A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Segmentation and Classification of Remotely Sensed Images: Object-Based Image Analysis

Land-use-and-land-cover (LULC) mapping is crucial in precision agriculture, environmental monitoring, disaster response, and military applications. The demand for improved and more accurate LULC maps has led to the emergence of a key methodology known as Geographic Object-Based Image Analysis (GEOBIA). The core idea of the GEOBIA for an object-based classification system (OBC) is to change the unit of analysis from single-pixels to groups-of-pixels called `objects\u27 through segmentation. While this new paradigm solved problems and improved global accuracy, it also raised new challenges such as the loss of accuracy in categories that are less abundant, but potentially important. Although this trade-off may be acceptable in some domains, the consequences of such an accuracy loss could be potentially fatal in others (for instance, landmine detection). This thesis proposes a method to improve OBC performance by eliminating such accuracy losses. Specifically, we examine the two key players of an OBC system : Hierarchical Segmentation and Supervised Classification. Further, we propose a model to understand the source of accuracy errors in minority categories and provide a method called Scale Fusion to eliminate those errors. This proposed fusion method involves two stages. First, the characteristic scale for each category is estimated through a combination of segmentation and supervised classification. Next, these estimated scales (segmentation maps) are fused into one combined-object-map. Classification performance is evaluated by comparing results of the multi-cut-and-fuse approach (proposed) to the traditional single-cut (SC) scale selection strategy. Testing on four different data sets revealed that our proposed algorithm improves accuracy on minority classes while performing just as well on abundant categories. Another active obstacle, presented by today\u27s remotely sensed images, is the volume of information produced by our modern sensors with high spatial and temporal resolution. For instance, over this decade, it is projected that 353 earth observation satellites from 41 countries are to be launched. Timely production of geo-spatial information, from these large volumes, is a challenge. This is because in the traditional methods, the underlying representation and information processing is still primarily pixel-based, which implies that as the number of pixels increases, so does the computational complexity. To overcome this bottleneck, created by pixel-based representation, this thesis proposes a dart-based discrete topological representation (DBTR), where the DBTR differs from pixel-based methods in its use of a reduced boundary based representation. Intuitively, the efficiency gains arise from the observation that, it is lighter to represent a region by its boundary (darts) than by its area (pixels). We found that our implementation of DBTR, not only improved our computational efficiency, but also enhanced our ability to encode and extract spatial information. Overall, this thesis presents solutions to two problems of an object-based classification system: accuracy and efficiency. Our proposed Scale Fusion method demonstrated improvements in accuracy, while our dart-based topology representation (DBTR) showed improved efficiency in the extraction and encoding of spatial information

Multiscale combinatorial grouping

We propose a unified approach for bottom-up hierarchical image segmentation and object candidate generation for recognition, called Multiscale Combinatorial Grouping (MCG). For this purpose, we first develop a fast normalized cuts algorithm. We then propose a high-performance hierarchical segmenter that makes effective use of multiscale information. Finally, we propose a grouping strategy that combines our multiscale regions into highly-accurate object candidates by exploring efficiently their combinatorial space. We conduct extensive experiments on both the BSDS500 and on the PASCAL 2012 segmentation datasets, showing that MCG produces state-of-the-art contours, hierarchical regions and object candidates. 1

Shape and Topology Constrained Image Segmentation with Stochastic Models

The central theme of this thesis has been to develop robust algorithms for the task of image segmentation. All segmentation techniques that have been proposed in this thesis are based on the sound modeling of the image formation process. This approach to image partition enables the derivation of objective functions, which make all modeling assumptions explicit. Based on the Parametric Distributional Clustering (PDC) technique, improved variants have been derived, which explicitly incorporate topological assumptions in the corresponding cost functions. In this thesis, the questions of robustness and generalizability of segmentation solutions have been addressed in an empirical manner, giving comprehensive example sets for both problems. It has been shown, that the PDC framework is indeed capable of producing highly robust image partitions. In the context of PDC-based segmentation, a probabilistic representation of shape has been constructed. Furthermore, likelihood maps for given objects of interest were derived from the PDC cost function. Interpreting the shape information as a prior for the segmentation task, it has been combined with the likelihoods in a Bayesian setting. The resulting posterior probability for the occurrence of an object of a specified semantic category has been demonstrated to achieve excellent segmentation quality on very hard testbeds of images from the Corel gallery

Skeletonization and segmentation of binary voxel shapes

Preface. This dissertation is the result of research that I conducted between January 2005 and December 2008 in the Visualization research group of the Technische Universiteit Eindhoven. I am pleased to have the opportunity to thank a number of people that made this work possible. I owe my sincere gratitude to Alexandru Telea, my supervisor and first promotor. I did not consider pursuing a PhD until my Master’s project, which he also supervised. Due to our pleasant collaboration from which I learned quite a lot, I became convinced that becoming a doctoral student would be the right thing to do for me. Indeed, I can say it has greatly increased my knowledge and professional skills. Alex, thank you for our interesting discussions and the freedom you gave me in conducting my research. You made these four years a pleasant experience. I am further grateful to Jack vanWijk, my second promotor. Our monthly discussions were insightful, and he continuously encouraged me to take a more formal and scientific stance. I would also like to thank Prof. Jan de Graaf from the department of mathematics for our discussions on some of my conjectures. His mathematical rigor was inspiring. I am greatly indebted to the Netherlands Organisation for Scientific Research (NWO) for funding my PhD project (grant number 612.065.414). I thank Prof. Kaleem Siddiqi, Prof. Mark de Berg, and Dr. Remco Veltkamp for taking part in the core doctoral committee and Prof. Deborah Silver and Prof. Jos Roerdink for participating in the extended committee. Our Visualization group provides a great atmosphere to do research in. In particular, I would like to thank my fellow doctoral students Frank van Ham, Hannes Pretorius, Lucian Voinea, Danny Holten, Koray Duhbaci, Yedendra Shrinivasan, Jing Li, NielsWillems, and Romain Bourqui. They enabled me to take my mind of research from time to time, by discussing political and economical affairs, and more trivial topics. Furthermore, I would like to thank the senior researchers of our group, Huub van de Wetering, Kees Huizing, and Michel Westenberg. In particular, I thank Andrei Jalba for our fruitful collaboration in the last part of my work. On a personal level, I would like to thank my parents and sister for their love and support over the years, my friends for providing distractions outside of the office, and Michelle for her unconditional love and ability to light up my mood when needed

Cube-Cut: Vertebral Body Segmentation in MRI-Data through Cubic-Shaped Divergences

In this article, we present a graph-based method using a cubic template for volumetric segmentation of vertebrae in magnetic resonance imaging (MRI) acquisitions. The user can define the degree of deviation from a regular cube via a smoothness value Delta. The Cube-Cut algorithm generates a directed graph with two terminal nodes (s-t-network), where the nodes of the graph correspond to a cubic-shaped subset of the image's voxels. The weightings of the graph's terminal edges, which connect every node with a virtual source s or a virtual sink t, represent the affinity of a voxel to the vertebra (source) and to the background (sink). Furthermore, a set of infinite weighted and non-terminal edges implements the smoothness term. After graph construction, a minimal s-t-cut is calculated within polynomial computation time, which splits the nodes into two disjoint units. Subsequently, the segmentation result is determined out of the source-set. A quantitative evaluation of a C++ implementation of the algorithm resulted in an average Dice Similarity Coefficient (DSC) of 81.33% and a running time of less than a minute.Comment: 23 figures, 2 tables, 43 references, PLoS ONE 9(4): e9338

Multigranularity Representations for Human Inter-Actions: Pose, Motion and Intention

Tracking people and their body pose in videos is a central problem in computer vision. Standard tracking representations reason about temporal coherence of detected people and body parts. They have difficulty tracking targets under partial occlusions or rare body poses, where detectors often fail, since the number of training examples is often too small to deal with the exponential variability of such configurations. We propose tracking representations that track and segment people and their body pose in videos by exploiting information at multiple detection and segmentation granularities when available, whole body, parts or point trajectories. Detections and motion estimates provide contradictory information in case of false alarm detections or leaking motion affinities. We consolidate contradictory information via graph steering, an algorithm for simultaneous detection and co-clustering in a two-granularity graph of motion trajectories and detections, that corrects motion leakage between correctly detected objects, while being robust to false alarms or spatially inaccurate detections. We first present a motion segmentation framework that exploits long range motion of point trajectories and large spatial support of image regions. We show resulting video segments adapt to targets under partial occlusions and deformations. Second, we augment motion-based representations with object detection for dealing with motion leakage. We demonstrate how to combine dense optical flow trajectory affinities with repulsions from confident detections to reach a global consensus of detection and tracking in crowded scenes. Third, we study human motion and pose estimation. We segment hard to detect, fast moving body limbs from their surrounding clutter and match them against pose exemplars to detect body pose under fast motion. We employ on-the-fly human body kinematics to improve tracking of body joints under wide deformations. We use motion segmentability of body parts for re-ranking a set of body joint candidate trajectories and jointly infer multi-frame body pose and video segmentation. We show empirically that such multi-granularity tracking representation is worthwhile, obtaining significantly more accurate multi-object tracking and detailed body pose estimation in popular datasets

Unsupervised video segmentation using temporal coherence of motion

Includes bibliographical references.2015 Fall.Spatio-temporal video segmentation groups pixels with the goal of representing moving objects in scenes. It is a difficult task for many reasons: parts of an object may look very different from each other, while parts of different objects may look similar and/or overlap. Of particular importance to this dissertation, parts of non-rigid objects such as animals may move in different directions at the same time. While appearance models are good for segmenting visually distinct objects and traditional motion models are good for segmenting rigid objects, there is a need for a new technique to segment objects that move non-rigidly. This dissertation presents a new unsupervised motion-based video segmentation approach. It segments non-rigid objects based on motion temporal coherence (i.e. the correlations of when points move), instead of motion magnitude and direction as in previous approaches. The hypothesis is that although non-rigid objects can move their parts in different directions, their parts tend to move at the same time. In the experiments, the proposed approach achieves better results than related state-of-the-art approaches on a video of zebras in the wild, and on 41 videos from the VSB100 dataset

Automatic Segmentation of Cells of Different Types in Fluorescence Microscopy Images

Recognition of different cell compartments, types of cells, and their interactions is a critical aspect of quantitative cell biology. This provides a valuable insight for understanding cellular and subcellular interactions and mechanisms of biological processes, such as cancer cell dissemination, organ development and wound healing. Quantitative analysis of cell images is also the mainstay of numerous clinical diagnostic and grading procedures, for example in cancer, immunological, infectious, heart and lung disease. Computer automation of cellular biological samples quantification requires segmenting different cellular and sub-cellular structures in microscopy images. However, automating this problem has proven to be non-trivial, and requires solving multi-class image segmentation tasks that are challenging owing to the high similarity of objects from different classes and irregularly shaped structures. This thesis focuses on the development and application of probabilistic graphical models to multi-class cell segmentation. Graphical models can improve the segmentation accuracy by their ability to exploit prior knowledge and model inter-class dependencies. Directed acyclic graphs, such as trees have been widely used to model top-down statistical dependencies as a prior for improved image segmentation. However, using trees, a few inter-class constraints can be captured. To overcome this limitation, polytree graphical models are proposed in this thesis that capture label proximity relations more naturally compared to tree-based approaches. Polytrees can effectively impose the prior knowledge on the inclusion of different classes by capturing both same-level and across-level dependencies. A novel recursive mechanism based on two-pass message passing is developed to efficiently calculate closed form posteriors of graph nodes on polytrees. Furthermore, since an accurate and sufficiently large ground truth is not always available for training segmentation algorithms, a weakly supervised framework is developed to employ polytrees for multi-class segmentation that reduces the need for training with the aid of modeling the prior knowledge during segmentation. Generating a hierarchical graph for the superpixels in the image, labels of nodes are inferred through a novel efficient message-passing algorithm and the model parameters are optimized with Expectation Maximization (EM). Results of evaluation on the segmentation of simulated data and multiple publicly available fluorescence microscopy datasets indicate the outperformance of the proposed method compared to state-of-the-art. The proposed method has also been assessed in predicting the possible segmentation error and has been shown to outperform trees. This can pave the way to calculate uncertainty measures on the resulting segmentation and guide subsequent segmentation refinement, which can be useful in the development of an interactive segmentation framework