[Show abstract][Hide abstract] ABSTRACT: Connected operators provide well-established solutions for digital image processing, typically in conjunction with hierarchical schemes. In graph-based frameworks, such operators basically rely on symmetric adjacency relations between pixels. In this article, we introduce a notion of directed connected operators for hierarchical image processing, by also considering non-symmetric adjacency relations. The induced image representation models are no longer partition hierarchies (i.e., trees), but directed acyclic graphs that generalize standard morphological tree structures such as component trees, binary partition trees or hierarchical watersheds. We describe how to efficiently build and handle these richer data structures, and we illustrate the versatility of the proposed framework in image filtering and image segmentation.
IEEE Transactions on Pattern Analysis and Machine Intelligence 06/2015; 37(6):1162-1176. DOI:10.1109/TPAMI.2014.2366145 · 5.78 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A new morphological operator, namely RORPO (Ranking Orientation Responses of Path Operators), was recently introduced as a semi-global, morphological alternative to the local, Hessian-based operators for thin structure filtering in 3D images. In this context, a previous study has already provided experimental proof of its relevance by comparison to such differential operators. In this article, we present a methodological study of RORPO, which completes the presentation of this new morphological filter. In particular, we expose the motivations of RORPO with respect to previous morphological strategies; we present algorithmic developments of this filter and the underlying robust path operator; and we discuss computational issues related to parametricity and time efficiency. We conclude this study by a discussion on the methodological and applicative potentiality of RORPO in various fields of image processing and analysis.
[Show abstract][Hide abstract] ABSTRACT: The extension of mathematical morphology to multivalued images is an important issue. This is particularly true in the context of connected operators based on morphological hierarchies, which aim to provide efficient image filtering and segmentation tools in various application fields, e. g. (bio)medical imaging, remote sensing, or astronomy. In this article, we propose a preliminary study that describes how two notions recently introduced for connected filtering, namely component-graphs (that extend component-trees from a spectral point of view) and shaping (that extend component-trees from a conceptual point of view) can be associated for the effective processing of multivalued images. Structural, algorithmic and experimental developments are proposed. This study opens the way to new paradigms for connected filtering based on hierarchies.
[Show abstract][Hide abstract] ABSTRACT: Object-based image analysis (OBIA) has been widely adopted as a common paradigm to deal with very high-resolution remote sensing images. Nevertheless, OBIA methods strongly depend on the results of image segmentation. Many segmentation quality metrics have been proposed. Supervised metrics give accurate quality estimation but require a ground-truth segmentation as reference. Unsupervised metrics only make use of intrinsic image and segment properties; yet most of them strongly depend on the application and do not deal well with the variability of objects in remote sensing images. Furthermore, the few metrics developed in a remote sensing context mainly focus on global evaluation. In this paper, we propose a novel unsupervised metric, which evaluates local quality (per segment) by analyzing segment neighborhood, thus quantifying under- and over-segmentation given a certain homogeneity criterion. Additionally, we propose two variants of this metric, for estimating global quality of remote sensing image segmentation by the aggregation of local quality scores. Finally, we analyze the behavior of the proposed metrics and validate their applicability for finding segmentation results having good tradeoff between both kinds of errors.
IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 05/2015; 8(5):1-10. DOI:10.1109/JSTARS.2015.2424457 · 3.03 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Positron Emission Tomography (PET) image segmentation is essential for detecting lesions and quantifying their metabolic activity. Due to the spatial and spectral properties of PET images, most methods rely on intensity-based strategies. Recent methods also propose to integrate anatomical priors to improve the segmentation process. In this article, we show how the hierarchical approaches proposed in mathematical morphology can efficiently handle these different strategies. Our contribution is twofold. First, we present the component-tree as a relevant data-structure for developing interactive, real-time, intensity-based segmentation of PET images. Second, we prove that thanks to the recent concept of shaping, we can efficiently involve a priori knowledge for lesion segmentation, while preserving the good properties of component-tree segmentation. Preliminary experiments on synthetic and real PET images of lymphoma demonstrate the relevance of our approach.
[Show abstract][Hide abstract] ABSTRACT: To deal with the issue of tubular object segmentation, we propose a new model involving a non-local fitting term, in the Chan-Vese framework. This model aims at detecting objects whose intensities are not necessarily piecewise constant, or even composed of multiple piecewise constant regions. Our problem formulation exploits object sparsity in the image domain and a local ordering relationship between foreground and background. A continuous optimization scheme can then be efficiently considered in this context. This approach is validated on both synthetic and real retinal images. The nonlocal data fitting term is shown to be superior to the classical piecewise-constant model, robust to noise and to low contrast.
[Show abstract][Hide abstract] ABSTRACT: Image segmentation is generally performed in a “one image, one algorithm” paradigm. However, it is sometimes required to consider several images of a same scene, or to carry out several (or several occurrences of a same) algorithm(s) to fully capture relevant information. To solve the induced segmentation fusion issues, various strategies have been already investigated for allowing a consensus between several segmentation outputs. This article proposes a contribution to segmentation fusion, with a specific focus on the “n images” part of the paradigm. Its main originality is to act on the segmentation research space, i. e., to work at an earlier stage than standard segmentation fusion approaches. To this end, an algorithmic framework is developed to build a binary partition tree in a collaborative fashion, from several images, thus allowing to obtain a unified hierarchical segmentation space. This framework is, in particular, designed to embed consensus policies inherited from the machine learning domain. Application examples proposed in remote sensing emphasise the potential usefulness of our approach for satellite image processing.
[Show abstract][Hide abstract] ABSTRACT: We introduce the new notion of multivalued component-tree, that extends the classical component-tree initially devoted to grey-level images, in the mathematical morphology framework. We prove that multivalued component-trees can model images whose values are hierarchically organized. We also show that they can be efficiently built from standard component-tree construction algorithms, and involved in antiextensive filtering procedures. The relevance and usefulness of multivalued component-trees is illustrated by an applicative example on hierarchically classified remote sensing images.
[Show abstract][Hide abstract] ABSTRACT: In recent works, a new notion of component-graph was introduced. It extends the classical notion of componenttree initially proposed in mathematical morphology to model the structure of grey-level images. Component-graphs can indeed model the structure of any - grey-level or multivalued - images. We now extend the antiextensive filtering scheme based on component-trees, in order to make it tractable in the framework of component-graphs. More precisely, we provide solutions for building a component-graph; reducing it based on selection criteria; and reconstructing a filtered image from a reduced component-graph. In this article, we first consider the cases where component-graphs still have a tree structure; they are then called multivalued component-trees. The relevance and usefulness of such multivalued component-trees are illustrated by applicative examples on hierarchically classified remote sensing images.
[Show abstract][Hide abstract] ABSTRACT: Rigid transformations are involved in a wide variety of image processing applications, including image registration. In this context, we recently proposed to deal with the associated optimization problem from a purely discrete point of view, using the notion of discrete rigid transformation (DRT) graph. In particular, a local search scheme within the DRT graph to compute a locally optimal solution without any numerical approximation was formerly proposed. In this article, we extend this study, with the purpose to reduce the algorithmic complexity of the proposed optimization scheme. To this end, we propose a novel algorithmic framework for just-in-time computation of sub-graphs of interest within the DRT graph. Experimental results illustrate the potential usefulness of our approach for image registration.
[Show abstract][Hide abstract] ABSTRACT: In the continuous domain, rigid transformations are topology-preserving operations. Due to digitization, this is not the case when considering digital images, i.e., images defined on Z^n. In this article, we begin to investigate this problem by studying conditions for digital images to preserve their topological properties under all rigid transformations on Z^2. Based on (i) the recently introduced notion of DRT graph, and (ii) the notion of simple point, we propose an algorithm for evaluating digital images topological invariance.
Journal of Mathematical Imaging and Vision 06/2014; 49(2):418-433. DOI:10.1007/s10851-013-0474-z · 1.55 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Component-trees model the structure of grey-level images by considering their binary level-sets obtained from successive thresholdings. They also enable to define anti-extensive filtering procedures for such images. In order to extend this image processing approach to any (grey-level or multivalued) images, both the notion of component-tree, and its associated filtering framework, have to be generalised. In this article we deal with the generalisation of the component-tree structure. We define a new data structure, the component-graph, which extends the notion of component-tree to images taking their values in any (partially or totally) ordered set. The component-graphs are declined in three variants, of increasing richness and size, whose structural properties are studied.
Journal of Mathematical Imaging and Vision 05/2014; 49(1). DOI:10.1007/s10851-013-0438-3 · 1.55 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Rigid transformations are involved in a wide range of digital image processing applications. In such a context, they are generally considered as continuous processes, followed by a digitization of the results. Recently, rigid transformations on ℤ 2 have been alternatively formulated as a fully discrete process. Following this paradigm, we investigate – from a combinatorial point of view – the effects of pixel-invariance constraints on such transformations. In particular we describe the impact of these constraints on both the combinatorial structure of the transformation space and the algorithm leading to its generation.
Annals of Mathematics and Artificial Intelligence 03/2014; 75(1-2). DOI:10.1007/s10472-014-9406-x · 0.69 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We provide conditions under which 2D digital images preserve their topological properties under rigid transformations. We consider the two most common digital topology models, namely dual adjacency and well-composedness. This paper leads to the proposal of optimal preprocessing strategies that ensure the topological invariance of images under arbitrary rigid transformations. These results and methods are proved to be valid for various kinds of images (binary, gray-level, label), thus providing generic and efficient tools, which can be used in particular in the context of image registration and warping.
[Show abstract][Hide abstract] ABSTRACT: The automated detection and mapping of landslides from Very High Resolution (VHR) images present several challenges related to the heterogeneity of landslide sizes, shapes and soil surface characteristics. However, a common geomorphological characteristic of landslides is to be organized with a series of embedded and scaled features. These properties motivated the use of a multiresolution image analysis approach for their detection. In this work, we propose a hybrid segmentation/classification region-based method, devoted to this specific issue. The method, which uses images of the same area at various spatial resolutions (Medium to Very High Resolution), relies on a recently introduced top-down hierarchical framework. In the specific context of landslide analysis, two main novelties are introduced to enrich this framework. The first novelty consists of using non-spectral information, obtained from Digital Terrain Model (DTM), as a priori knowledge for the guidance of the segmentation/classification process. The second novelty consists of using a new domain adaptation strategy, that allows to reduce the expert’s interaction when handling large image datasets. Experiments performed on satellite images acquired over terrains affected by landslides demonstrate the efficiency of the proposed method with different hierarchical levels of detail addressing various operational needs.
ISPRS Journal of Photogrammetry and Remote Sensing 01/2014; 87:122-136. DOI:10.1016/j.isprsjprs.2013.11.003 · 3.13 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Curvature is a continuous and infinitesimal notion. These properties induce geometrical difficulties in digital frameworks, and the following question is naturally asked: "How to define and compute curvatures of digital shapes?" In fact, not only geometrical but also topological difficulties are also induced in digital frameworks. The deeper question thus arises: "Can we still define and compute curvatures?" This latter question, that is relevant in the context of digitization, i.e., when passing from R^n to Z^n, can also be stated in Z^n itself, when applying geometric transformations on digital shapes. This paper proposes a preliminary discussion on this topic.
[Show abstract][Hide abstract] ABSTRACT: We propose a new distance called Hierarchical Semantic-Based Distance (HSBD), devoted to the comparison of nominal histograms equipped with a dissimilarity matrix providing the semantic correlations between the bins. The computation of this distance is based on a hierarchical strategy, progressively merging the considered instances (and their bins) according to their semantic proximity. For each level of this hierarchy, a standard bin-to-bin distance is computed between the corresponding pair of histograms. In order to obtain the proposed distance, these bin-to-bin distances are then fused by taking into account the semantic coherency of their associated level. From this modus operandi, the proposed distance can handle histograms which are generally compared thanks to cross-bin distances. It preserves the advantages of such cross-bin distances (namely robustness to histogram translation and histogram bin size issues), while inheriting the low computational cost of bin-to-bin distances. Validations in the context of geographical data classification emphasize the relevance and usefulness of the proposed distance.