A hierarchy is a series of nested partitions in which a coarser partition results from merging regions of finer ones. Each hierarchy derived from an image provides a particular structural description of the image content, depending upon the criteria for merging neighboring regions. Distinct hierarchies derived from a same image reflect its various facets and the distances between them nicely characterize its content. In this paper the hierarchies are constructed with the versatile stochastic watershed algorithm and their inter-distances are measured with the Gromov-Hausdorff distance. Experiments conducted on images simulated by dead leaves model illustrate the advantages of our approach in terms of learning efficiency and understandability of the results.

This paper presents significant improvements of Gray Level Size Zone Matrix (GLSZM) which is a bivariate statistical representation of texture, based on the co-occurrences of size/intensity of each flat zone (connected pixels of the same gray level). The first improvement is a multi-scale extension of the matrix which merges various quantizations of gray levels. A second alternative is proposed to take into account radial distribution of zone intensities. The third variant is a generalization of the matrix structure which allows to analyze fibrous textures, by changing the pair intensity/size for the pair length/orientation of each region. The interest of these improved descriptors is illustrated by texture classification problems arising from quantitative cell biology.

Successive levelings are applied on document images. The residues of successive levelings are made of flat zones for which morphological transforms are described.

This paper presents the binary flattenings of shapes, first as a connected operator suppressing particles or holes, second as an erosion in a particular lattice of shapes. Using this erosion, it is then possible to construct a distance from a shape to another and derive from it an interpolation function between shapes.

The main focus of this paper is related to anisotropic morphological edge preserving filters. We present in this work neighborhood filters defined on the minimal spanning tree (MST) of an image (according to a local dissimilarity measure between adjacent pixels). The designed filters take advantage of the property of the MST to detect and follow the local features of an image. This approach leads to neighborhood filters where the structuring elements adapt their shape to the minimal spanning tree structure and therefore to the local image features. We demonstrate the quality of this method on natural and synthetic images.

This article presents the use of morphological amoebas for the enhancement of 3D medical images. Morphological amoebas are kernels adapting their shape in such a way that they do not cross the contours of the image. They can be used in morphological operations in quite a similar way as classical kernel and are well-fitted for noise-reduction in 3D medical images.

The construction of a minimum spanning forest on a graph, where the trees are rooted in a predefined set of nodes, is shown to be equivalent to constructing the Voronoi tesselation of the nodes for a lexicographic distance function. The domain of application here is morphological segmentation with markers.

Attribute graphs offer a compact representation of 2D or 3D images, as each node represents a region with its attributes and the edges convey the neighborhood relations between adjacent regions. Such graphs may be used in the analysis of video sequences and the tracking of objects of interest. Each image of a sequence is segmented and represented as a region adjacency graph. Object tracking becomes a particular graph-matching problem, in which the nodes representing the same object are to be matched. The intrinsic complexity of graph matching is greatly reduced by coupling it with the segmentation. An attractive feature of our approach is its ability to keep track of occluded objects. Results on real sequences show the potential of this approach.

Mathematical morphology offers a rich framework for segmenting images and video sequences. We propose a unified presentation of these tools, expressed as a small number of distance transforms on graphs. The classical approach based on watershed and markers is reinterpreted in a multiscale framework and new results are presented, considerably enlarging the palette of available tools.

Object oriented representation of image sequences requires accurate motion segmentation and depth ordering techniques. Unfortunately, the lack of precise motion estimates at the object boundaries makes these two tasks very difficult. We present a detailed analysis of the behaviour of dense motion estimation techniques at object boundaries which reveals the systematic nature of the motion estimation error; the motion of the occluding surface is observed in a small neighbourhood on the occluded side. We then show how the joint use of still image segmentation and robust regression can eliminate this error. Furthermore we present a novel technique which uses the position of the error as a depth cue. The validity of this technique, which requires only sub-pixel motion and which is capable of distinguishing between different types of intensity discontinuities, such as object boundaries, surface marks and illumination discontinuities, is then demonstrated on several synthetic and real image sequences.

We present a nonlinear partial differential equation (PDE) that models the generation of a large class of advanced morphological filters, the levelings and the openings/closings by reconstruction. These types of filters are very useful in numerous image analysis and vision tasks ranging from enhancement, feature detection, image simplification, to segmentation. The developed PDE models these nonlinear filters as the limit of a controlled growth starting from an initial seed signal. This growth is of the multiscale dilation or erosion type and the controlling mechanism is a switch that reverses the growth when the difference between the current evolution and a reference signal switches signs. We discuss theoretical aspects of this PDE, propose a discrete algorithm for its numerical solution and corresponding filter implementation, and provide insights via several experiments. Finally, we outline its use for improving the Gaussian scale-space by using the latter as initial seed to generate multiscale levelings that have a superior preservation of image edges and boundaries.

This paper focuses on a novel class of morphological filters called levelings and their extension to vector spaces. Unlike many filtering techniques reported in the literature, levelings suppress details while preserving perfectly the contours of the remaining objects. This feature makes them ideal tools for simplifying images in a large set of applications. They are particularly useful as preprocessing films for segmentation and coding. However when dealing with color images, new colors may be introduced if each color component is treated separately. In order to solve this drawback two extensions of scalar levelings to vector spaces are presented.

This paper presents a toolbox for interactive image segmentation based on a series of nested partitions of increasing coarseness. The user can navigate among the different resolution levels and select regions with simple mouse clicks. The whole family of partitions can be created during a single morphological flooding of the image, leading to a very fast algorithm. The information is stored in a minimum spanning tree.

This paper presents a generic video coding algorithm allowing the content-based manipulation of objects. This manipulation is possible thanks to the definition of a spatiotemporal segmentation of the sequences. The coding strategy relies on a joint optimization in the rate-distortion sense of the partition definition and of the coding techniques to be used within each region. This optimization creates the link between the analysis and synthesis parts of the coder. The analysis defines the time evolution of the partition, as well as the elimination or the appearance of regions that are homogeneous either spatially or in motion. The coding of the texture as well as of the partition relies on region-based motion compensation techniques. The algorithm offers a good compromise between the ability to track and manipulate objects and the coding efficiency.

This paper presents a technique for tracking areas of interest in the framework of segmentation-based video coding. The technique is independent of the type of segmentation technique used in the coding approach. Therefore, it can also be used in block-based coding schemes. The algorithm relies on a double segmentation of the image based on morphological tools. This double segmentation permits to obtain the position and shape of the previous area of interest in the current image. In order to demonstrate the potentialities of this algorithm, it is applied in a specific coding scheme so that content-based selective coding is allowed.

We present a coding scheme that achieves, for each image in the sequence, the best segmentation in terms of rate-distortion theory. It is obtained from a set of initial regions and a set of available coding techniques. The segmentation combines spatial and motion criteria. It selects at each area of the image the most adequate criterion for defining a partition in order to obtain the best compromise between cost and quality. In addition, the proposed scheme is very suitable for addressing content-based functionalities.

This paper deals with the use of some morphological tools for video coding at very low bit rates. Rather than describing a complete coding algorithm, the purpose of this paper is to focus on morphological connected operators and segmentation tools that have proved to be attractive for compression.

This paper presents a region-based coding algorithm for video sequences. The coding approach involves a time-recursive segmentation relying on the pixels homogeneity, a region-based motion estimation, and motion compensated contour and texture coding. This algorithm is mainly devoted to very low bit rate video coding applications. One of the important features of the approach is that no assumption is made about the sequence content. Moreover the algorithm structure leads to a scalable coding process giving various levels of quality and bit rates. The coding as well as the segmentation are controlled to regulate the bit stream. Finally, the interest of morphological tools in the content of region-based coding is extensively reviewed.>

The digitization of the skeleton is the source of many difficulties. The skeleton of a binary set can be defined as the set of crest points and their upstream on the distance function10, 12. The final result depends on the quality of the distance function which has been used. The result is particularly coarse with the hexagonal distance function. The use of an euclidean distance function yields a beautiful skeleton, once some subtle interactions with the grid have been solved.

One of the major tools in the daily routine world of image processing is certainly... the lightpen. A contour which should be closed is broken. A moving particle has a continuous trajectory, but a camera will see only a dotted trail. Single cells overlap, and one wishes to separate them. The algorithm we propose here, which connects neighbouring points or particles, will bring a solution in such situations. Noteworthy is the fact that the execution time does not depend upon the number of points to be processed. Two particles are to be connected if in a given sense, the are neighbours. The neighborhood criterion used here goes back to Dirichlet and Delaunay. For its nice visual properties S. Sternberg called the result perceptual graph.