Data fusion for a multi-scale model of a wheat leaf surface: a unifying approach using a radial basis function partition of unity method

Realistic digital models of plant leaves are crucial to fluid dynamics simulations of droplets for optimising agrochemical spray technologies. The presence and nature of small features (on the order of 100$\mathrm{\mu m}$) such as ridges and hairs on the surface have been shown to significantly affect the droplet evaporation, and thus the leaf's potential uptake of active ingredients. We show that these microstructures can be captured by implicit radial basis function partition of unity (RBFPU) surface reconstructions from micro-CT scan datasets. However, scanning a whole leaf ($20\mathrm{cm^2}$) at micron resolutions is infeasible due to both extremely large data storage requirements and scanner time constraints. Instead, we micro-CT scan only a small segment of a wheat leaf ($4\mathrm{mm^2}$). We fit a RBFPU implicit surface to this segment, and an explicit RBFPU surface to a lower resolution laser scan of the whole leaf. Parameterising the leaf using a locally orthogonal coordinate system, we then replicate the now resolved microstructure many times across a larger, coarser, representation of the leaf surface that captures important macroscale features, such as its size, shape, and orientation. The edge of one segment of the microstructure model is blended into its neighbour naturally by the partition of unity method. The result is one implicit surface reconstruction that captures the wheat leaf's features at both the micro- and macro-scales.Comment: 23 pages, 11 figure

Scalable 3D Surface Reconstruction by Local Stochastic Fusion of Disparity Maps

Digital three-dimensional (3D) models are of significant interest to many application fields, such as medicine, engineering, simulation, and entertainment. Manual creation of 3D models is extremely time-consuming and data acquisition, e.g., through laser sensors, is expensive. In contrast, images captured by cameras mean cheap acquisition and high availability. Significant progress in the field of computer vision already allows for automatic 3D reconstruction using images. Nevertheless, many problems still exist, particularly for big sets of large images. In addition to the complex formulation necessary to solve an ill-posed problem, one has to manage extremely large amounts of data. This thesis targets 3D surface reconstruction using image sets, especially for large-scale, but also for high-accuracy applications. To this end, a processing chain for dense scalable 3D surface reconstruction using large image sets is defined consisting of image registration, disparity estimation, disparity map fusion, and triangulation of point clouds. The main focus of this thesis lies on the fusion and filtering of disparity maps, obtained by Semi-Global Matching, to create accurate 3D point clouds. For unlimited scalability, a Divide and Conquer method is presented that allows for parallel processing of subspaces of the 3D reconstruction space. The method for fusing disparity maps employs local optimization of spatial data. By this means, it avoids complex fusion strategies when merging subspaces. Although the focus is on scalable reconstruction, a high surface quality is obtained by several extensions to state-of-the-art local optimization methods. To this end, the seminal local volumetric optimization method by Curless and Levoy (1996) is interpreted from a probabilistic perspective. From this perspective, the method is extended through Bayesian fusion of spatial measurements with Gaussian uncertainty. Additionally to the generation of an optimal surface, this probabilistic perspective allows for the estimation of surface probabilities. They are used for filtering outliers in 3D space by means of geometric consistency checks. A further improvement of the quality is obtained based on the analysis of the disparity uncertainty. To this end, Total Variation (TV)-based feature classes are defined that are highly correlated with the disparity uncertainty. The correlation function is learned from ground-truth data by means of an Expectation Maximization (EM) approach. Because of the consideration of a statistically estimated disparity error in a probabilistic framework for fusion of spatial data, this can be regarded as a stochastic fusion of disparity maps. In addition, the influence of image registration and polygonization for volumetric fusion is analyzed and used to extend the method. Finally, a multi-resolution strategy is presented that allows for the generation of surfaces from spatial data with a largely varying quality. This method extends state-of-the-art methods by considering the spatial uncertainty of 3D points from stereo data. The evaluation of several well-known and novel datasets demonstrates the potential of the scalable stochastic fusion method. The strength and the weakness of the method are discussed and direction for future research is given.Digitale dreidimensionale (3D) Modelle sind in vielen Anwendungsfeldern, wie Medizin, Ingenieurswesen, Simulation und Unterhaltung von signifikantem Interesse. Eine manuelle Erstellung von 3D-Modellen ist äußerst zeitaufwendig und die Erfassung der Daten, z.B. durch Lasersensoren, ist teuer. Kamerabilder ermöglichen hingegen preiswerte Aufnahmen und sind gut verfügbar. Der rasante Fortschritt im Forschungsfeld Computer Vision ermöglicht bereits eine automatische 3D-Rekonstruktion aus Bilddaten. Dennoch besteht weiterhin eine Vielzahl von Problemen, insbesondere bei der Verarbeitung von großen Mengen hochauflösender Bilder. Zusätzlich zur komplexen Formulierung, die zur Lösung eines schlecht gestellten Problems notwendig ist, besteht die Herausforderung darin, äußerst große Datenmengen zu verwalten. Diese Arbeit befasst sich mit dem Problem der 3D-Oberflächenrekonstruktion aus Bilddaten, insbesondere für sehr große Modelle, aber auch Anwendungen mit hohem Genauigkeitsanforderungen. Zu diesem Zweck wird eine Prozesskette zur dichten skalierbaren 3D-Oberflächenrekonstruktion für große Bildmengen definiert, bestehend aus Bildregistrierung, Disparitätsschätzung, Fusion von Disparitätskarten und Triangulation von Punktwolken. Der Schwerpunkt dieser Arbeit liegt auf der Fusion und Filterung von durch Semi-Global Matching generierten Disparitätskarten zur Bestimmung von genauen 3D-Punktwolken. Für eine unbegrenzte Skalierbarkeit wird eine Divide and Conquer Methode vorgestellt, welche eine parallele Verarbeitung von Teilräumen des 3D-Rekonstruktionsraums ermöglicht. Die Methode zur Fusion von Disparitätskarten basiert auf lokaler Optimierung von 3D Daten. Damit kann eine komplizierte Fusionsstrategie für die Unterräume vermieden werden. Obwohl der Fokus auf der skalierbaren Rekonstruktion liegt, wird eine hohe Oberflächenqualität durch mehrere Erweiterungen von lokalen Optimierungsmodellen erzielt, die dem Stand der Forschung entsprechen. Dazu wird die wegweisende lokale volumetrische Optimierungsmethode von Curless and Levoy (1996) aus einer probabilistischen Perspektive interpretiert. Aus dieser Perspektive wird die Methode durch eine Bayes Fusion von räumlichen Messungen mit Gaußscher Unsicherheit erweitert. Zusätzlich zur Bestimmung einer optimalen Oberfläche ermöglicht diese probabilistische Fusion die Extraktion von Oberflächenwahrscheinlichkeiten. Diese werden wiederum zur Filterung von Ausreißern mittels geometrischer Konsistenzprüfungen im 3D-Raum verwendet. Eine weitere Verbesserung der Qualität wird basierend auf der Analyse der Disparitätsunsicherheit erzielt. Dazu werden Gesamtvariation-basierte Merkmalsklassen definiert, welche stark mit der Disparitätsunsicherheit korrelieren. Die Korrelationsfunktion wird aus ground-truth Daten mittels eines Expectation Maximization (EM) Ansatzes gelernt. Aufgrund der Berücksichtigung eines statistisch geschätzten Disparitätsfehlers in einem probabilistischem Grundgerüst für die Fusion von räumlichen Daten, kann dies als eine stochastische Fusion von Disparitätskarten betrachtet werden. Außerdem wird der Einfluss der Bildregistrierung und Polygonisierung auf die volumetrische Fusion analysiert und verwendet, um die Methode zu erweitern. Schließlich wird eine Multi-Resolution Strategie präsentiert, welche die Generierung von Oberflächen aus räumlichen Daten mit unterschiedlichster Qualität ermöglicht. Diese Methode erweitert Methoden, die den Stand der Forschung darstellen, durch die Berücksichtigung der räumlichen Unsicherheit von 3D-Punkten aus Stereo Daten. Die Evaluierung von mehreren bekannten und neuen Datensätzen zeigt das Potential der skalierbaren stochastischen Fusionsmethode auf. Stärken und Schwächen der Methode werden diskutiert und es wird eine Empfehlung für zukünftige Forschung gegeben

Integration of multiple overlapping range images

The work described in this document continues the developing of an online 3D reconstruction pipeline for the ESAT-PSI department of K.U. Leuven (Belgium). The idea of this 3D reconstruction pipeline is that only a digital photo camera and Internet connection is necessary for a user to reconstruct scenes in 3D. The process of obtaining a 3D model from the reconstruction pipeline involves the following main three phases: the data acquisition step of the desired object, the data 3D reconstruction of the partial views and the integration of partial reconstructions in one single 3D model. In the data acquisition phase, some regular images are taken by a consumer-grade digital camera of the target object and uploaded to the reconstruction server. In the reconstruction step, the position (and internal parameters) of the camera is computed for each image. Stereo algorithms are used to create partial reconstructions from each image that are all aligned in a common coordinate system. Both steps have already been developed. In the integration phase, we aim to all these partial reconstructions into single 3D model representation. It is this place that being developed in this Master Thesis. A volumetric integration technique for merging multiple aligned overlapping range images based on the Marching Intersections algorithm is implemented. Furthermore, several techniques are implemented to improve the quality of the 3D final representation. These techniques are: - A filtering procedure of the partial reconstructions. - A weighted function according to the data input confidence. - A triangular mesh-based hole-filling algorithm. - An algorithm for creating a texture by stitching color information from the set of RGB input images using camera’s visibility information. We analyze and obtain conclusions about the results of the implemented integration algorithm and how works the proposed improving techniques. Finally, we analyze a comparison between our application and the volumetric integration algorithm called VripPack

Scene Reconstruction from Multi-Scale Input Data

Geometry acquisition of real-world objects by means of 3D scanning or stereo reconstruction constitutes a very important and challenging problem in computer vision. 3D scanners and stereo algorithms usually provide geometry from one viewpoint only, and several of the these scans need to be merged into one consistent representation. Scanner data generally has lower noise levels than stereo methods and the scanning scenario is more controlled. In image-based stereo approaches, the aim is to reconstruct the 3D surface of an object solely from multiple photos of the object. In many cases, the stereo geometry is contaminated with noise and outliers, and exhibits large variations in scale. Approaches that fuse such data into one consistent surface must be resilient to such imperfections. In this thesis, we take a closer look at geometry reconstruction using both scanner data and the more challenging image-based scene reconstruction approaches. In particular, this work focuses on the uncontrolled setting where the input images are not constrained, may be taken with different camera models, under different lighting and weather conditions, and from vastly different points of view. A typical dataset contains many views that observe the scene from an overview perspective, and relatively few views capture small details of the geometry. What results from these datasets are surface samples of the scene with vastly different resolution. As we will show in this thesis, the multi-resolution, or, "multi-scale" nature of the input is a relevant aspect for surface reconstruction, which has rarely been considered in literature yet. Integrating scale as additional information in the reconstruction process can make a substantial difference in surface quality. We develop and study two different approaches for surface reconstruction that are able to cope with the challenges resulting from uncontrolled images. The first approach implements surface reconstruction by fusion of depth maps using a multi-scale hierarchical signed distance function. The hierarchical representation allows fusion of multi-resolution depth maps without mixing geometric information at incompatible scales, which preserves detail in high-resolution regions. An incomplete octree is constructed by incrementally adding triangulated depth maps to the hierarchy, which leads to scattered samples of the multi-resolution signed distance function. A continuous representation of the scattered data is defined by constructing a tetrahedral complex, and a final, highly-adaptive surface is extracted by applying the Marching Tetrahedra algorithm. A second, point-based approach is based on a more abstract, multi-scale implicit function defined as a sum of basis functions. Each input sample contributes a single basis function which is parameterized solely by the sample's attributes, effectively yielding a parameter-free method. Because the scale of each sample controls the size of the basis function, the method automatically adapts to data redundancy for noise reduction and is highly resilient to the quality-degrading effects of low-resolution samples, thus favoring high-resolution surfaces. Furthermore, we present a robust, image-based reconstruction system for surface modeling: MVE, the Multi-View Environment. The implementation provides all steps involved in the pipeline: Calibration and registration of the input images, dense geometry reconstruction by means of stereo, a surface reconstruction step and post-processing, such as remeshing and texturing. In contrast to other software solutions for image-based reconstruction, MVE handles large, uncontrolled, multi-scale datasets as well as input from more controlled capture scenarios. The reason lies in the particular choice of the multi-view stereo and surface reconstruction algorithms. The resulting surfaces are represented using a triangular mesh, which is a piecewise linear approximation to the real surface. The individual triangles are often so small that they barely contribute any geometric information and can be ill-shaped, which can cause numerical problems. A surface remeshing approach is introduced which changes the surface discretization such that more favorable triangles are created. It distributes the vertices of the mesh according to a density function, which is derived from the curvature of the geometry. Such a mesh is better suited for further processing and has reduced storage requirements. We thoroughly compare the developed methods against the state-of-the art and also perform a qualitative evaluation of the two surface reconstruction methods on a wide range of datasets with different properties. The usefulness of the remeshing approach is demonstrated on both scanner and multi-view stereo data

Automatic 3d modeling of environments (a sparse approach from images taken by a catadioptric camera)

La modélisation 3d automatique d'un environnement à partir d'images est un sujet toujours d'actualité en vision par ordinateur. Ce problème se résout en général en trois temps : déplacer une caméra dans la scène pour prendre la séquence d'images, reconstruire la géométrie, et utiliser une méthode de stéréo dense pour obtenir une surface de la scène. La seconde étape met en correspondances des points d'intérêts dans les images puis estime simultanément les poses de la caméra et un nuage épars de points 3d de la scène correspondant aux points d'intérêts. La troisième étape utilise l'information sur l'ensemble des pixels pour reconstruire une surface de la scène, par exemple en estimant un nuage de points dense.Ici nous proposons de traiter le problème en calculant directement une surface à partir du nuage épars de points et de son information de visibilité fournis par l'estimation de la géométrie. Les avantages sont des faibles complexités en temps et en espace, ce qui est utile par exemple pour obtenir des modèles compacts de grands environnements comme une ville. Pour cela, nous présentons une méthode de reconstruction de surface du type sculpture dans une triangulation de Delaunay 3d des points reconstruits. L'information de visibilité est utilisée pour classer les tétraèdres en espace vide ou matière. Puis une surface est extraite de sorte à séparer au mieux ces tétraèdres à l'aide d'une méthode gloutonne et d'une minorité de points de Steiner. On impose sur la surface la contrainte de 2-variété pour permettre des traitements ultérieurs classiques tels que lissage, raffinement par optimisation de photo-consistance ... Cette méthode a ensuite été étendue au cas incrémental : à chaque nouvelle image clef sélectionnée dans une vidéo, de nouveaux points 3d et une nouvelle pose sont estimés, puis la surface est mise à jour. La complexité en temps est étudiée dans les deux cas (incrémental ou non). Dans les expériences, nous utilisons une caméra catadioptrique bas coût et obtenons des modèles 3d texturés pour des environnements complets incluant bâtiments, sol, végétation ... Un inconvénient de nos méthodes est que la reconstruction des éléments fins de la scène n'est pas correcte, par exemple les branches des arbres et les pylônes électriques.The automatic 3d modeling of an environment using images is still an active topic in Computer Vision. Standard methods have three steps : moving a camera in the environment to take an image sequence, reconstructing the geometry of the environment, and applying a dense stereo method to obtain a surface model of the environment. In the second step, interest points are detected and matched in images, then camera poses and a sparse cloud of 3d points corresponding to the interest points are simultaneously estimated. In the third step, all pixels of images are used to reconstruct a surface of the environment, e.g. by estimating a dense cloud of 3d points. Here we propose to generate a surface directly from the sparse point cloud and its visibility information provided by the geometry reconstruction step. The advantages are low time and space complexities ; this is useful e.g. for obtaining compact models of large and complete environments like a city. To do so, a surface reconstruction method by sculpting 3d Delaunay triangulation of the reconstructed points is proposed.The visibility information is used to classify the tetrahedra in free-space and matter. Then a surface is extracted thanks to a greedy method and a minority of Steiner points. The 2-manifold constraint is enforced on the surface to allow standard surface post-processing such as denoising, refinement by photo-consistency optimization ... This method is also extended to the incremental case : each time a new key-frame is selected in the input video, new 3d points and camera pose are estimated, then the reconstructed surface is updated.We study the time complexity in both cases (incremental or not). In experiments, a low-cost catadioptric camera is used to generate textured 3d models for complete environments including buildings, ground, vegetation ... A drawback of our methods is that thin scene components cannot be correctly reconstructed, e.g. tree branches and electric posts.CLERMONT FD-Bib.électronique (631139902) / SudocSudocFranceF