deformable model segmentations in this thesis are validated using a physical phantom. The volume estimation of the phantom by the MSSCD segmentation is to within 13% of the physically determined volume

Automatic Reporting of TBI Lesion Location in CT based on Deep Learning and Atlas Mapping

Tese de mestrado integrado, Engenharia Biomédica e Biofísica (Biofísica Médica e Fisiologia de Sistemas), 2021, Universidade de Lisboa, Faculdade de CiênciasThe assessment of Computed Tomography (CT) scans for Traumatic Brain Injury (TBI) management remains a time consuming and challenging task for physicians. Computational methods for quantitative lesion segmentation and localisation may increase consistency in diagnosis and prognosis criteria. Our goal was to develop a registration-based tool to accurately localise several lesion classes (i.e., calculate the volume of lesion per brain region), as an extension of the Brain Lesion Analysis and Segmentation Tool for CT (BLAST-CT). Lesions were located by projecting a Magnetic Resonance Imaging (MRI) labelled atlas from the Montreal Neurological Institute (MNI MRI atlas) to a lesion map in native space. We created a CT template to work as an intermediate step between the two imaging spaces, using 182 non-lesioned CT scans and an unbiased iterative registration approach. We then non-linearly registered the parcellated atlas to the CT template, subsequently registering (affine) the result to native space. From the final atlas alignment, it was possible to calculate the volume of each lesion class per brain region. This pipeline was validated on a multi-centre dataset (n=839 scans), and defined three methods to flag any scans that presented sub-optimal results. The first one was based on the similarity metric of the registration of every scan to the study-specific CT template, the second aimed to identify any scans with regions that were completely collapsed post registration, and the final one identified scans with a significant volume of intra-ventricular haemorrhage outside of the ventricles. Additionally, an assessment of lesion prevalence and of the false negative and false positive rates of the algorithm, per anatomical region, was conducted, along with a bias assessment of the BLAST-CT tool. Our results show that the constructed pipeline is able to successfully localise TBI lesions across the whole brain, although without voxel-wise accuracy. We found the error rates calculated for each brain region to be inversely correlated with the lesion volume within that region. No considerable bias was identified on BLAST-CT, as all the significant correlation coefficients calculated between the Dice scores and clinical variables (i.e., age, Glasgow Coma Scale, Extended Glasgow Outcome Scale and Injury Severity Score) were below 0.2. Our results also suggest that the variation in DSC between male and female patients within a specific age range was caused by the discrepancy in lesion volume presented by the scans included in each sample