Luc Vincent

Mathematical Morphology and its Applications to Image and Signal Processing

Preface. Introduction. Theory. A Morphological View on Traditional Signal Processing R. Keshet. From the Sup-Decomposition to a Sequential Decomposition R.F. Hashimoto, et al. Decomposition of Separable Concave Structuring Functions R. Van Den Boomgaard, et al. Minkowski Sum Volume Minimization for Convex Polyhedra A.V. Tuzikov, S.A. Sheynin. Topological Properties of Hausdorff Discretizations M. Tajine, C. Ronse. Vectorial Levelings and Flattenings F. Meyer. A Lattice Control Model of Fuzzy Dynamical Systems in State-Space P. Maragos, et al. Shape Analysis and Interpolation. A Morphological Interpolation Approach - Geodesic Set Definition in Case of Empty Intersection I. Granado, et al. The Morphological-Affine Object Deformation M. Iwanowski, J. Serra. Affine Invariant Mathematical Morphology Applied to a Generic Shape Recognition Algorithm J.L. Lisani, et al. Filtering. Folding Induced Self-Dual Filters A.J.H. Mehnert, P.T. Jackway. Flexible Linear Openings and Closings M. Buckley, H. Talbot. Some Applications of Aperture Filters R. Hirata Jr., et al. GA Optimisation of Multidimensional Grey-Scale Soft Morphological Filters with Applications in Archive Film Restoration N.R. Harvey, S. Marshall. Connectivity and Connected Operators. New Insight on Digital Topology G.J.F. Banon. Approximate Connectivity and Mathematical Morphology A.T. Popov. Multiresolution Connectivity: An Axiomatic Approach U.M. Braga-Neto, J. Goutsias. Connected Operators Based on Region-Tree Pruning P. Salembier, L. Garrido. Segmentation. Image Segmentation Based on the Derivative of the Morphological Profile M. Pesaresi, J.A. Benediktsson. Flooding and Segmentation F. Meyer. A Morphological Multi-Scale Gradient for Color Image Segmentation M.C. DOrnellas, R. Van Den Boomgaard. Automatic Watershed Segmentation of Color Images I. Vanhamel, et al. Motion Segmentation using Seeded Region Growing R. Beare, H. Talbot. A Segmentation Pyramid for the Interactive Segmentation of 3-D Images and Video Sequences F. Zanoguera, et al. Partition Lattice Operators for Extraction of Semantic Video Objects D. Gatica-Perez, et al. Texture Analysis. Morphological Granulometric Deconstruction P. Pina. Surface Texture Classification from Morphological Transformations A. Aubert, et al. Content Dependent Image Sampling using Mathematical Morphology: Application to Mipmapping E.D. Ferrandiere, et al. Multiresolution Techniques and Scale-Spaces. Morphological Pyramids and Wavelets Based on the Quincunx Lattice H.J.A.M. Heijmans, J. Goutsias. Morphological Scale-Space Operators: An Algebraic Framework R. Van Den Boomgaard, H.J.A.M. Heijmans. An Idempotent Scale-Space Approach for Morphological Segmentation N.J. Leite, M.D. Teixeira. Algorithms. Efficient Dilation, Erosion, Opening and Closing Algorithms J. Gil, R. Kimmel. Fast Morphological Attribute Operations Using Tarjans Union-Find Algorithm M.H.F. Wilkinson, J.B.T.M. Roerdink. A Change Detector Based on Level Sets F. Guichard, et al. A General Algorithm for Computing Distance Transforms in Linear Time A. Meijster, et al. The Ordered Queue and the Optimality of the Watershed Approaches R. Lotufo, A. Falcao. Discrete 3D Wave Propagation for Computing Morphological Operations from Surface Patches and Unorganized Points F.F. Leymarie, B.B. Kimia. Applications. T

Morphological Area Openings and Closings for Grey-scale Images

The filter that removes from a binary image the components with area smaller than a parameter λ is called area opening. Together with its dual, the area closing, it is first extended to grey-scale images. It is then proved to be equivalent to a maximum of morphological openings with all the connected structuring elements of area greater than or equal to λ. The study of the relationships between these filters and image extrema leads to a very efficient area opening/closing algorithm. Grey-scale area openings and closings can be seen as transformations with a structuring element which locally adapts its shape to the image structures, and therefore have very nice filtering capabilities. Their effect is compared to that of more standard morphological filters. Some applications in image segmentation and hierarchical decomposition are also briefly described.

PINK PANTHER: A COMPLETE ENVIRONMENT FOR GROUND-TRUTHING AND BENCHMARKING DOCUMENT PAGE SEGMENTATION

We describe a new approach for the automatic evaluation of document page segmentation algorithms. Unlike techniques that rely on OCR output, our method is region-based: segmentation quality is assessed by comparing the segmentation output, described as a set of regions, to the corresponding ground-truth. Error maps are used to keep track of all the errors associated with each pixel, regardless of the document complexity. Misclassifications, splitting, and merging of regions are among the errors detected by the system. Each error can be weighted individually and the system can be customized to benchmark virtually any type of segmentation task.

Automatic Plankton Image Recognition

Plankton form the base of the food chain in the ocean and are fundamental to marine ecosystem dynamics. The rapid mapping of plankton abundance together with taxonomic and size composition is very important for ocean environmental research, but difficult or impossible to accomplish using traditional techniques. In this paper, we present a new pattern recognition system to classify large numbers of plankton images detected in real time by the Video Plankton Recorder (VPR), a towed underwater video microscope system. The difficulty of such classification is compounded because: 1) underwater images are typically very noisy, 2) many plankton objects are in partial occlusion, 3) the objects are deformable and 4) images are projection variant, i.e., the images are video records of three-dimensional objects in arbitrary positions and orientations. Our approach combines traditional invariant moment features and Fourier boundary descriptors with gray-scale morphological granulometries to form a feature vector capturing both shape and texture information of plankton images. With an improved learning vector quantization network classifier, we achieve 95% classification accuracy on six plankton taxa taken from nearly 2,000 images. This result is comparable with what a trained biologist can achieve by using conventional manual techniques, making possible for the first time a fully automated, at sea-approach to real-time mapping of plankton populations.

Euclidean skeletons and conditional bisectors

This paper deals with the determination of skeletons and conditional bisectors in discrete binary images using the Euclidean metrics. The algorithm proceeds in two steps: first, the Centers of the Euclidean Maximal Discs (CMD) included in the set to skeletonize are characterized and robustly identified. Second, a firefront propagation is simulated starting from the set boundaries, in which pixels which are not centers of maximal discs and are not crucial to homotopy preservation are removed. Not only is the resulting algorithm fast and accurate, it allows the computation of a vast variety of skeletons. Furthermore, it can be extended to provide conditional bisectors of any angular parameter (theta) . This leads to the introduction of a new morphological transformation, the bisector function, which synthesizes the information contained in all the (theta) -conditional bisectors. The interest of all these skeleton-like transformations is illustrated on the segmentation of binary images of glass fibers.

Morphological grayscale reconstruction: definition, efficient algorithm and applications in image analysis

Gray-scale reconstruction is formally defined for discrete images. A brief summary of the existing techniques to compute it is provided, and a hybrid algorithm that is an order of magnitude faster than any other algorithm is introduced. Some of its application to image filtering and segmentation are listed.<<ETX>>

Fast Grayscale Granulometry Algorithms

Granulometries constitute an extremely useful set of morphological operators, applicable to a variety of image analysis tasks. Traditional granulometry algorithms involve sequences of openings or closings of increasing size, and are therefore very slow on non-dedicated hardware. Efficient techniques have been proposed to compute granulometries in binary images, based on the concept of opening functions. In the present paper, a class of algorithms for computing granulometries in grayscale images is introduced. The most advanced among them are based on the new concept of opening tree. These algorithms are several orders of magnitude faster than traditional techniques, thereby opening up a range of new applications for grayscale granulometries.

Morphological image processing and network analysis of cornea endothelial cell images

In this paper, we propose a robust and accurate method for segmenting grayscale images of corneal endothelial tissue. Its first step consists of the extraction of markers of the corneal cells using a dome extractor based on morphological grayscale reconstruction. Then, marker- driven watershed segmentation yields binary images of the corneal cell network. From these images, we derive histograms of the cell sizes and number of neighbors, which provide quantitative information about the condition of the cornea. We also construct the neighborhood graph of the corneal cells, whose granulometric analysis yields information on the distribution of cells with large number of neighbors in the tissue. Lastly, these results help us propose a model for the corneal cell death phenomenon. The numerical simulation of this model exhibits a very good match with our experimental results. This model not only allows us to refine our understanding of the phenomenon: combined with our results, it enables the estimation of the percentage of cells having died in a given corneal endothelial tissue.

Local Grayscale Granulometries Based on Opening Trees

Granulometries are morphological image analysis tools that are particularly useful for estimating object sizes in binary and grayscale images, or for characterizing textures based on their pattern spectra (i.e., granulometric curves). Though granulometric information is typically extracted globally for an image or a collection of images, local granulometries can also be useful for such applications as segmentation of texture images. However, computing local granulometries from a grayscale image by means of traditional sequences of openings and closings is either prohibitively slow, or produces results that are too coarse to be really useful. In the present paper, using the concept of opening trees proposed in [14], new local grayscale granulometry algorithms are introduced, that are both accurate and efficient. These algorithms can be used for any granulometry based on openings or closings with line segments or combinations of line segments. Among others, these local granulometries can be used to compute size transforms directly from grayscale images, a grayscale extension of the concept of an opening function. Other applications include adaptive openings and closings, as well as granulometric texture segmentation.

Fast opening functions and morphological granulometries

In this paper, a comprehensive set of fast algorithms for computing granulometries in binary images is first proposed: linear granulometries (i.e., granulometries based on openings with line segments) constitute the easiest case, and are computed using image `run-length. The 2D case (granulometries with square or `diamond-shaped structuring elements, or granulometries with unions of line-segments at different orientations) involves the determination of opening functions or granulometry functions. The grayscale case is then addressed, and a new algorithm for computing grayscale linear granulometries is introduced. This algorithm is orders of magnitude faster than any previously available technique. The techniques introduced in this paper open up a new range of applications for granulometries, examples of which are described in the paper.