[show abstract][hide abstract] ABSTRACT: In this article, a tractable modus operandi is proposed to model a (binary) digital image (i.e., an image defined on ℤ
and equipped with a standard pair of adjacencies) as an image defined in the space () of cubical complexes. In particular, it is shown that all the standard pairs of adjacencies (namely the (4,8) and (8,4)-adjacencies
in ℤ2, the (6,18), (18,6), (6,26), and (26,6)-adjacencies in ℤ3, and more generally the (2n,3
−1) and (3
−1,2n)-adjacencies in ℤ
) can then be correctly modelled in . Moreover, it is established that the digital fundamental group of a digital image in ℤ
is isomorphic to the fundamental group of its corresponding image in , thus proving the topological correctness of the proposed approach. From these results, it becomes possible to establish
links between topology-oriented methods developed either in classical digital spaces (ℤ
) or cubical complexes (), and to potentially unify some of them.
Journal of Mathematical Imaging and Vision 08/2013; · 1.77 Impact Factor
[show abstract][hide abstract] ABSTRACT: Rigid transformations are involved in a wide range of digital image processing applications. When applied on discrete images, rigid transformations are usually performed in their associated continuous space, requiring a subsequent digitization of the result. In this article, we propose to study rigid transformations of digital images as fully discrete processes. In particular, we investigate a combinatorial structure modelling the whole space of digital rigid transformations on arbitrary subset of Z2Z2 of size N × N. We describe this combinatorial structure, which presents a space complexity O(N9)O(N9) and we propose an algorithm enabling to construct it in linear time with respect to its space complexity. This algorithm, which handles real (i.e., non-rational) values related to the continuous transformations associated to the discrete ones, is however defined in a fully discrete form, leading to exact computation.
[show abstract][hide abstract] ABSTRACT: In the last 20years, 3D angiographic imaging has proven its usefulness in the context of various clinical applications. However, angiographic images are generally difficult to analyse due to their size and the complexity of the data that they represent, as well as the fact that useful information is easily corrupted by noise and artifacts. Therefore, there is an ongoing necessity to provide tools facilitating their visualisation and analysis, while vessel segmentation from such images remains a challenging task. This article presents new vessel segmentation and filtering techniques, relying on recent advances in mathematical morphology. In particular, methodological results related to spatially variant mathematical morphology and connected filtering are stated, and included in an angiographic data processing framework. These filtering and segmentation methods are evaluated on real and synthetic 3D angiographic data.
Medical image analysis 09/2012; · 3.09 Impact Factor
[show abstract][hide abstract] ABSTRACT: In digital imaging, after several decades devoted to the study of
topological properties of binary images, there is an increasing need
of new methods enabling to take into (topological) consideration
n-ary images (also called label images). Indeed, while binary images
enable to handle one object of interest, label images authorise to
simultaneously deal with a plurality of objects, which is a frequent
requirement in several application fields. In this context, one of
the main purposes is to propose topology-preserving transformation
procedures for such label images, thus extending the ones (e.g.,
growing, reduction, skeletonisation) existing for binary images.
In this article, we propose, for a wide range of digital images,
a new approach that permits to locally modify a label image, while
preserving not only the topology of each label set, but also the
topology of any arrangement of the labels understood as the topology
of any union of label sets. This approach enables in particular to
unify and extend some previous attempts devoted to the same purpose.
Journal of Mathematical Imaging and Vision 08/2012; · 1.77 Impact Factor
[show abstract][hide abstract] ABSTRACT: Preserving topological properties of objects during thinning procedures is an important issue in the field of image analysis.
This paper constitutes an introduction to the study of non-trivial simple sets in the framework of cubical 3-D complexes.
A simple set has the property that the homotopy type of the object in which it lies is not changed when the set is removed.
The main contribution of this paper is a characterisation of the non-trivial simple sets composed of exactly two voxels, such
sets being called minimal simple pairs.
Journal of Mathematical Imaging and Vision 04/2012; 32(3):239-249. · 1.77 Impact Factor
[show abstract][hide abstract] ABSTRACT: Preserving topological properties of objects during reduction procedures is an important issue in the field of discrete image
analysis. Such procedures are generally based on the notion of simple point, the exclusive use of which may result in the appearance of “topological artifacts.” This limitation leads to consider a
more general category of objects, the simple sets, which also enable topology-preserving image reduction. A study of two-dimensional simple sets in two-dimensional spaces
has been proposed recently. This article is devoted to the study of two-dimensional simple sets in spaces of higher dimension
(i.e., n-dimensional spaces, n≥3). In particular, several properties of minimal simple sets (i.e., which do not strictly include any other simple sets) are proposed, leading to a characterisation theorem.
It is also proved that the removal of a two-dimensional simple set from an object can be performed by only considering the
minimal ones, thus authorising the development of efficient thinning algorithms.
KeywordsDigital topology-Thinning-Topology preservation-Simple sets-Cubical complexes-
Discrete and Computational Geometry 04/2012; 43(4):893-913. · 0.65 Impact Factor
[show abstract][hide abstract] ABSTRACT: The development of digital imaging (and its subsequent applications) has led to consideration and investigation of topological
notions that are well-defined in continuous spaces, but not necessarily in discrete/digital ones. In this article, we focus
on the classical notion of path. We establish in particular that the standard definition of path in algebraic topology is
coherent w.r.t. the ones (often empirically) used in digital imaging. From this statement, we retrieve, and actually extend,
an important result related to homotopy-type preservation, namely the equivalence between the fundamental group of a digital
space and the group induced by digital paths. Based on this sound definition of paths, we also (re)explore various (and sometimes
equivalent) ways to reduce a digital image in a homotopy-type preserving fashion.
KeywordsTopology–Digital imaging–Paths–Fundamental group–Homotopy-type preservation
[show abstract][hide abstract] ABSTRACT: The extraction of urban patterns from very high spatial resolution (VHSR) optical images presents several challenges related to the size, the accuracy and the complexity of the considered data. Based on the availability of several optical images of a same scene at various resolutions (medium, high, and very high spatial resolution), a hierarchical approach is proposed to progressively extract segments of interest from the lowest to the highest resolution data, and then finally determine urban patterns from VHSR images. This approach, inspired by the principle of photo-interpretation, has for purpose to use as much as possible the user's skills while minimising his/her interaction. In order to do so, at each resolution, an interactive segmentation of one sample region is required for each semantic class of the image. Then, the user's behaviour is automatically reproduced in the remainder of the image. This process is mainly based on tree-cuts in binary partition trees. Since it strongly relies on user-defined segmentation examples, it can involve only low level—spatial and radiometric—criteria, then enabling fast computation of comprehensive results. Experiments performed on urban images datasets provide satisfactory results which may be further used for classification purpose.
[show abstract][hide abstract] ABSTRACT: In the last 20 years, progress in 3D medical imaging (such as MRI and CT) has led to the development of modalities devoted
to visualise vascular structures. These angiographic images progressively proved their usefulness in the context of various
clinical applications. However, such data are generally complex to analyse due to their size and low amount of relevant (vascular)
information versus noise, artifacts and other anatomical structures. Therefore, there is an ongoing necessity to provide tools facilitating
image visualisation and analysis. In this chapter, we first focus on vascular image analysis. In particular, we present a
survey on both standard and recent vessel segmentation methodologies. We then discuss the existing ways to model anatomical
knowledge via the computation of vascular atlases. Such atlases can notably be embedded in computer-aided radiology tools.
[show abstract][hide abstract] ABSTRACT: The extraction of urban patterns from very high spatial resolution optical images presents challenges related to the size,
the accuracy and the complexity of the data. In order to efficiently carry out this task, a multiresolution hierarchical approach
is proposed. It enables to progressively segment several images (of increasing resolutions) of a same scene, based on low
level criteria. The process, based on binary partition trees, is partially performed in an interactive fashion, and then automatically
completed. Experiments on urban images datasets provide encouraging results which may be further used for detection and classification
KeywordsHierarchical segmentation–multisource images–multiresolution–interactive/automated segmentation–partition-trees–remote sensing–urban analysis
[show abstract][hide abstract] ABSTRACT: The estimation of one-to-one mappings is one of the most intensively studied topics in the research field of nonrigid registration. Although the computation of such mappings can be now accurately and efficiently performed, the solutions for using them in the context of binary image deformation is much less satisfactory. In particular, warping a binary image with such transformations may alter its discrete topological properties if common resampling strategies are considered. In order to deal with this issue, this paper proposes a method for warping such images according to continuous and bijective mappings while preserving their discrete topological properties (i.e., their homotopy type). Results obtained in the context of the atlas-based segmentation of complex anatomical structures highlight the advantages of the proposed approach.
[show abstract][hide abstract] ABSTRACT: The extraction of urban patterns from Very High Spatial Resolution (VHSR) images presents several challenges related to the size, the accuracy and the complexity of the considered data. In order to assist the end-user to efficiently carry out this task, a new approach is proposed for hierarchically extracting segments of interest from lower resolution data and finally determining urban patterns in these segments from VHSR ones. Based on an intuitive modus operandi, it allows the end-user to progressively segment images based on low level -spatial and radiometric- criteria. Experiments performed on urban images datasets provide encouraging results which may be further used for objects detection and classification purpose.
[show abstract][hide abstract] ABSTRACT: The Fuzzy C-Means (FCM) algorithm is a widely used and flexible approach to automated image segmentation, especially in the field of brain tissue segmentation from 3D MRI, where it addresses the problem of partial volume effects. In order to improve its robustness to classical image deterioration, namely noise and bias field artifacts, which arise in the MRI acquisition process, we propose to integrate into the FCM segmentation methodology concepts inspired by the non-local (NL) framework, initially defined and considered in the context of image restoration. The key algorithmic contributions of this article are the definition of an NL data term and an NL regularisation term to efficiently handle intensity inhomogeneities and noise in the data. The resulting new energy formulation is then built into an NL-FCM brain tissue segmentation algorithm. Experiments performed on both synthetic and real MRI data, leading to the classification of brain tissues into grey matter, white matter and cerebrospinal fluid, indicate a significant improvement in performance in the case of higher noise levels, when compared to a range of standard algorithms.
[show abstract][hide abstract] ABSTRACT: This article introduces the notion of component-hypertree, which models the component-trees of an image at various connectivity levels, and the relations of the nodes/connected components
between these levels. This data structure is then used to extend a recently proposed interactive segmentation method based
on component-trees. In this multiscale connectivity context, the use of a component-hypertree appears to be less costly than
the use of several component-trees. Application examples illustrate the relevance of this approach.
Mathematical Morphology and Its Applications to Image and Signal Processing - 10th International Symposium, ISMM 2011, Verbania-Intra, Italy, July 6-8, 2011. Proceedings; 01/2011
[show abstract][hide abstract] ABSTRACT: Segmentation of cerebral vascular networks from 3D angiographic data remains a challenge. Automation generally induces a high computational cost and possible errors, while interactive methods are hard to use due to the dimension and complexity of images. This article presents a compromise between both approaches, by using the concept of examplebased segmentation. Segmentation examples of vascular structures are involved in a scheme relying on connected filtering, in order to obtain an interactive –but strongly assisted– segmentation method. This strategy, which uses componenttrees in a non-standard fashion, leads to promising results, when applied on cerebral MR angiographic data.
Proceedings of the 8th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2011, March 30 - April 2, 2011, Chicago, Illinois, USA; 01/2011
[show abstract][hide abstract] ABSTRACT: Component-trees associate to a discrete grey-level image a descriptive data structure induced by the inclusion relation between
the binary components obtained at successive level-sets. This article presents a method to extract a subset of the component-tree
of an image enabling to fit at best a given binary target selected beforehand in the image. A proof of the algorithmic efficiency
of this method is proposed. Application examples related to the extraction of drop caps from ancient documents emphasise the
usefulness of this technique in the context of assisted segmentation.
Discrete Geometry for Computer Imagery - 16th IAPR International Conference, DGCI 2011, Nancy, France, April 6-8, 2011. Proceedings; 01/2011
[show abstract][hide abstract] ABSTRACT: Component-trees associate to a discrete grey-level image a descriptive data structure induced by the inclusion relation between the binary components obtained at successive level-sets. This article presents an original interactive segmentation methodology based on component-trees. It consists of the extraction of a subset of the image component-tree, enabling the generation of a binary object which fits at best (with respect to the grey-level structure of the image) a given binary target selected beforehand in the image. A proof of the algorithmic efficiency of this methodological scheme is proposed. Concrete application examples on magnetic resonance imaging (MRI) data emphasise its actual computational efficiency and its usefulness for interactive segmentation of real images.
[show abstract][hide abstract] ABSTRACT: The study of in utero fetal MR images is essential for the diagnosis of abnormal brain development and the study of the maturation of the brain structures. Because of the particular properties of these images, only a few automated segmentation methods have been developed so far compared to the numerous ones existing for the adult brain anatomy. In this paper, we propose a two-step cortex segmentation technique including anatomical priors and a topological model. Experiments performed on in utero MR data and validation by comparison to experts segmentation emphasize the relevance of the method.
Proceedings of the 8th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2011, March 30 - April 2, 2011, Chicago, Illinois, USA; 01/2011