A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Image Decomposition and Separation Using Sparse Representations: An Overview

This paper gives essential insights into the use of sparsity and morphological diversity in image decomposition and source separation by reviewing our recent work in this field. The idea to morphologically decompose a signal into its building blocks is an important problem in signal processing and has far-reaching applications in science and technology. Starck , proposed a novel decomposition method—morphological component analysis (MCA)—based on sparse representation of signals. MCA assumes that each (monochannel) signal is the linear mixture of several layers, the so-called morphological components, that are morphologically distinct, e.g., sines and bumps. The success of this method relies on two tenets: sparsity and morphological diversity. That is, each morphological component is sparsely represented in a specific transform domain, and the latter is highly inefficient in representing the other content in the mixture. Once such transforms are identified, MCA is an iterative thresholding algorithm that is capable of decoupling the signal content. Sparsity and morphological diversity have also been used as a novel and effective source of diversity for blind source separation (BSS), hence extending the MCA to multichannel data. Building on these ingredients, we will provide an overview the generalized MCA introduced by the authors in and as a fast and efficient BSS method. We will illustrate the application of these algorithms on several real examples. We conclude our tour by briefly describing our software toolboxes made available for download on the Internet for sparse signal and image decomposition and separation

High-quality Image Restoration from Partial Mixed Adaptive-Random Measurements

A novel framework to construct an efficient sensing (measurement) matrix, called mixed adaptive-random (MAR) matrix, is introduced for directly acquiring a compressed image representation. The mixed sampling (sensing) procedure hybridizes adaptive edge measurements extracted from a low-resolution image with uniform random measurements predefined for the high-resolution image to be recovered. The mixed sensing matrix seamlessly captures important information of an image, and meanwhile approximately satisfies the restricted isometry property. To recover the high-resolution image from MAR measurements, the total variation algorithm based on the compressive sensing theory is employed for solving the Lagrangian regularization problem. Both peak signal-to-noise ratio and structural similarity results demonstrate the MAR sensing framework shows much better recovery performance than the completely random sensing one. The work is particularly helpful for high-performance and lost-cost data acquisition.Comment: 16 pages, 8 figure

Flat zones filtering, connected operators, and filters by reconstruction

This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described.Peer ReviewedPostprint (published version

Morphological Residues And A General Framework For Image Filtering And Segmentation

Morphological residues represent an image in a hierarchical way by means of a decomposition of its structures and according to a size parameter λ. From this decomposition, we can obtain a relation between the different residual levels associated with the complexity of the image structures. In this work, we introduce a new method to filter out components of gray-scale images based on the morphological residue decomposition which takes into account a size parameter and a certain level of complexity of the different structures to be filtered. As we will illustrate, this complexity is associated with a set of new attributes of the image defined according to the information contained in its multi-resolution representation.20014219229Serra, J., (1982) Image Analysis and Mathematical Morphology, 1. , Academic PressSerra, J., (1988) Image Analysis and Mathematical Morphology: Theoretical Advances, 2. , Academic PressHeijmans, H.J.A.M., (1994) Morphological Image Operators, , Academic Press, Boston, MABreen, E.J., Jones, R., Attribute openings, thinnings, and granulometries (1996) Computer Vision and Image Processing, 64 (3), pp. 377-389Rosenfeld, A., Kak, A.C., (1982) Digital Picture Processing, 1. , Academic Press, 2nd editionGonzalez, R.C., Woods, R.E., (1993) Digital Image Processing, , Addison-WesleyVincent, L., Grayscale area opennings and closings, their efficient implementation and applications (1993) Mathematical Morphology and Its Applications to Signal Processing, pp. 22-27. , J. Serra and P. Salembier, Eds., UPC Publications, MayVachier, C., (1995) Extraction de caractéristiques, segmentation d'image et morphologie mathématique, , Ph.D. thesis, École Nationale des Mines de Paris, DecemberHaralick, R.M., Shapiro, L.G., Image segmentation techniques (1985) Computer, Vision, Graphics and Image Processing, 35, pp. 100-132Vincent, L., Soillet, P., Watersheds in digital spaces: An efficient algorithm based on immersion simmulations (1991) IEEE Trans. on Pattern Analysis and Machine Intelligence, 13 (6), pp. 583-598Beucher, S., Yu, X., Road recognition in complex traffic situations (1994) 7th IFAC/IFORS Simposium on Transportation Systems: Theory and Application of Advanced Technology, pp. 413-418. , Tianjin, China, AugustBeucher, S., Meyer, F., The morphological approach to segmentation: The watershed transformation (1993) Mathematical Morphology in Image Processing, 34, pp. 433-481. , Edward R. Dougherty, Ed., chapter 12, Marcel Dekker, New YorkGoutsias, J., Heijmans, H.J.A.M., (1997) Multiresolution signal decomposition schemes. Part 1: Linear and morphological pyramids, , Tech. Rep., Center of Imaging Science and Department of Electric and Computer EngineeringMatheron, G., (1975) Random Sets and Integral Geometry, , John Wiley, New YorkMatheron, G., (1967) Eléments pour une Théorie des Milieux Poreux, , MassonParis, ParisVincent, L., Fast opening functions and morphological granulometries (1994) SPIE Image Algebra and Morphological Image Processing V, 2300, pp. 253-267. , San Diego, CA, JulyTang, X., Vincent, L., Stewart, K., Automatic plankton image classification (1996) International Artificial Intelligence Review JournalDougherty, E., Pelz, J., Sand, F., Lent, A., Morphological image segmentation by local granulometric size distributions (1992) Journal of Electronic Imaging, 1 (1), pp. 46-60Regazzoni, C., Foresti, G., Venetsanopoulos, A., Statistical pattern spectrum for binary pattern recognition (1994) Mathematical Morphology and Its Applications to Image Processing, pp. 185-192. , Jean Serra and Pierre Soile, Eds., Computational Imaging and Vision, Kluwer Academic Publishers, The NetherlandsVincent, L., Local grayscale granulometries based on opening trees (1996) Mathematical Morphology and Its Applications to Image Signal and Processing, pp. 273-280. , Petro Maragos, Ronald W. Schafer, and Muhammad Akmal Butt, Eds., Computational Image and Vision, Kluwer Academic Publishers, The NetherlandsVincent, L., Morphological grayscale reconstruction in image analysis: Applications and efficient algorithms (1993) IEEE Trans. Image Processing, 2 (2), pp. 176-201Serra, J., Salembier, P., Connected operators and pyramids (1993) Proceeding of SPIE Image Algebra and Mathematical Morphology, 93, pp. 164-175. , FebruarySalembier, P., Oliveiras, A., Garrido, L., Antiextensive connected operators for image and sequence processing (1998) IEEE Trans. Image Processing, 7 (4), pp. 555-57

Hyperspectral colon tissue cell classification

A novel algorithm to discriminate between normal and malignant tissue cells of the human colon is presented. The microscopic level images of human colon tissue cells were acquired using hyperspectral imaging technology at contiguous wavelength intervals of visible light. While hyperspectral imagery data provides a wealth of information, its large size normally means high computational processing complexity. Several methods exist to avoid the so-called curse of dimensionality and hence reduce the computational complexity. In this study, we experimented with Principal Component Analysis (PCA) and two modifications of Independent Component Analysis (ICA). In the first stage of the algorithm, the extracted components are used to separate four constituent parts of the colon tissue: nuclei, cytoplasm, lamina propria, and lumen. The segmentation is performed in an unsupervised fashion using the nearest centroid clustering algorithm. The segmented image is further used, in the second stage of the classification algorithm, to exploit the spatial relationship between the labeled constituent parts. Experimental results using supervised Support Vector Machines (SVM) classification based on multiscale morphological features reveal the discrimination between normal and malignant tissue cells with a reasonable degree of accuracy

New approaches to texture coding in segmentation and feature-based image coding schemes

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A new design tool for feature extraction in noisy images based on grayscale hit-or-miss transforms

The Hit-or-Miss transform (HMT) is a well known morphological transform capable of identifying features in digital images. When image features contain noise, texture or some other distortion, the HMT may fail. Various researchers have extended the HMT in different ways to make it more robust to noise. The most successful, and most recent extensions of the HMT for noise robustness, use rank order operators in place of standard morphological erosions and dilations. A major issue with the proposed methods is that no technique is provided for calculating the parameters that are introduced to generalize the HMT, and, in most cases, these parameters are determined empirically. We present here, a new conceptual interpretation of the HMT which uses a percentage occupancy (PO) function to implement the erosion and dilation operators in a single pass of the image. Further, we present a novel design tool, derived from this PO function that can be used to determine the only parameter for our routine and for other generalizations of the HMT proposed in the literature. We demonstrate the power of our technique using a set of very noisy images and draw a comparison between our method and the most recent extensions of the HMT