Efficient Decomposition of Image and Mesh Graphs by Lifted Multicuts

Formulations of the Image Decomposition Problem as a Multicut Problem (MP) w.r.t. a superpixel graph have received considerable attention. In contrast, instances of the MP w.r.t. a pixel grid graph have received little attention, firstly, because the MP is NP-hard and instances w.r.t. a pixel grid graph are hard to solve in practice, and, secondly, due to the lack of long-range terms in the objective function of the MP. We propose a generalization of the MP with long-range terms (LMP). We design and implement two efficient algorithms (primal feasible heuristics) for the MP and LMP which allow us to study instances of both problems w.r.t. the pixel grid graphs of the images in the BSDS-500 benchmark. The decompositions we obtain do not differ significantly from the state of the art, suggesting that the LMP is a competitive formulation of the Image Decomposition Problem. To demonstrate the generality of the LMP, we apply it also to the Mesh Decomposition Problem posed by the Princeton benchmark, obtaining state-of-the-art decompositions

A semi-automatic computer-aided method for surgical template design

This paper presents a generalized integrated framework of semi-automatic surgical template design. Several algorithms were implemented including the mesh segmentation, offset surface generation, collision detection, ruled surface generation, etc., and a special software named TemDesigner was developed. With a simple user interface, a customized template can be semi- automatically designed according to the preoperative plan. Firstly, mesh segmentation with signed scalar of vertex is utilized to partition the inner surface from the input surface mesh based on the indicated point loop. Then, the offset surface of the inner surface is obtained through contouring the distance field of the inner surface, and segmented to generate the outer surface. Ruled surface is employed to connect inner and outer surfaces. Finally, drilling tubes are generated according to the preoperative plan through collision detection and merging. It has been applied to the template design for various kinds of surgeries, including oral implantology, cervical pedicle screw insertion, iliosacral screw insertion and osteotomy, demonstrating the efficiency, functionality and generality of our method.Comment: 18 pages, 16 figures, 2 tables, 36 reference

Automatic 3D tooth segmentation using convolutional neural networks in harmonic parameter space

Automatic segmentation of 3D tooth models into individual teeth is an important step in orthodontic CAD systems. 3D tooth segmentation is a mesh instance segmentation task. Complex geometric features on the surface of 3D tooth models often lead to failure of tooth boundary detection, so it is difficult to achieve automatic and accurate segmentation by traditional mesh segmentation methods. We propose a novel solution to address this problem. We map a 3D tooth model isomorphically to a 2D harmonic parameter space and convert it into an image. This allows us to use a CNN to learn a highly robust image segmentation model to achieve automated and accurate segmentation of 3D tooth models. Finally, we map the image segmentation mask back to the 3D tooth model and refine the segmentation result using an improved Fuzzy Clustering-and-Cuts algorithm. Our method has been incorporated into an orthodontic CAD system, and performs well in practice

Graph-based Object Understanding

Computer Vision algorithms become increasingly prevalent in our everyday lives. Especially recognition systems are often employed to automatize certain tasks (i.e. quality control). In State-of-the-Art approaches global shape char acteristics are leveraged, discarding nuanced shape varieties in the individual parts of the object. Thus, these systems fall short on both learning and utilizing the inherent underlying part structures of objects. By recognizing common substructures between known and queried objects, part-based systems may identify objects more robustly in lieu of occlusion or redundant parts. As we observe these traits, there are theories that such part-based approaches are indeed present in humans. Leveraging abstracted representations of decomposed objects may additionally offer better generalization on less training data. Enabling computer systems to reason about objects on the basis of their parts is the focus of this dissertation. Any part-based method first requires a segmentation approach to assign object regions to individual parts. Therefore, a 2D multi-view segmentation approach for 3D mesh segmentation is extended. The approach uses the normal and depth information of the objects to reliably extract part boundary contours. This method significantly reduces training time of the segmentation model compared to other segmentation approaches while still providing good segmentation results on the test data. To explore the benefits of part-based systems, a symbolic object classification dataset is created that inherently adheres to underlying rules made of spatial relations between part entities. This abstract data is also transformed into 3D point clouds. This enables us to benchmark conventional 3D point cloud classification models against the newly developed model that utilizes ground truth symbol segmentations for the classification task. With the new model, improved classification performance can be observed. This offers empirical evidence that part segmentation may boost classification accuracy if the data obey part-based rules. Additionally, prediction results of the model on segmented 3D data are compared against a modified variant of the model that directly uses the underlying symbols. The perception gap, representing issues with extracting the symbols from the segmented point clouds, is quantified. Furthermore, a framework for 3D object classification on real world objects is developed. The designed pipeline automatically segments an object into its parts, creates the according part graph and predicts the object class based on the similarity to graphs in the training dataset. The advantage of subgraph similarity is utilized in a second experiment, where out-of-distribution samples ofobjects are created, which contain redundant parts. Whereas traditional classification methods working on the global shape may misinterpret extracted feature vectors, the model creates robust predictions. Lastly, the task of object repairment is considered, in which a single part of the given object is compromised by a certain manipulation. As human-made objects follow an underlying part structure, a system to exploit this part structure in order to mend the object is developed. Given the global 3D point cloud of a compromised object, the object is automatically segmented, the shape features are extracted from the individual part clouds and are fed into a Graph Neural Network that predicts a manipulation action for each part. In conclusion, the opportunities of part-graph based methods for object understanding to improve 3D classification and regression tasks are explored. These approaches may enhance robotic computer vision pipelines in the future.2021-06-2

Human perception-oriented segmentation for triangle meshes

A segmentação de malhas é um tópico importante de investigação em computação gráfica, em particular em modelação geométrica. Isto deve-se ao facto de as técnicas de segmentaçãodemalhasteremváriasaplicações,nomeadamentenaproduçãodefilmes, animaçãoporcomputador, realidadevirtual, compressãodemalhas, assimcomoemjogosdigitais. Emconcreto, asmalhastriangularessãoamplamenteusadasemaplicações interativas, visto que sua segmentação em partes significativas (também designada por segmentação significativa, segmentação perceptiva ou segmentação perceptualmente significativa ) é muitas vezes vista como uma forma de acelerar a interação com o utilizador ou a deteção de colisões entre esses objetos 3D definidos por uma malha, bem como animar uma ou mais partes significativas (por exemplo, a cabeça de uma personagem) de um dado objeto, independentemente das restantes partes. Acontece que não se conhece nenhuma técnica capaz de segmentar correctamente malhas arbitrárias −ainda que restritas aos domínios de formas livres e não-livres− em partes significativas. Algumas técnicas são mais adequadas para objetos de forma não-livre (por exemplo, peças mecânicas definidas geometricamente por quádricas), enquanto outras são mais talhadas para o domínio dos objectos de forma livre. Só na literatura recente surgem umas poucas técnicas que se aplicam a todo o universo de objetos de forma livre e não-livre. Pior ainda é o facto de que a maioria das técnicas de segmentação não serem totalmente automáticas, no sentido de que quase todas elas exigem algum tipo de pré-requisitos e assistência do utilizador. Resumindo, estes três desafios relacionados com a proximidade perceptual, generalidade e automação estão no cerne do trabalho descrito nesta tese. Para enfrentar estes desafios, esta tese introduz o primeiro algoritmo de segmentação baseada nos contornos ou fronteiras dos segmentos, cuja técnica se inspira nas técnicas de segmentação baseada em arestas, tão comuns em análise e processamento de imagem,porcontraposiçãoàstécnicasesegmentaçãobaseadaemregiões. Aideiaprincipal é a de encontrar em primeiro lugar a fronteira de cada região para, em seguida, identificar e agrupar todos os seus triângulos internos. As regiões da malha encontradas correspondem a saliências e reentrâncias, que não precisam de ser estritamente convexas, nem estritamente côncavas, respectivamente. Estas regiões, designadas regiões relaxadamenteconvexas(ousaliências)eregiõesrelaxadamentecôncavas(oureentrâncias), produzem segmentações que são menos sensíveis ao ruído e, ao mesmo tempo, são mais intuitivas do ponto de vista da perceção humana; por isso, é designada por segmentação orientada à perceção humana (ou, human perception- oriented (HPO), do inglês). Além disso, e ao contrário do atual estado-da-arte da segmentação de malhas, a existência destas regiões relaxadas torna o algoritmo capaz de segmentar de maneira bastante plausível tanto objectos de forma não-livre como objectos de forma livre. Nesta tese, enfrentou-se também um quarto desafio, que está relacionado com a fusão de segmentação e multi-resolução de malhas. Em boa verdade, já existe na literatura uma variedade grande de técnicas de segmentação, bem como um número significativo de técnicas de multi-resolução, para malhas triangulares. No entanto, não é assim tão comum encontrar estruturas de dados e algoritmos que façam a fusão ou a simbiose destes dois conceitos, multi-resolução e segmentação, num único esquema multi-resolução que sirva os propósitos das aplicações que lidam com malhas simples e segmentadas, sendo que neste contexto se entende que uma malha simples é uma malha com um único segmento. Sendo assim, nesta tese descreve-se um novo esquema (entenda-seestruturasdedadosealgoritmos)demulti-resoluçãoesegmentação,designado por extended Ghost Cell (xGC). Este esquema preserva a forma das malhas, tanto em termos globais como locais, ou seja, os segmentos da malha e as suas fronteiras, bem como os seus vincos e ápices são preservados, não importa o nível de resolução que usamos durante a/o simplificação/refinamento da malha. Além disso, ao contrário de outros esquemas de segmentação, tornou-se possível ter segmentos adjacentes com dois ou mais níveis de resolução de diferença. Isto é particularmente útil em animação por computador, compressão e transmissão de malhas, operações de modelação geométrica, visualização científica e computação gráfica. Em suma, esta tese apresenta um esquema genérico, automático, e orientado à percepção humana, que torna possível a simbiose dos conceitos de segmentação e multiresolução de malhas trianguladas que sejam representativas de objectos 3D.The mesh segmentation is an important topic in computer graphics, in particular in geometric computing. This is so because mesh segmentation techniques find many applications in movies, computer animation, virtual reality, mesh compression, and games. Infact, trianglemeshesarewidelyusedininteractiveapplications, sothattheir segmentation in meaningful parts (i.e., human-perceptually segmentation, perceptive segmentationormeaningfulsegmentation)isoftenseenasawayofspeedinguptheuser interaction, detecting collisions between these mesh-covered objects in a 3D scene, as well as animating one or more meaningful parts (e.g., the head of a humanoid) independently of the other parts of a given object. It happens that there is no known technique capable of correctly segmenting any mesh into meaningful parts. Some techniques are more adequate for non-freeform objects (e.g., quadricmechanicalparts), whileothersperformbetterinthedomainoffreeform objects. Only recently, some techniques have been developed for the entire universe of objects and shapes. Even worse it is the fact that most segmentation techniques are not entirely automated in the sense that almost all techniques require some sort of pre-requisites and user assistance. Summing up, these three challenges related to perceptual proximity, generality and automation are at the core of the work described in this thesis. In order to face these challenges, we have developed the first contour-based mesh segmentation algorithm that we may find in the literature, which is inspired in the edgebased segmentation techniques used in image analysis, as opposite to region-based segmentation techniques. Its leading idea is to firstly find the contour of each region, and then to identify and collect all of its inner triangles. The encountered mesh regions correspond to ups and downs, which do not need to be strictly convex nor strictly concave, respectively. These regions, called relaxedly convex regions (or saliences) and relaxedly concave regions (or recesses), produce segmentations that are less-sensitive to noise and, at the same time, are more intuitive from the human point of view; hence it is called human perception- oriented (HPO) segmentation. Besides, and unlike the current state-of-the-art in mesh segmentation, the existence of these relaxed regions makes the algorithm suited to both non-freeform and freeform objects. In this thesis, we have also tackled a fourth challenge, which is related with the fusion of mesh segmentation and multi-resolution. Truly speaking, a plethora of segmentation techniques, as well as a number of multiresolution techniques, for triangle meshes already exist in the literature. However, it is not so common to find algorithms and data structures that fuse these two concepts, multiresolution and segmentation, into a symbiotic multi-resolution scheme for both plain and segmented meshes, in which a plainmeshisunderstoodasameshwithasinglesegment. So, weintroducesuchanovel multiresolution segmentation scheme, called extended Ghost Cell (xGC) scheme. This scheme preserves the shape of the meshes in both global and local terms, i.e., mesh segments and their boundaries, as well as creases and apices are preserved, no matter the level of resolution we use for simplification/refinement of the mesh. Moreover, unlike other segmentation schemes, it was made possible to have adjacent segments with two or more resolution levels of difference. This is particularly useful in computer animation, mesh compression and transmission, geometric computing, scientific visualization, and computer graphics. In short, this thesis presents a fully automatic, general, and human perception-oriented scheme that symbiotically integrates the concepts of mesh segmentation and multiresolution

Generalizations of the Multicut Problem for Computer Vision

Graph decomposition has always been a very important concept in machine learning and computer vision. Many tasks like image and mesh segmentation, community detection in social networks, as well as object tracking and human pose estimation can be formulated as a graph decomposition problem. The multicut problem in particular is a popular model to optimize for a decomposition of a given graph. Its main advantage is that no prior knowledge about the number of components or their sizes is required. However, it has several limitations, which we address in this thesis: Firstly, the multicut problem allows to specify only cost or reward for putting two direct neighbours into distinct components. This limits the expressibility of the cost function. We introduce special edges into the graph that allow to define cost or reward for putting any two vertices into distinct components, while preserving the original set of feasible solutions. We show that this considerably improves the quality of image and mesh segmentations. Second, multicut is notorious to be NP-hard for general graphs, that limits its applications to small super-pixel graphs. We define and implement two primal feasible heuristics to solve the problem. They do not provide any guarantees on the runtime or quality of solutions, but in practice show good convergence behaviour. We perform an extensive comparison on multiple graphs of different sizes and properties. Third, we extend the multicut framework by introducing node labels, so that we can jointly optimize for graph decomposition and nodes classification by means of exactly the same optimization algorithm, thus eliminating the need to hand-tune optimizers for a particular task. To prove its universality we applied it to diverse computer vision tasks, including human pose estimation, multiple object tracking, and instance-aware semantic segmentation. We show that we can improve the results over the prior art using exactly the same data as in the original works. Finally, we use employ multicuts in two applications: 1) a client-server tool for interactive video segmentation: After the pre-processing of the video a user draws strokes on several frames and a time-coherent segmentation of the entire video is performed on-the-fly. 2) we formulate a method for simultaneous segmentation and tracking of living cells in microscopy data. This task is challenging as cells split and our algorithm accounts for this, creating parental hierarchies. We also present results on multiple model fitting. We find models in data heavily corrupted by noise by finding components defining these models using higher order multicuts. We introduce an interesting extension that allows our optimization to pick better hyperparameters for each discovered model. In summary, this thesis extends the multicut problem in different directions, proposes algorithms for optimization, and applies it to novel data and settings.Die Zerlegung von Graphen ist ein sehr wichtiges Konzept im maschinellen Lernen und maschinellen Sehen. Viele Aufgaben wie Bild- und Gittersegmentierung, Kommunitätserkennung in sozialen Netzwerken, sowie Objektverfolgung und Schätzung von menschlichen Posen können als Graphzerlegungsproblem formuliert werden. Der Mehrfachschnitt-Ansatz ist ein populäres Mittel um über die Zerlegungen eines gegebenen Graphen zu optimieren. Sein größter Vorteil ist, dass kein Vorwissen über die Anzahl an Komponenten und deren Größen benötigt wird. Dennoch hat er mehrere ernsthafte Limitierungen, welche wir in dieser Arbeit behandeln: Erstens erlaubt der klassische Mehrfachschnitt nur die Spezifikation von Kosten oder Belohnungen für die Trennung von zwei Nachbarn in verschiedene Komponenten. Dies schränkt die Ausdrucksfähigkeit der Kostenfunktion ein und führt zu suboptimalen Ergebnissen. Wir fügen dem Graphen spezielle Kanten hinzu, welche es erlauben, Kosten oder Belohnungen für die Trennung von beliebigen Paaren von Knoten in verschiedene Komponenten zu definieren, ohne die Menge an zulässigen Lösungen zu verändern. Wir zeigen, dass dies die Qualität von Bild- und Gittersegmentierungen deutlich verbessert. Zweitens ist das Mehrfachschnittproblem berüchtigt dafür NP-schwer für allgemeine Graphen zu sein, was die Anwendungen auf kleine superpixel-basierte Graphen einschränkt. Wir definieren und implementieren zwei primal-zulässige Heuristiken um das Problem zu lösen. Diese geben keine Garantien bezüglich der Laufzeit oder der Qualität der Lösungen, zeigen in der Praxis jedoch gutes Konvergenzverhalten. Wir führen einen ausführlichen Vergleich auf vielen Graphen verschiedener Größen und Eigenschaften durch. Drittens erweitern wir den Mehrfachschnitt-Ansatz um Knoten-Kennzeichnungen, sodass wir gemeinsam über Zerlegungen und Knoten-Klassifikationen mit dem gleichen Optimierungs-Algorithmus optimieren können. Dadurch wird der Bedarf der Feinabstimmung einzelner aufgabenspezifischer Löser aus dem Weg geräumt. Um die Allgemeingültigkeit dieses Ansatzes zu überprüfen, haben wir ihn auf verschiedenen Aufgaben des maschinellen Sehens, einschließlich menschliche Posenschätzung, Mehrobjektverfolgung und instanz-bewusste semantische Segmentierung, angewandt. Wir zeigen, dass wir Resultate von vorherigen Arbeiten mit exakt den gleichen Daten verbessern können. Abschließend benutzen wir Mehrfachschnitte in zwei Anwendungen: 1) Ein Nutzer-Server-Werkzeug für interaktive Video Segmentierung: Nach der Vorbearbeitung eines Videos zeichnet der Nutzer Striche auf mehrere Einzelbilder und eine zeit-kohärente Segmentierung des gesamten Videos wird in Echtzeit berechnet. 2) Wir formulieren eine Methode für simultane Segmentierung und Verfolgung von lebenden Zellen in Mikroskopie-Aufnahmen. Diese Aufgabe ist anspruchsvoll, da Zellen sich aufteilen und unser Algorithmus dies in der Erstellung von Eltern-Hierarchien mitberücksichtigen muss. Wir präsentieren außerdem Resultate zur Mehrmodellanpassung. Wir berechnen Modelle in stark verrauschten Daten indem wir mithilfe von Mehrfachschnitten höherer Ordnung Komponenten finden, die diesen Modellen entsprechen. Wir führen eine interessante Erweiterung ein, die es unserer Optimierung erlaubt, bessere Hyperparameter für jedes entdeckte Modell auszuwählen. Zusammenfassend erweitert diese Arbeit den Mehrfachschnitt-Ansatz in unterschiedlichen Richtungen, schlägt Algorithmen zur Inferenz in den resultierenden Modellen vor und wendet ihn auf neuartigen Daten und Umgebungen an