Catálogo de publicaciones - libros

This papers presents a comprehensive and general form of the Tarjan’s union-find algorithm dedicated to connected operators. An interesting feature of this form is to introduce the notion of separated domains. The properties of this form and its flexibility are discussed and highlighted with examples. In particular, we give clues to handle correctly the constraint of domain-disjointness preservation and, as a consequence, we show how we can rely on “union-find” to obtain algorithms for self-dual filters approaches and levelings with a marker function.

The of a binary image is the distance transform of the image sampled on its skeleton. In principle the original image can be from the quench function by drawing a disk at each point on the skeleton with radius given by the corresponding quench function value. This reconstruction process is of more than theoretical interest. One possible use is in coding of binary images, but our interest is in an applied image analysis context where the skeleton has been (1) by, for example, deletion of barbs or other segments, and/or (2) so that segments, or indeed individual pixels, have identifying labels. A useful reconstruction, or partial reconstruction, in such a case would be a labelled image, with labels propagated from the skeleton in some intuitive fashion, and the support of this labelled output would be the theoretical union of disks.

An algorithm which directly draws disks would, in many situations, be very inefficient. Moreover the label value for each pixel in the reconstruction is highly ambiguous in most cases where disks are highly overlapping. We propose a vector propagation algorithm based on Ragnelmalm’s Euclidean distance transform algorithm which is both efficient and provides a natural label value for each pixel in the reconstruction. The algorithm is based on near-exact Euclidean distances in the sense that the reconstruction from a single-pixel skeleton is, to a very good approximation, a Euclidean digital disk. The method is illustrated using a biological example of neurite masks originating from images of neurons in culture.

In [5], a novel concept of connectivity for grayscale images was introduced, which is called . In that framework, a grayscale image is connected if all its threshold sets below a given level are connected. It was shown that grayscale level connectivity defines a , in the sense introduced by Jean Serra in [10]. In the present paper, we extend grayscale level connectivity to the case where different connectivities are used for different threshold sets, a concept we call . In particular, this leads to the definition of a new operator, called the multiconnected grayscale reconstruction operator. We show that grayscale level multiconnectivity defines a connection, provided that the connectivities used for the threshold sets obey a nesting condition. Multiconnected grayscale reconstruction is illustrated with an example of scale-space representation.

The shape-tree semilattice is a new framework for quasi-self-dual morphological processing, where eroded images have all shapes shrunk in a contrast-invariant way. This approach was recently introduced, and is further investigated here. Apart of reviewing their original definition, different algorithms for computing the shape-tree morphological operators are presented.

Colour images are multivariable functions, and for segmenting them one must go through a reducing step. It is classically obtained by calculating a gradient module, which is then segmented as a gray tone image. An alternative solution is proposed in the paper. It is based on separated segmentations, followed by a final merging into a unique partition. Three problems are treated this way. First, the search for alignments in the 2-D saturation/luminance histograms. It yields partial, but instructive results which suggest a model for the distribution of the light over the space. Second, the combination of luminance dominant and hue dominant regions in images. Third, the synthesis between colour and shape information in human bust tracking.

The waterfall algorithm is a contrast-based hierarchical segmentation approach. In this paper we propose an efficient implementation based on the minimum spanning tree of the neighborhood graph. Furthermore, other hierarchies are proposed and compared to the original version of the algorithm.

We investigate the effectiveness of the divide set produced by watershed algorithms. We introduce the mosaic to retrieve the altitude of points along the divide set. A desirable property is that, when two minima are separated by a crest in the original image, they are still separated by a crest of the same altitude in the mosaic. Our main result states that this is the case the mosaic is obtained through a topological thinning.

We investigate the new definition of the ordered dynamics proposed in [4]. We show that this definition leads to several properties. In particular we give necessary and sufficient conditions which indicate when a transformation preserves the dynamics of the regional maxima. We also establish a link between the dynamics and minimum spanning trees.

This paper presents a strategy for content-based image retrieval. It is based on a meaningful segmentation procedure that can provide proper distributions for matching via the Earth mover’s distance as a similarity metric. The segmentation procedure is based on a hierarchical watershed-driven algorithm that extracts automatically meaningful regions. In this framework, the proposed robust feature extraction plays a major role along with a novel region weighting for enhancing feature discrimination. Experimental results demonstrate the performance of the proposed strategy.

The watershed transform and seeded region growing are well known tools for image segmentation. They are members of a class of greedy region growing algorithms that are simple, fast and largely parameter free. The main control over these algorithms come from the selection of the marker image, which defines the number of regions and a starting position for each region.

Recently a number of alternative region segmentation approaches have been introduced that allow other types of constraints to be imposed on growing regions, such as limitations on border curvature. Examples of this type of algorithm include the geodesic active contour and classical PDEs.

This paper introduces an approach that allows similar sorts of border constraints to be applied to the watershed transform and seeded region growing. These constraints are imposed at all stages of the growing process and can therefore be used to restrict region leakage.