A graph based model for the detection of tidal channels using marked point processes

In this paper we propose a new method for the automatic extraction of tidal channels in digital terrain models (DTM) using a sampling approach based on marked point processes. In our model, the tidal channel system is represented by an undirected, acyclic graph. The graph is iteratively generated and fitted to the data using stochastic optimization based on a Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampler and simulated annealing. The nodes of the graph represent junction points of the channel system and the edges straight line segments with a certain width in between. In each sampling step, the current configuration of nodes and edges is modified. The changes are accepted or rejected depending on the probability density function for the configuration which evaluates the conformity of the current status with a pre-defined model for tidal channels. In this model we favour high DTM gradient magnitudes at the edge borders and penalize a graph configuration consisting of non-connected components, overlapping segments and edges with atypical intersection angles. We present the method of our graph based model and show results for lidar data, which serve of a proof of concept of our approach.Ministry of Environment, Energy, and Climate ProtectionMinistry of Science and Culture of Lower Saxon

Extracting Geometric Structures in Images with Delaunay Point Processes

International audienceWe introduce Delaunay Point Processes, a framework for the extraction of geometric structures from images. Our approach simultaneously locates and groups geometric primitives (line segments, triangles) to form extended structures (line networks, polygons) for a variety of image analysis tasks. Similarly to traditional point processes, our approach uses Markov Chain Monte Carlo to minimize an energy that balances fidelity to the input image data with geometric priors on the output structures. However, while existing point processes struggle to model structures composed of interconnected components, we propose to embed the point process into a Delaunay triangulation, which provides high-quality connectivity by construction. We further leverage key properties of the Delaunay triangulation to devise a fast Markov Chain Monte Carlo sampler. We demonstrate the flexibility of our approach on a variety of applications, including line network extraction, object contouring, and mesh-based image compression

Geometric Feature Extraction by a Multi-Marked Point Process

International audienceThis paper presents a new stochastic marked point process for describing images in terms of a finite library of geometric objects. Image analysis based on conventional marked point processes has already produced convincing results but at the expense of parameter tuning, computing time, and model specificity. Our more general multimarked point process has simpler parametric setting, yields notably shorter computing times, and can be applied to a variety of applications. Both linear and areal primitives extracted from a library of geometric objects are matched to a given image using a probabilistic Gibbs model, and a Jump-Diffusion process is performed to search for the optimal object configuration. Experiments with remotely sensed images and natural textures show that the proposed approach has good potential. We conclude with a discussion about the insertion of more complex object interactions in the model by studying the compromise between model complexity and efficiency

A Marked Point Process for Modeling Lidar Waveforms

International audienceLidar waveforms are 1-D signals representing a train of echoes caused by reflections at different targets. Modeling these echoes with the appropriate parametric function is useful to retrieve information about the physical characteristics of the targets. This paper presents a new probabilistic model based upon a marked point process which reconstructs the echoes from recorded discrete waveforms as a sequence of parametric curves. Such an approach allows to fit each mode of a waveform with the most suitable function and to deal with both, symmetric and asymmetric, echoes. The model takes into account a data term, which measures the coherence between the models and the waveforms, and a regularization term, which introduces prior knowledge on the reconstructed signal. The exploration of the associated configuration space is performed by a reversible jump Markov chain Monte Carlo (RJMCMC) sampler coupled with simulated annealing. Experiments with different kinds of lidar signals, especially from urban scenes, show the high potential of the proposed approach. To further demonstrate the advantages of the suggested method, actual laser scans are classified and the results are reported

Automated Reconstruction of Dendritic and Axonal Trees by Global Optimization with Geometric Priors

We present a novel probabilistic approach to fully automated delineation of tree structures in noisy 2D images and 3D image stacks. Unlike earlier methods that rely mostly on local evidence, ours builds a set of candidate trees over many different subsets of points likely to belong to the optimal tree and then chooses the best one according to a global objective function that combines image evidence with geometric priors. Since the best tree does not necessarily span all the points, the algorithm is able to eliminate false detections while retaining the correct tree topology. Manually annotated brightfield micrographs, retinal scans and the DIADEM challenge datasets are used to evaluate the performance of our method. We used the DIADEM metric to quantitatively evaluate the topological accuracy of the reconstructions and showed that the use of the geometric regularization yields a substantial improvement

Real-Time Automatic Linear Feature Detection in Images

Linear feature detection in digital images is an important low-level operation in computer vision that has many applications. In remote sensing tasks, it can be used to extract roads, railroads, and rivers from satellite or low-resolution aerial images, which can be used for the capture or update of data for geographic information and navigation systems. In addition, it is useful in medical imaging for the extraction of blood vessels from an X-ray angiography or the bones in the skull from a CT or MR image. It also can be applied in horticulture for underground plant root detection in minirhizotron images. In this dissertation, a fast and automatic algorithm for linear feature extraction from images is presented. Under the assumption that linear feature is a sequence of contiguous pixels where the image intensity is locally maximal in the direction of the gradient, linear features are extracted as non-overlapping connected line segments consisting of these contiguous pixels. To perform this task, point process is used to model line segments network in images. Specific properties of line segments in an image are described by an intensity energy model. Aligned segments are favored while superposition is penalized. These constraints are enforced by an interaction energy model. Linear features are extracted from the line segments network by minimizing a modified Candy model energy function using a greedy algorithm whose parameters are determined in a data-driven manner. Experimental results from a collection of different types of linear features (underground plant roots, blood vessels and urban roads) in images demonstrate the effectiveness of the approach

Automated Reconstruction of Evolving Curvilinear Tree Structures

Curvilinear networks are prevalent in nature and span many different scales, ranging from micron-scale neural structures in the brain to petameter-scale dark-matter arbors binding massive galaxy clusters. Reliably reconstructing them in an automated fashion is of great value in many different scientific domains. However, it remains an open Computer Vision problem. In this thesis we focus on automatically delineating curvilinear tree structures in images of the same object of interest taken at different time instants. Unlike virtually all of the existing methods approaching the task of tree structures delineation we process all the images at once. This is useful in the more ambiguous regions and allows to reason for the tree structure that fits best to all the acquired data. We propose two methods that utilize this principle of temporal consistency to achieve results of higher quality compared to single time instant methods. The first, simpler method starts by building an overcomplete graph representation of the final solution in all time instants while simultaneously obtaining correspondences between image features across time. We then define an objective function with a temporal consistency prior and reconstruct the structures in all images at once by solving a mathematical optimization. The role of the prior is to encourage solutions where for two consecutive time instants corresponding candidate edges are either both retained or both rejected from the final solution. The second multiple time instant method uses the same overcomplete graph principle but handles the temporal consistency in a more robust way. Instead of focusing on the very local consistency of single edges of the overcomplete graph we propose a method for describing topological relationships. This favors solutions whose connectivity is consistent over time. We show that by making the temporal consistency more global we achieve additional robustness to errors in the initial features matching step, which is shared by both the approaches. In the end, this yields superior performance. Furthermore, an added benefit of both our approaches is the ability to automatically detect places where significant changes have occurred over time, which is challenging when considering large amounts of data. We also propose a simple single time instant method for delineating tree structures. It computes a Minimum Spanning Arborescence of an initial overcomplete graph and proceeds to optimally prune spurious branches. This yields results of lower but still competitive quality compared to the mathematical optimization based methods, while keeping low computational complexity. Our methods can applied to both 2D and 3D data. We demonstrate their performance in 3D on microscopy volumes of mouse brain and rat brain. We also test them in 2D on time-lapse images of a growing runner bean and aerial images of a road network

Reconstructing Curvilinear Networks using Path Classifiers and Integer Programming

We propose a novel Bayesian approach to automated delineation of curvilinear structures that form complex and potentially loopy networks. By representing the image data as a graph of potential paths, we first show how to weight these paths using discriminatively-trained classifiers that are both robust and generic enough to be applied to very different imaging modalities. We then present an Integer Programming approach to finding the optimal subset of paths, subject to structural and topological constraints that eliminate implausible solutions. Unlike earlier approaches that assume a tree topology for the networks, ours explicitly models the fact that the networks may contain loops, and can reconstruct both cyclic and acyclic ones. We demonstrate the effectiveness of our approach on a variety of challenging datasets including aerial images of road networks and micrographs of neural arbors, and show that it outperforms state-of-the-art techniques

Learning Approach to Delineation of Curvilinear Structures in 2D and 3D Images

Detection of curvilinear structures has long been of interest due to its wide range of applications. Large amounts of imaging data could be readily used in many fields, but it is practically not possible to analyze them manually. Hence, the need for automated delineation approaches. In the recent years Computer Vision witnessed a paradigm shift from mathematical modelling to data-driven methods based on Machine Learning. This led to improvements in performance and robustness of the detection algorithms. Nonetheless, most Machine Learning methods are general-purpose and they do not exploit the specificity of the delineation problem. In this thesis, we present learning methods suited for this task and we apply them to various kinds of microscopic and natural images, proving the general applicability of the presented solutions. First, we introduce a topology loss - a new training loss term, which captures higher-level features of curvilinear networks such as smoothness, connectivity and continuity. This is in contrast to most Deep Learning segmentation methods that do not take into account the geometry of the resulting prediction. In order to compute the new loss term, we extract topology features of prediction and ground-truth using a pre-trained network, whose filters are activated by structures at different scales and orientations. We show that this approach yields better results in terms of conventional segmentation metrics and overall topology of the resulting delineation. Although segmentation of curvilinear structures provides useful information, it is not always sufficient. In many cases, such as neuroscience and cartography, it is crucial to estimate the network connectivity. In order to find the graph representation of the structure depicted in the image, we propose an approach for joint segmentation and connection classification. Apart from pixel probabilities, this approach also returns the likelihood of a proposed path being a part of the reconstructed network. We show that segmentation and path classification are closely related tasks and can benefit from the synergy. The aforementioned methods rely on Machine Learning, which requires significant amounts of annotated ground-truth data to train models. The labelling process often requires expertise, it is costly and tiresome. To alleviate this problem, we introduce an Active Learning method that significantly decreases the time spent on annotating images. It queries the annotator only about the most informative examples, in this case the hypothetical paths belonging to the structure of interest. Contrary to conventional Active Learning methods, our approach exploits local consistency of linear paths to pick the ones that stand out from their neighborhood. Our final contribution is a method suited for both Active Learning and proofreading the result, which often requires more time than the automated delineation itself. It investigates edges of the delineation graph and determines the ones that are especially significant for the global reconstruction by perturbing their weights. Our Active Learning and proofreading strategies are combined with a new efficient formulation of an optimal subgraph computation and reduce the annotation effort by up to 80%

High-Level Facade Image Interpretation using Marked Point Processes

In this thesis, we address facade image interpretation as one essential ingredient for the generation of high-detailed, semantic meaningful, three-dimensional city-models. Given a single rectified facade image, we detect relevant facade objects such as windows, entrances, and balconies, which yield a description of the image in terms of accurate position and size of these objects. Urban digital three-dimensional reconstruction and documentation is an active area of research with several potential applications, e.g., in the area of digital mapping for navigation, urban planning, emergency management, disaster control or the entertainment industry. A detailed building model which is not just a geometric object enriched with texture, allows for semantic requests as the number of floors or the location of balconies and entrances. Facade image interpretation is one essential step in order to yield such models. In this thesis, we propose the interpretation of facade images by combining evidence for the occurrence of individual object classes which we derive from data, and prior knowledge which guides the image interpretation in its entirety. We present a three-step procedure which generates features that are suited to describe relevant objects, learns a representation that is suited for object detection, and that enables the image interpretation using the results of object detection while incorporating prior knowledge about typical configurations of facade objects, which we learn from training data. According to these three sub-tasks, our major achievements are: We propose a novel method for facade image interpretation based on a marked point process. Therefor, we develop a model for the description of typical configurations of facade objects and propose an image interpretation system which combines evidence derived from data and prior knowledge about typical configurations of facade objects. In order to generate evidence from data, we propose a feature type which we call shapelets. They are scale invariant and provide large distinctiveness for facade objects. Segments of lines, arcs, and ellipses serve as basic features for the generation of shapelets. Therefor, we propose a novel line simplification approach which approximates given pixel-chains by a sequence of lines, circular, and elliptical arcs. Among others, it is based on an adaption to Douglas-Peucker's algorithm, which is based on circles as basic geometric elements We evaluate each step separately. We show the effects of polyline segmentation and simplification on several images with comparable good or even better results, referring to a state-of-the-art algorithm, which proves their large distinctiveness for facade objects. Using shapelets we provide a reasonable classification performance on a challenging dataset, including intra-class variations, clutter, and scale changes. Finally, we show promising results for the facade interpretation system on several datasets and provide a qualitative evaluation which demonstrates the capability of complete and accurate detection of facade objectsHigh-Level Interpretation von Fassaden-Bildern unter Benutzung von Markierten PunktprozessenDas Thema dieser Arbeit ist die Interpretation von Fassadenbildern als wesentlicher Beitrag zur Erstellung hoch detaillierter, semantisch reichhaltiger dreidimensionaler Stadtmodelle. In rektifizierten Einzelaufnahmen von Fassaden detektieren wir relevante Objekte wie Fenster, Türen und Balkone, um daraus eine Bildinterpretation in Form von präzisen Positionen und Größen dieser Objekte abzuleiten. Die digitale dreidimensionale Rekonstruktion urbaner Regionen ist ein aktives Forschungsfeld mit zahlreichen Anwendungen, beispielsweise der Herstellung digitaler Kartenwerke für Navigation, Stadtplanung, Notfallmanagement, Katastrophenschutz oder die Unterhaltungsindustrie. Detaillierte Gebäudemodelle, die nicht nur als geometrische Objekte repräsentiert und durch eine geeignete Textur visuell ansprechend dargestellt werden, erlauben semantische Anfragen, wie beispielsweise nach der Anzahl der Geschosse oder der Position der Balkone oder Eingänge. Die semantische Interpretation von Fassadenbildern ist ein wesentlicher Schritt für die Erzeugung solcher Modelle. In der vorliegenden Arbeit lösen wir diese Aufgabe, indem wir aus Daten abgeleitete Evidenz für das Vorkommen einzelner Objekte mit Vorwissen kombinieren, das die Analyse der gesamten Bildinterpretation steuert. Wir präsentieren dafür ein dreistufiges Verfahren: Wir erzeugen Bildmerkmale, die für die Beschreibung der relevanten Objekte geeignet sind. Wir lernen, auf Basis abgeleiteter Merkmale, eine Repräsentation dieser Objekte. Schließlich realisieren wir die Bildinterpretation basierend auf der zuvor gelernten Repräsentation und dem Vorwissen über typische Konfigurationen von Fassadenobjekten, welches wir aus Trainingsdaten ableiten. Wir leisten dazu die folgenden wissenschaftlichen Beiträge: Wir schlagen eine neuartige Me-thode zur Interpretation von Fassadenbildern vor, die einen sogenannten markierten Punktprozess verwendet. Dafür entwickeln wir ein Modell zur Beschreibung typischer Konfigurationen von Fassadenobjekten und entwickeln ein Bildinterpretationssystem, welches aus Daten abgeleitete Evidenz und a priori Wissen über typische Fassadenkonfigurationen kombiniert. Für die Erzeugung der Evidenz stellen wir Merkmale vor, die wir Shapelets nennen und die skaleninvariant und durch eine ausgesprochene Distinktivität im Bezug auf Fassadenobjekte gekennzeichnet sind. Als Basismerkmale für die Erzeugung der Shapelets dienen Linien-, Kreis- und Ellipsensegmente. Dafür stellen wir eine neuartige Methode zur Vereinfachung von Liniensegmenten vor, die eine Pixelkette durch eine Sequenz von geraden Linienstücken und elliptischen Bogensegmenten approximiert. Diese basiert unter anderem auf einer Adaption des Douglas-Peucker Algorithmus, die anstelle gerader Linienstücke, Bogensegmente als geometrische Basiselemente verwendet. Wir evaluieren jeden dieser drei Teilschritte separat. Wir zeigen Ergebnisse der Liniensegmen-tierung anhand verschiedener Bilder und weisen dabei vergleichbare und teilweise verbesserte Ergebnisse im Vergleich zu bestehende Verfahren nach. Für die vorgeschlagenen Shapelets weisen wir in der Evaluation ihre diskriminativen Eigenschaften im Bezug auf Fassadenobjekte nach. Wir erzeugen auf einem anspruchsvollen Datensatz von skalenvariablen Fassadenobjekten, mit starker Variabilität der Erscheinung innerhalb der Klassen, vielversprechende Klassifikationsergebnisse, die die Verwendbarkeit der gelernten Shapelets für die weitere Interpretation belegen. Schließlich zeigen wir Ergebnisse der Interpretation der Fassadenstruktur anhand verschiedener Datensätze. Die qualitative Evaluation demonstriert die Fähigkeit des vorgeschlagenen Lösungsansatzes zur vollständigen und präzisen Detektion der genannten Fassadenobjekte