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

Part decomposition of 3D surfaces

This dissertation describes a general algorithm that automatically decomposes realworld scenes and objects into visual parts. The input to the algorithm is a 3 D triangle mesh that approximates the surfaces of a scene or object. This geometric mesh completely specifies the shape of interest. The output of the algorithm is a set of boundary contours that dissect the mesh into parts where these parts agree with human perception. In this algorithm, shape alone defines the location of a bom1dary contour for a part. The algorithm leverages a human vision theory known as the minima rule that states that human visual perception tends to decompose shapes into parts along lines of negative curvature minima. Specifically, the minima rule governs the location of part boundaries, and as a result the algorithm is known as the Minima Rule Algorithm. Previous computer vision methods have attempted to implement this rule but have used pseudo measures of surface curvature. Thus, these prior methods are not true implementations of the rule. The Minima Rule Algorithm is a three step process that consists of curvature estimation, mesh segmentation, and quality evaluation. These steps have led to three novel algorithms known as Normal Vector Voting, Fast Marching Watersheds, and Part Saliency Metric, respectively. For each algorithm, this dissertation presents both the supporting theory and experimental results. The results demonstrate the effectiveness of the algorithm using both synthetic and real data and include comparisons with previous methods from the research literature. Finally, the dissertation concludes with a summary of the contributions to the state of the art

Segmentation hiérarchique de maillage 3D à partir des dynamiques de contour

La segmentation de maillage 3D est un problème fondamental en synthèse d'image et est devenu un enjeu important pour de nombreuses applications. Cet article introduit une nouvelle méthode de segmentation hiérarchique basée sur la ligne de partage des eaux (LPE), les cascades et les dynamiques de contour. La LPE génère une première partition composée de petits patchs surfaciques ; les dynamiques de contour offrent une bonne caractérisation des frontières et les cascades mettent à disposition plusieurs niveaux de segmentation pour l'utilisateur. Le procédé de fusion hiérarchique basé sur les cascades génère un arbre qui contient plusieurs schémas de segmentation ; l'utilisateur a ainsi la possibilité de parcourir facilement chacun des niveaux de segmentation contenus dans cet arbre pour sélectionner le plus adapté à son application

Advanced Visual Computing for Image Saliency Detection

Saliency detection is a category of computer vision algorithms that aims to filter out the most salient object in a given image. Existing saliency detection methods can generally be categorized as bottom-up methods and top-down methods, and the prevalent deep neural network (DNN) has begun to show its applications in saliency detection in recent years. However, the challenges in existing methods, such as problematic pre-assumption, inefficient feature integration and absence of high-level feature learning, prevent them from superior performances. In this thesis, to address the limitations above, we have proposed multiple novel models with favorable performances. Specifically, we first systematically reviewed the developments of saliency detection and its related works, and then proposed four new methods, with two based on low-level image features, and two based on DNNs. The regularized random walks ranking method (RR) and its reversion-correction-improved version (RCRR) are based on conventional low-level image features, which exhibit higher accuracy and robustness in extracting the image boundary based foreground / background queries; while the background search and foreground estimation (BSFE) and dense and sparse labeling (DSL) methods are based on DNNs, which have shown their dominant advantages in high-level image feature extraction, as well as the combined strength of multi-dimensional features. Each of the proposed methods is evaluated by extensive experiments, and all of them behave favorably against the state-of-the-art, especially the DSL method, which achieves remarkably higher performance against sixteen state-of-the-art methods (including ten conventional methods and six learning based methods) on six well-recognized public datasets. The successes of our proposed methods reveal more potential and meaningful applications of saliency detection in real-life computer vision tasks

Neutro-Connectedness Theory, Algorithms and Applications

Connectedness is an important topological property and has been widely studied in digital topology. However, three main challenges exist in applying connectedness to solve real world problems: (1) the definitions of connectedness based on the classic and fuzzy logic cannot model the “hidden factors” that could influence our decision-making; (2) these definitions are too general to be applied to solve complex problem; and (4) many measurements of connectedness are heavily dependent on the shape (spatial distribution of vertices) of the graph and violate the intuitive idea of connectedness. This research focused on solving these challenges by redesigning the connectedness theory, developing fast algorithms for connectedness computation, and applying the newly proposed theory and algorithms to solve challenges in real problems. The newly proposed Neutro-Connectedness (NC) generalizes the conventional definitions of connectedness and can model uncertainty and describe the part and the whole relationship. By applying the dynamic programming strategy, a fast algorithm was proposed to calculate NC for general dataset. It is not just calculating NC map, and the output NC forest can discover a dataset’s topological structure regarding connectedness. In the first application, interactive image segmentation, two approaches were proposed to solve the two most difficult challenges: user interaction-dependence and intense interaction. The first approach, named NC-Cut, models global topologic property among image regions and reduces the dependence of segmentation performance on the appearance models generated by user interactions. It is less sensitive to the initial region of interest (ROI) than four state-of-the-art ROI-based methods. The second approach, named EISeg, provides user with visual clues to guide the interacting process based on NC. It reduces user interaction greatly by guiding user to where interacting can produce the best segmentation results. In the second application, NC was utilized to solve the challenge of weak boundary problem in breast ultrasound image segmentation. The approach can model the indeterminacy resulted from weak boundaries better than fuzzy connectedness, and achieved more accurate and robust result on our dataset with 131 breast tumor cases

Watersheds on edge or node weighted graphs

The literature on the watershed is separated in two families: the watersheds on node weighted graphs and the watersheds on edge weighted graphs. The simplest node weighted graphs are images, where the nodes are the pixels ; neighboring pixels being linked by unweighted pixels. The edge weights on an edge weighted graph express dissimilarities between the unweighted nodes. Distinct definitions of minima and catchment basins have been given for both types of graphs from which different algorithms have been derived. This paper aims at showing that watersheds on edge or node weighted graphs are strictly equivalent. Moreover, all algorithms developed for edge weighted graphs may be applied on node weighted graphs and vice versa. From any node or edge weighted graph it is possible to derive a flooding graph with node and edge weights. Its regional minima and catchment basins are identical whether one considers the node weights alone or the edge weights alone. A lexicographic order relation permits to compare non ascending paths with the same origin according to their steepness. Overlapping zones between neighboring catchment basins are reduced or even suppressed by pruning edges in the flooding graph through which does not pass a steepest path and reduces, without arbitrary choices the overlapping zones between adjacent catchment basins. We propose several ways to break the remaining ties, the simplest being to assign slightly distinct weights to regional minima with the same weight. Like that each node is linked with only one regional minimum by a path of maximal steepness

Clustering Of Complex Shaped Data Sets Via Kohonen Maps And Mathematical Morphology

Clustering is the process of discovering groups within the data, based on similarities, with a minimal, if any, knowledge of their structure. The self-organizing (or Kohonen) map (SOM) is one of the best known neural network algorithms. It has been widely studied as a software tool for visualization of high-dimensional data. Important features include information compression while preserving topological and metric relationship of the primary data items. Although Kohonen maps had been applied for clustering data, usually the researcher sets the number of neurons equal to the expected number of clusters, or manually segments a two-dimensional map using some a priori knowledge of the data. This paper proposes techniques for automatic partitioning and labeling SOM networks in clusters of neurons that may be used to represent the data clusters. Mathematical morphology operations, such as watershed, are performed on the U-matrix, which is a neuron-distance image. The direct application of watershed leads to an oversegmented image. It is used markers to identify significant clusters and homotopy modification to suppress the others. Markers are automatically found by performing a multi-level scan of connected regions of the U-matrix. Each cluster of neurons is a sub-graph that defines, in the input space, complex and nonparametric geometries which approximately describes the shape of the clusters. The process of map partitioning is extended recursively. Each cluster of neurons gives rise to a new map, which are trained with the subset of data that were classified to it. The algorithm produces dynamically a hierarchical tree of maps, which explains the cluster's structure in levels of granularity. 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