Fernand Meyer

Topographic distance and watershed lines

Abstract The watershed line is the basic tool for segmenting images in mathematical morphology. A rigorous definition is given in terms of a distance function called topographic distance. If the topographical function is itself a distance function, then the topographical distance becomes identical with the geodesic distance function and the watershed becomes identical with the skeleton by zone of influence. The classical shortest paths algorithms of the graph theory are then revisited in order to derive new watershed algorithms, which are either new or more easy to implement in hardware.

Region-based video coding using mathematical morphology

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. >

Image filtering using morphological amoebas

This paper presents morphological operators with non-fixed shape kernels, or amoebas, which take into account the image contour variations to adapt their shape. Experiments on grayscale and color images demonstrate that these novel filters outperform classical morphological operations with a fixed, space-invariant structuring element for noise reduction applications.

Segmentation-based video coding system allowing the manipulation of objects

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.

Nonlinear Scale-Space Representation with Morphological Levelings

In this paper we present a nonlinear scale-space representation based on a general class of morphological strong filters, the levelings, which include the openings and closings by reconstruction. These filters are very useful for image simplification and segmentation. From one scale to the next, details vanish, but the contours of the remaining objects are preserved sharp and perfectly localized. Both the lattice algebraic and the scale-space properties of levelings are analyzed and illustrated. We also develop a nonlinear partial differential equation that models the generation of levelings as the limit of a controlled growth starting from an initial seed signal. Finally, we outline the use of levelings in improving the Gaussian scale-space by using the latter as an initial seed to generate multiscale levelings that have a superior preservation of image edges.

The flat zone approach: a general low-level region merging segmentation method

Abstract This paper presents a segmentation method, the flat zone approach, that avoids some limitations of the watershed-plus-markers method. The watershed-plus-markers approach, which is the traditional segmentation technique in mathematical morphology, has two inherent problems: (1) the possible separation of a piecewise-constant region of the input image into several regions in the output partition, and (2) the problem of obtaining markers (connected components of pixels signaling significant regions) for features that are one or two pixels wide. These problems are related to the limited resolution power (for feature extraction) of gradient operators. The flat zone approach extends the region marker concept (to contain the entire (and not part of) regions) and requires neither the computation of a gradient function nor the modification of the support of the input image in order to increase the size of the features. Our approach works on the graph formed by the image flat zones (or piecewise-constant regions). This fact ensures that the input image regions are not broken and can consider all input flat zones regardless their size. An inclusion relationship between the flat zones of the input image and the regions of the output partition is imposed. That is, a flat zone segmentation method is a region (flat zone) merging method and behaves like a connected operator. Our method is robust (in the sense that it is invariant under certain intensity value transformations) and uses a hierarchical waiting queue algorithm that makes it extremely efficient.

Levelings, Image Simplification Filters for Segmentation

Before segmenting an image, one has often to simplify it. In this paper we investigate a class of filters able to simplify an image without blurring or displacing its contours: the simplified image has less details, hence less contours. As the contours of the simplified image are as accurate as in the initial image, the segmentation may be done on the simplified image, without going back to the initial image. The corresponding filters are called levelings. Their properties and construction are described in the present paper.

Multiscale Morphological Segmentations Based on Watershed, Flooding, and Eikonal PDE

The classical morphological segmentation paradigm is based on the watershed transform, constructed by flooding the gradient image seen as a topographic surface. For flooding a topographic surface, a topographic distance is defined from which a minimum distance algorithm is derived for the watershed. In a continuous formulation, this is modeled via the eikonal PDE, which can be solved using curve evolution algorithms. Various ultrametric distances between the catchment basins may then be associated to the flooding itself. To each ultrametric distance is associated a multiscale segmentation; each scale being the closed balls of the ultrametric distance.

Contrasts and activity lattice

Starting from the set P(E) of all the subsets of an arbitrary space E, one considers the class A of all the mappings from P(E) into itself. It is proved that A is a complete lattice with respect to the activity ordering, according to which a mapping is more active than another, when it modifies more elements of E. In this lattice, the infinum ⋏ is nothing but the already known morphological center. The class F of the real-valued functions f: E → R is closed under the supremum ⋎ iff some supplementary requirements are fulfilled. It is the case on the class of the contrast mappings, where at each point x, function f(x) may be transformed only into (ζf)(x), (ηf)(x) or f(x), where ζ and η are two mappings F → F. A contrast κ is idempotent when ζ and η are a compact ∨-underfilter and a compact ∧-overfilter respectively. Examples are given.

Minimum Spanning Forests for Morphological Segmentation

Image segmentation in mathematical morphology is essentially based on one method: the watershed of a gradient image from a set of markers. We show that this watershed can be obtained from the neighbourhood graph of the initial image. The result of the segmentation is then a minimum spanning forest of the neighbourhood graph. Powerful interactive and very fast segmentation methods are derived